Patent Publication Number: US-11029233-B2

Title: Input/output characteristic estimation method for drivetrain testing system

Description:
TECHNICAL FIELD 
     The present invention relates to an input/output characteristic estimation method for a testing system. More particularly, the present invention relates to an input/output characteristic estimation method which estimates an input/output characteristic from a predetermined input to a predetermined output in a testing system for a test piece including at least two shafts. 
     BACKGROUND ART 
     Patent Document 1 shows an engine testing system configured by linking an engine which is a test piece to a dynamometer via a joint shaft (hereinafter, referred to as an “engine bench system”). In the engine bench system, torque, a speed, and others of the dynamometer are controlled by a dynamometer control device, while a throttle opening of the engine is controlled by use of an engine control device. Thereby, durability, fuel efficiency, exhaust gas purification performance, and others of the engine are evaluated. In the engine bench system, a characteristic, particularly, moment of inertia of the engine may be measured before implementation of a test of evaluating performance of the engine, and utilized as a control parameter for torque control or speed control in the dynamometer control device. 
     Patent Document 1 shows a method of performing excitation control of vibrating torque of a dynamometer linked to the engine via the joint shaft, thereby measuring an input/output characteristic (more specifically, a transfer function G1 from a torque current command signal to an angular speed detection signal, and a transfer function G2 from a torque current command signal to a shaft torque detection signal) of a signal in an engine bench system, and estimating moment of inertia of an engine by utilizing the measurement result. In an engine bench system, only one dynamometer is linked to the engine which is a test piece, so that an input/output characteristic of the engine can be easily measured by measuring a response of a predetermined signal to an excitation input to the dynamometer. 
     Patent Document 1: Japanese Unexamined Patent Application, Publication No. 2008-76061 
     DISCLOSURE OF THE INVENTION 
     Problems to be Solved by the Invention 
     By the way, testing systems using dynamometers include not only the engine bench system as shown in Patent Document 1 in which the engine is a test piece, but also a drive train bench system in which a drive train of a vehicle is a test piece. A drive train refers to a generic term for a plurality of devices for transmitting energy generated in an engine to a driving wheel, and is configured by combining an engine, a clutch, a transmission, a drive shaft, a propeller shaft, a differential gear, a driving wheel, and others. The drive train has three shafts, including one input shaft linked to an output shaft of the engine, and first and second output shafts connected to the input shaft so as to be able to transmit power. 
     The drive train bench system connects a power generation source such as an actual engine or a dynamometer to the input shaft of the drive train, controls, by a speed control device, rotation speeds of first and second dynamometers respectively linked to the first and second output shafts while inputting power generated in the power generation source to the input shaft and driving the test piece, and absorbs the power by the first and second dynamometers, thereby evaluating performance of the test piece. 
     In such a drive train bench system as well as in the engine bench system previously described, it maybe necessary to estimate an input/output characteristic of a signal. However, in the drive train bench system, two or three dynamometers are linked to a test piece in contrast to the engine bench system, and therefore, the input/output characteristic cannot be estimated with accuracy by merely applying the method of the invention in Patent Document 1 as it is. More specifically, in the drive train bench system, not only a dynamometer to be excited but also a dynamometer controlled by the speed control device is connected to a test piece, and therefore, due to the influence of this speed control device, the input/output characteristic cannot be estimated with accuracy by simply measuring a response of a target output signal to an excitation input signal as in the invention in Patent Document 1. 
     An object of the present invention is to provide an input/output characteristic estimation method for a testing system capable of estimating, with accuracy, an input/output characteristic from a predetermined input to a predetermined output, in a testing system which targets, for testing, a test piece including at least two shafts. 
     Means for Solving the Problems 
     (1) A testing system (e.g., a testing system S described later) includes: a test piece (e.g., a test piece W described later) including a first shaft (e.g., a first shaft S 1  described later), and a second shaft (e.g., a second shaft S 2  described later) and a third shaft (e.g., a third shaft S 3  described later) connected to the first shaft so as to be able to transmit power; a second electric motor (e.g., a second dynamometer  22  described later) linked to the second shaft; a third electric motor (e.g., a third dynamometer  23  described later) linked to the third shaft; a second state detection means (e.g., a second rotation speed detector  52  and a second shaft torque detector  62  described later) for detecting a state of the second shaft or the second electric motor and generating a second state detection signal (t 2  and w 2 ); a third state detection means (e.g., a third rotation speed detector  53  and a third torque detector  63  described later) for detecting a state of the third shaft or the third electric motor and generating a third state detection signal (t 3  and w 3 ); a speed control device (e.g., a speed control device  73  described later) which generates a second torque control input (e.g., a second torque control input ib 2  described later) to the second electric motor for controlling a rotation speed of the second electric motor and a third torque control input (e.g., a third torque control input ib 3  described later) to the third electric motor for controlling a rotation speed of the third electric motor on the basis of a predetermined input signal (w 2 , w 3 , w_av, and dw); and an excitation input generation means (e.g., an excitation torque generation unit  72  described later) for generating an excitation input (d 1 , d 2 , and d 3 ) changing at a predetermined frequency. An input/output characteristic estimation method for this testing system includes: a first excitation measurement step (e.g., steps of S 3  to S 5  in  FIG. 3  described later) of inputting, to the second electric motor as a second input (i 2 ), the second torque control input (ib 2 ) on which the excitation input (d 2 ) is superimposed, also inputting, to the third electric motor as a third input (i 3 ), the third torque control input (ib 3 ), and measuring a response (e.g., frequency responses i 2 d 2 , t 2 d 2 , w 2 d 2 , i 3 d 2 , t 3 d 2 , and w 3 d 2  described later) to the excitation input (d 2 ); a second excitation measurement step (e.g., steps of S 7  to S 9  in  FIG. 3  described later) of inputting, to the second electric motor as a second input (i 2 ), the second torque control input (ib 2 ), also inputting, to the third electric motor as a third input, the third torque control input (ib 3 ) on which the excitation input (d 3 ) is superimposed, and measuring a response (e.g., frequency responses i 2 d 3 , t 2 d 3 , w 2 d 3 , i 3 d 3 , t 3 d 3 , and w 3 d 3  described later) to the excitation input (d 3 ); and a mechanical characteristic estimation step (e.g., steps of S 11  to S 12  in  FIG. 3  described later) of estimating a transfer function (e.g., Gt 2 _i 2 , Gt 2 _i 3 , Gt 3 _i 2 , Gt 3 _i 3 , Gw 2 _i 2 , Gw 2 _i 3 , Gw 3 _i 2 , and Gw 3 _i 3  described later) from the second or third input (i 2  or i 3 ) to the second or third state detection signal (t 2 , t 3 , w 2 , and w 3 ) by using the response measured in the first excitation measurement step and the response measured in the second excitation measurement step. 
     (2) In this case, it is preferable that the second state detection means includes a second torque detector (e.g., a second shaft torque detector  62  described later) which detects torque of the second shaft and generates a second torque detection signal (t 2 ), and a second rotation speed detector (e.g., a second rotation speed detector  52  described later) which detects a rotation speed of the second electric motor and generates a second speed signal (w 2 ), the third state detection means includes a third torque detector (e.g., a third shaft torque detector  63  described later) which detects torque of the third shaft and generates a third torque detection signal (t 3 ), and a third rotation speed detector (e.g., a third rotation speed detector  53  described later) which detects a rotation speed of the third electric motor and generates a third speed signal (w 3 ), and the speed control device generates the second and third torque control inputs on the basis of the second and third speed signals, measures the response (i 2 d 2  or i 3 d 2 ) of at least either the second or third input to the excitation input superimposed on the second torque control input, in the first excitation measurement step, measures the response (i 2 d 3  or i 3 d 3 ) of at least either the second or third input to the excitation input superimposed on the third torque control input, in the second excitation measurement step, and estimates a transfer function (Gt 2 _i 2 , Gt 2 _i 3 , Gt 3 _i 2 , Gt 3 _i 3 , Gw 2 _i 2 , Gw 2 _i 3 , Gw 3 _i 2 , and Gw 3 _i 3 ) from the second or third input (i 2  or i 3 ) to the second or third torque detection signal (t 2  or t 3 ) or the second or third speed signal (w 2  or w 3 ) by using the responses measured in the first and second excitation measurement steps, in the mechanical characteristic estimation step. 
     (3) In this case, it is preferable that, in the first excitation measurement step, the responses (i 2 d 2 , i 3 d 2 , t 2 d 2 , and t 3 d 2 ) of the second input, the third input, the second torque detection signal, and the third torque detection signal to the excitation input are measured, in the second excitation measurement step, the responses (i 2 d 3 , i 3 d 3 , t 2 d 3 , and t 3 d 3 ) of the second input, the third input, the second torque detection signal, and the third torque detection signal to the excitation input are measured, and in the mechanical characteristic estimation step, a transfer function (Gt 2 _i 2 , Gt 2 _i 3 , Gt 3 _i 2 , and Gt 3 _i 3 ) from the second or third input to the second or third torque detection signal is estimated by using the responses measured in the first and second excitation measurement steps. 
     (4) In this case, it is preferable that, in the first excitation measurement step, the responses (i 2 d 2 , i 3 d 2 , w 2 d 2 , and w 3 d 2 ) of the second input, the third input, the second speed signal, and the third speed signal to the excitation input are measured, in the second excitation measurement step, the responses (i 2 d 3 , i 3 d 3 , w 2 d 3 , and w 3 d 3 ) of the second input, the third input, the second speed signal, and the third speed signal to the excitation input are measured, and in the mechanical characteristic estimation step, a transfer function (Gw 2 _i 2 , Gw 2 _i 3 , Gw 3 _i 2 , and Gw 3 _i 3 ) from the second or third input to the second or third speed signal is estimated by using the responses measured in the first and second excitation measurement steps. 
     (5) In this case, it is preferable that the input/output characteristic estimation method further includes a control circuit characteristic estimation step (e.g., a step of S 31  in  FIG. 5  described later) of estimating a transfer function from the input signal (w 2  or w 3 ) to the second or third input (i 2  or i 3 ) in the speed control device by using the response measured in the first excitation measurement step and the response measured in the second excitation measurement step. 
     (6) In this case, it is preferable that the testing system further includes a first electric motor (e.g., a first dynamometer  21 ) linked to the first shaft; and a first state detection means (e.g., a first rotation speed detector  51  and a first shaft torque detector  61  described later) for detecting a state of the first shaft or the first electric motor and generating a first state detection signal (t 1  and w 1 ), the input/output characteristic estimation method further includes a third excitation measurement step (e.g., steps of S 64  to S 66  in  FIG. 6B  described later) of inputting, to the first electric motor as a first input (i 1 ), a predetermined reference input (ib 1 ) on which the excitation input (d 1 ) is superimposed, also inputting the second and third torque control inputs to the second and third electric motors as second and third inputs, and measuring a response (e.g., t 1 d 1 ,w 1 d 1 , t 2 d 1 , w 2 d 1 , t 3 d 1 , and w 3 d 1 ) to the excitation input, and in the mechanical characteristic estimation step, a transfer function (Gt 1 _i 1 , Gt 2 _i 1 , Gt 3 _i 1 , Gw 1 _i 1 , Gw 2 _i 1 , and Gw 3 _i 1 ) from the first input to the first, second, or third state detection signal or a transfer function, (Gt 1 _i 2 , Gt 1 _i 3 , Gw 1 _i 2 , and Gw 1 _i 3 ) from the second or third input to the first state detection signal is estimated by using the responses measured in one or both of the first and second excitation measurement step and the response measured in the third excitation measurement step. 
     (7) A testing system includes: a test piece including a first shaft, and a second shaft and a third shaft connected to the first shaft so as to be able to transmit power; a second electric motor linked to the second shaft; a third electric motor linked to the third shaft; a second state detection means for detecting a state of the second shaft or the second electric motor and generating a second state detection signal; a third state detection means for detecting a state of the third shaft or the third electric motor and generating a third state detection signal; a speed control device which generates a second torque control input to the second electric motor for controlling a rotation speed of the second electric motor on the basis of a predetermined input signal, and a third torque control input to the third electric motor for controlling a rotation speed of the third electric motor; and an excitation input generation means for generating an excitation input changing at a predetermined frequency. An input/output characteristic estimation method for this testing system includes: a first excitation measurement step (e.g., steps of S 23  to S 25  in  FIG. 5  described later) of inputting, to the second electric motor as a second input, the second torque control input on which the excitation input is superimposed, also inputting the third torque control input to the third electric motor as a third input, and measuring a response to the excitation input; a second excitation measurement step (e.g., steps of S 27  to S 29  in  FIG. 5  described later) of inputting the second torque control input to the second electric motor as a second input, also inputting, to the third electric motor as a third input, the third torque control input on which the excitation input is superimposed, and measuring a response to the excitation input; and a control circuit characteristic estimation step (e.g., a step of S 31  in  FIG. 5  described later) of estimating a transfer function (e.g., C 22 , C 23 , C 32 , and C 33 ) from the input signal (w 2  or w 3 ) to the second or third input (i 2  or i 3 ) in the speed control device by using the response measured in the first excitation measurement step and the response measured in the second excitation measurement step. 
     (8) In this case, it is preferable that the second state detection means includes a second torque detector which detects torque of the second shaft and generates a second torque detection signal, and a second rotation speed detector which detects a rotation speed of the second electric motor and generates a second speed signal, the third state detection means includes a third torque detector which detects torque of the third shaft and generates a third torque detection signal, and a third rotation speed detector which detects a rotation speed of the third electric motor and generates a third speed signal, and the speed control device generates the second and third torque control inputs on the basis of the second and third speed signals, measures the responses of the second and third speed signals to the excitation input superimposed on the second torque control input, in the first excitation measurement step, measures the responses of the second and third speed signals to the excitation input superimposed on the third torque control input, in the second excitation measurement step, and estimates a transfer function (C 22 , C 23 , C 32 , and C 33 ) from the second or third speed signal to the second or third input in the speed control device by using the responses measured in the first and second excitation measurement steps, in the control circuit characteristic estimation step. 
     (9) A testing system includes: a test piece (e.g., a test piece W described later) including a first shaft (e.g., a first shaft S 1  described later), and a second shaft (e.g., a second shaft S 2  or a third shaft S 3  described later) connected to the first shaft so as to be able to transmit power; a first electric motor (e.g., a first dynamometer  21 ) linked to the first shaft; a second electric motor (e.g., a second dynamometer  22  or third dynamometer  23  described later) linked to the second shaft; a first state detection means (e.g., a first rotation speed detector  51  and a first shaft torque detector  61  described later) for detecting a state of the first shaft or the first electric motor and generating a first state detection signal; a second state detection means (e.g., a second rotation speed detector  52  and a second shaft torque detector  62  or a third rotation speed detector  53  and a third torque detector  63  described later) for detecting a state of the second shaft or the second electric motor and generating a second state detection signal; a speed control device (e.g., a speed control device  73  described later) which generates a second torque control input (ib 2  or ib 3 ) to the second electric motor for controlling a rotation speed of the second electric motor on the basis of a predetermined input signal (w 2  or w 3 ); and an excitation input generation means (e.g., an excitation torque generation unit  72  described later) for generating an excitation input (d 1 , d 2 , and d 3 ) changing at a predetermined frequency. An input/output characteristic estimation method for this testing system includes: a first excitation measurement step (e.g., steps of S 64  to S 66  in  FIG. 6B  described later) of inputting, to the first electric motor as a first input (i 1 ), a predetermined reference input (ib 1 ) on which the excitation input (d 1 ) is superimposed, also inputting, to the second electric motor as a second input (i 2  or i 3 ), the second torque control input (ib 2  or ib 3 ), and measuring a response to the excitation input; a second excitation measurement step (e.g., steps of S 53  to S 55  or steps of S 57  to S 59  in  FIG. 6A  described later) of inputting the reference input to the first electric motor as a first input, also inputting, to the second electric motor as a second input, the second torque control input on which the excitation input is superimposed, and measuring a response to the excitation input; and a mechanical characteristic estimation step (e.g., a steps of S 68  and S 69  in  FIG. 6B  described later) of estimating a transfer function (e.g., Gt 1 _Gt 2  Gt 3 _i 1 , Gw 1 _i 1 , Gw 2 _i 1 , and Gw 3 _i 1 ) from the first input to the first or second state detection signal, by using the response (t 1 d 1 , w 1 d 1 , t 2 d 1 , w 2 d 1 , t 3 d 1 , and w 3 d 1 ) measured in the first excitation measurement step and the response (i 2 d 2 , i 2 d 3 , and others) measured in the second excitation measurement step. 
     (10) In this case, it is preferable that the first state detection means includes a first, torque detector which detects torque of the first shaft and generates a first torque detection signal, and a first rotation speed detector which detects a rotation speed of the first electric motor and generates a first speed signal, the second state detection means includes a second torque detector which detects torque of the second shaft and generates a second torque detection signal, and a second rotation speed detector which detects a rotation speed of the second electric motor and generates a second speed signal, in the first excitation measurement step, the responses of the second speed signal and the first torque detection signal to the excitation input superimposed on the reference input are measured, and in the mechanical characteristic estimation step, a transfer function (Gt 1 _i 1 ) from the first input to the first torque detection signal is estimated by using the responses measured in the first and second excitation measurement steps. 
     (11) In this case, it is preferable that, in the first excitation measurement step, the responses of the second speed signal and the first and second torque detection signals to the excitation input superimposed on the reference input are measured, and in the mechanical characteristic estimation step, a transfer function from the first input to the first torque detection signal and a transfer function (Gt 2 _i 1  or Gt 3 _i 1 ) from the first input to the second torque detection signal are estimated by using the responses measured in the first and second excitation measurement steps. 
     (12) In this case, it is preferable that the first state detection means includes a first torque detector which detects torque of the first shaft and generates a first torque detection signal, and a first rotation speed detector which detects a rotation speed of the first electric motor and generates a first speed signal, the second state detection means includes a second torque detector which detects torque of the second shaft and generates a second torque detection signal, and a second rotation speed detector which detects a rotation speed of the second electric motor and generates a second speed signal, in the first excitation measurement step, the responses of the first and second speed signals to the excitation input superimposed on the reference input are measured, and in the mechanical characteristic estimation step, a transfer function (Gw 1 _i 1 ) from the first input to the first speed signal and a transfer function (Gw 2 _i 1  or Gw 3 _i 1 ) from the first input to the second speed signal are estimated by using the responses measured in the first and second excitation measurement steps. 
     Effects of the Invention 
     (1) In the present invention, second and third electric motors are respectively linked to second and third shafts of a test piece. In a first excitation measurement step, a response to an excitation input when the second electric motor is excitation-controlled is measured. In a second excitation measurement step, a response to an excitation input when the third electric motor is excitation-controlled is measured. Further, a mechanical characteristic estimation step estimates a transfer function from a second or third input to a second or third state detection signal by using the responses to the excitation input obtained in the first and second excitation measurement steps. In this way, in the present invention, a transfer function from the second or third input to the second or third state detection signal is estimated by combining the response when the second electric motor is excitation-controlled with the response when the third electric motor is excitation-controlled. Thereby, it is possible to eliminate an influence of an input/output characteristic of a speed control device, and thus estimate a transfer function with accuracy. 
     (2) In a first excitation measurement step of the present invention, responses of second and third inputs to an excitation input which is input to the second electric motor are measured. In a second excitation measurement step, responses of second and third inputs to an excitation input which is input to the third electric motor are measured. A mechanical characteristic estimation step estimates a transfer function from a second or third torque detection signal or second or speed signal by use of the four responses. Consequently, these transfer functions can be estimated with higher accuracy. 
     (3) In a mechanical characteristic estimation step of the present invention, transfer functions from, a second or third input to a second or third torque detection signal are estimated by use of eight responses including responses of the second and third inputs and the second and third torque detection signals to an excitation input which is input to a second electric motor, and responses of the second and third inputs and the second and third torque detection signals to an excitation input which is input to the third electric motor. Consequently, these transfer functions can be estimated with higher accuracy. 
     (4) In a mechanical characteristic estimation step of the present invention, transfer functions from, a second or third input to a second or third speed signal are, estimated by use of eight responses including responses of the second and third inputs and the second and third speed signals to an excitation input which is input to a second electric motor, and responses of the second and third inputs and the second and third speed signals to an excitation input which is input to the third electric motor. Consequently, these transfer functions can be estimated with higher accuracy. 
     (5) In a control circuit characteristic estimation step of the present invention, a transfer function from an input signal to a second or third input in a speed control device is estimated by using responses measured in the first and second excitation measurement steps. In this way, in the present invention, a transfer function representing an input/output characteristic of a speed control device is estimated by combining the response when a second electric motor is excitation-controlled with the response when a third electric motor is excitation-controlled. Thereby, it is possible to estimate the transfer function with accuracy in a state where the speed control device is actually operated. In addition, an actual speed control device is configured by combining various control circuits. Thus, it maybe difficult to operate only a particular control circuit and then estimate an input/output characteristic thereof, or it may take time. In the present invention, an input/output characteristic of a speed control device can be estimated in a state where the speed control device is actually operated. Therefore, the input/output characteristic can be estimated with ease and in a short time. 
     (6) In the present invention, a first electric motor is linked to a first shaft of a test piece. In a third excitation measurement step, a response to an excitation input when a first electric motor is excitation-controlled is measured. Further, in the mechanical characteristic estimation step, a transfer function from a first input to first to third state detection signals and a transfer function from a second or third input to a first state detection signal are estimated by using responses measured in one or both of first and second excitation measurement steps, and a response measured in a third excitation measurement step. Thereby, according to the present invention, it is possible to eliminate an influence of an input/output characteristic of a speed control device, and thus estimate a transfer function with accuracy. 
     (7) In the present invention, second and third electric motors are respectively linked to second and third shafts of a test piece. In a first excitation measurement step, a response to an excitation input when the second electric motor is excitation-controlled is measured. In a second excitation measurement step, a response to an excitation input when the third electric motor is excitation-controlled is measured. Further, in the control circuit characteristic estimation step, a transfer function from an input signal to a second or third input in the speed control device is estimated by using responses measured in the first and second excitation measurement steps. In this way, in the present invention, a transfer function representing an input/output characteristic of a speed control device is estimated by combining the response when the second electric motor is excitation-controlled with the response when the third electric motor is excitation-controlled. Thereby, it is possible to estimate the transfer function with accuracy in a state where the speed control device is actually operated. In addition, an actual speed control device is configured by combining various control circuits. Thus, it may be difficult to operate only a particular control circuit and then estimate an input/output characteristic thereof, or it may take time. In the present invention, an input/output characteristic of a speed control device can be estimated in a state where the speed control device is actually operated. Therefore, the input/output characteristic can be estimated with ease and in a short time. 
     (8) In a first excitation measurement step of the present invention, responses of second and third speed signals to an excitation input, which is input to the second electric motor are measured. In a second excitation measurement step, responses of second and third speed signals to an excitation input which is input to the third electric motor are measured. In a control circuit characteristic estimation step, a transfer function from the second or third speed signal to the second or third speed signal in the speed control device is estimated by use of the four responses. Consequently, these transfer functions can be estimated with higher accuracy. 
     (9) In the present invention, first and second electric motors are respectively linked to first and second shafts of a test piece, and a rotation speed of the second electric motor is controlled by a speed control device. In a first excitation measurement step, a response to an excitation input when the first electric motor is excitation-controlled is measured. In a second excitation measurement step, a response to an excitation input when the second electric motor is excitation-controlled is measured. Further, in a mechanical characteristic estimation step, a transfer function from a first input to a first or second state detection signal is estimated by using the responses to the excitation input obtained in the first and second excitation measurement steps. In this way, in the present invention, a transfer function from the first input to the first or second state detection signal is estimated by combining the response when the first electric motor is excitation-controlled with the response when the second electric motor is excitation-controlled. Thereby, it is possible to eliminate an influence of an input/output characteristic of a speed control device, and thus estimate a transfer function with accuracy. 
     (10) In a first excitation measurement step of the present invention, responses of a second speed signal and a first torque detection signal to an excitation input which is input to the first electric motor are measured. In a mechanical characteristic estimation step, a transfer function from the first input to the first torque detection signal is estimated by use of the two responses measured in the first excitation measurement step and the response measured in the second excitation measurement step. Consequently, this transfer function can be estimated with higher accuracy. 
     (11) In a first excitation measurement step of the present invention, responses of a second speed signal and first and second torque detection signals to an excitation input which is input to the first electric motor are measured. In a mechanical characteristic estimation step, a transfer function from the first input to the first torque detection signal, and a transfer function from the first input to the second torque detection signal are estimated by use of the three responses measured in the first excitation measurement step and the response measured in the second excitation measurement step. Consequently, these transfer functions can be estimated with higher accuracy. 
     (12) In a first excitation measurement step of the present invention, responses of first and second speed signals to an excitation input which is input to the first electric motor are measured. In a mechanical characteristic estimation step, a transfer function from the first input to the first speed signal, and a transfer function from the first input to the second speed signal are estimated by use of the two responses measured by the first excitation measurement step and the response measured by the second excitation measurement step. Consequently, these transfer functions can be estimated with higher accuracy. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a configuration of a testing system and an input/output characteristic estimation method thereof according to one embodiment of the present invention. 
         FIG. 2  is a diagram illustrating a configuration of a control circuit of a dynamometer control device when an input/output characteristic is estimated. 
         FIG. 3  is a flowchart illustrating a specific calculation procedure of an input/output characteristic estimation method in Example 1. 
         FIG. 4A  is a graph illustrating an estimation result (Gt 2 _i 2 ) in Example 1. 
         FIG. 4B  is a graph illustrating an estimation result (Gt 3 _i 2 ) in Example 1. 
         FIG. 4C  is a graph illustrating an estimation result (Gw 2 _i 2 ) in Example 1. 
         FIG. 4D  is a graph illustrating an estimation result (Gw 3 _i 2 ) in Example 1. 
         FIG. 4E  is a graph illustrating an estimation result (Gt 2 _i 3 ) in Example 1. 
         FIG. 4F  is a graph illustrating an estimation result (Gt 3 _i 3 ) in Example 1. 
         FIG. 4G  is a graph illustrating an estimation result (Gw 2 _i 3 ) in Example 1. 
         FIG. 4H  is a graph illustrating an estimation result (Gw 3 _i 3 ) in Example 1. 
         FIG. 5  is a flowchart illustrating a specific calculation procedure of an input/output characteristic estimation method in Example 2. 
         FIG. 6A  is a flowchart, illustrating a specific calculation procedure of an input/output characteristic estimation method in Example 3. 
         FIG. 6B  is a flowchart illustrating a specific calculation procedure of an input/output characteristic estimation method in Example 3. 
         FIG. 7A  is a graph illustrating an estimation result (Gt 1 _i 1 ) in Example 3. 
         FIG. 7B  is a graph illustrating an estimation result (Gt 2 _i 1 ) in Example 3. 
         FIG. 7C  is a graph illustrating an estimation result (Gt 3 _i 1 ) in Example 3. 
         FIG. 7D  is a graph illustrating an estimation result (Gw 1 _i 1 ) in Example 3. 
         FIG. 7E  is a graph illustrating an estimation result (Gw 2 _i 1 ) in Example 3. 
         FIG. 7F  is a graph illustrating an estimation result (Gw 3 _i 1 ) in Example 3. 
         FIG. 7G  is a graph illustrating an estimation result (Gt 1 _i 2 ) in Example 3. 
         FIG. 7H  is a graph illustrating an estimation result (Gt 1 _i 3 ) in Example 3. 
         FIG. 7I  is a graph illustrating an estimation result (Gw 1 _i 2 ) in Example 3. 
         FIG. 7J  is a graph illustrating an estimation result (Gw 1 _i 3 ) in Example 3. 
     
    
    
     PREFERRED MODE FOR CARRYING OUT THE INVENTION 
     Hereinafter, one embodiment of the present invention will be described in detail with reference to the drawings.  FIG. 1  is a diagram illustrating a configuration of a testing system S to which an input/output characteristic estimation method according to the present embodiment is applied. The testing system S is intended to evaluate performance of a test piece W, using, as the test piece W, a drive train including a first shaft S 1  as at least one input shaft, and a second shaft S 2  and a third shaft S 3  as output shafts each connected to the first shaft S 1  so as to be able to transmit power. 
     The testing system S includes the test piece W, a first dynamometer  21 , a second dynamometer  22 , and a third dynamometer  23  linked to the test piece W, a first inverter  31 , a second inverter  32 , and a third inverter  33  which supply electric power to the respective dynamometers  21  to  23 , a first rotation speed detector  51 , a second rotation speed detector  52 , and a third rotation speed detector  53  which detect rotation speeds of shafts in the respective dynamometers  21  to  23 , a first shaft torque detector  61 , a second shaft torque detector  62 , and a third torque detector  63  which detect shaft torque in the respective dynamometers  21  to  23 , a dynamometer control device  7  which inputs a torque current command signal to each of the inverters  31  to  33 , and an estimation device  8  which estimates an input/output characteristic from a predetermined input to a predetermined output in the testing system S. 
     An output shaft of the first dynamometer  21  is coaxially linked to the first shaft S 1  of the test piece W. An output shaft of the second dynamometer  22  is coaxially linked to the second shaft S 2  of the test piece W. An output shaft of the third dynamometer  23  is coaxially linked to the third shaft S 3  of the test piece W. 
     The first rotation speed detector  51  detects a first rotation speed which is the number of rotations per unit time of the output shaft of the first dynamometer  21 , and generates a first speed detection signal w 1  associated with the first rotation speed. The second rotation speed detector  52  detects a second rotation speed which is the number of rotations per unit time of the output shaft of the second dynamometer  22 , and generates a second speed detection signal w 2  associated with the second rotation speed. The third rotation speed detector  53  detects a third rotation speed which is the number of rotations per unit time of the output shaft of the third dynamometer  23 , and generates a third speed detection signal w 3  associated with the third rotation speed. 
     The first shaft torque detector  61  detects torsional torque (hereinafter, referred to as a “first shaft torque”) generated in the first shaft S 1 , and generates a first shaft torque detection signal t 1  associated with the first shaft torque. The second shaft torque detector  62  detects torsional torque (hereinafter, referred to as a “second shaft torque”) generated in. the second shaft S 2 , and generates a second shaft torque detection signal t 2  associated with the second shaft torque. The third torque detector  63  detects torsional torque (hereinafter, referred to as a “third shaft torque”) generated in the third shaft S 3 , and generates a third shaft torque detection signal t 3  associated with the third shaft torque. 
     The dynamometer control device  7  generates, on the basis of a predetermined algorithm, a first torque current command signal i 1  which is a torque current command signal to the first dynamometer  21 , a second torque current command signal i 2  which is a torque current command signal to the second dynamometer  22 , and a third torque current command signal i 3  which is a torque current command signal to the third dynamometer  23 , by using the speed detection signals w 1  to w 3 , the shaft torque detection signals t 1  to t 3 , and a predetermined command signal, and inputs each of the signals it to i 3  to each of the inverters  31  to  33 . The first inverter  31  supplies electric power associated with the first torque current command signal i 1  to the first dynamometer  21 . The second inverter  32  supplies electric power associated with the second torque current command signal i 2  to the second dynamometer  22 . The third inverter  33  supplies electric power associated with the third torque current command signal i 3  to the third dynamometer  23 . 
     The estimation device  8  estimates an input/output characteristic from a predetermined input signal to a predetermined output signal in the testing system S by using the speed detection signals w 1  to w 3 , the shaft torque detection signals t 1  to t 3 , and the torque current command signals i 1  to i 3 , under control of the respective dynamometers  21  to  23  by the dynamometer control device  7  described above. 
       FIG. 2  is a diagram illustrating a configuration of a control circuit of the dynamometer control device  7 . More specifically,  FIG. 2  illustrates, out of the control circuit configured in the dynamometer control device  7 , only parts used when an input/output characteristic of the testing system S is estimated by use of the estimation device  8 . 
     The dynamometer control device  7  includes a base torque generation unit  71 , an excitation torque generation unit  72 , a speed control device  73 , a first command signal generation unit  74 , a second command signal generation unit  75 , and a third command signal generation unit  76 . When an input/output characteristic is estimated, the dynamometer control device  7  generates the torque current command signals i 1  to i 3  by using the above components. 
     The base torque generation unit  71  generates a base torque command signal ib 1  of certain magnitude which does not temporally change. In response to a predetermined request, the excitation torque generation unit  72  generates a first excitation torque input d 1 , a second excitation torque input d 2 , and a third excitation torque input d 3  which randomly vary under a predetermined excitation frequency within a predetermined range around 0. 
     The first command signal generation unit  74  outputs the first base torque command signal ib 1  as the first torque current command signal i 1 , when the first excitation torque input d 1  is not generated. The first command signal generation unit  74  outputs, as the first torque current command signal i 1 , the base torque command signal ib 1  on which the first excitation torque input d 1  is superimposed, when the first excitation torque input d 1  is generated. 
     The speed control device  73  generates a second torque control input ib 2  which is an input to the second dynamometer  22  and a third torque control input ib 3  which is an input to the third dynamometer  23  for controlling the second rotation speed and the third rotation speed to a predetermined target by using a predetermined command signal, the second speed detection signal w 2 , and the third speed detection signal w 3 . More specifically, when an average speed command signal w_av which is a command signal to an average speed of the second rotation speed and the third rotation speed and which does not temporally change, and a difference speed command signal dw (hereinafter, assumed to be 0) which is a command signal to a difference between the second rotation speed and the third rotation speed and which does not temporally change are input, the speed control device  73  generates the second torque control input ib 2  and the third torque control input ib 3  by a known feedback algorithm so that an average ((w 2 +w 3 )/2) of the second speed detection signal w 2  and the third speed detection signal w 3  becomes the average speed command signal w_av and so that a difference (w 2 −w 3 ) between the second speed detection signal w 2  and the third speed detection signal w 3  becomes the difference speed command signal dw. 
     The second command signal generation unit  75  outputs the second torque control input ib 2  as the second torque current command signal i 2 , when the second excitation torque input. d 2  is not generated. The second command signal generation unit  75  outputs, as the second torque current command signal i 2 , the second torque control input ib 2  on which the input d 2  is superimposed, when the second excitation torque input d 2  is generated. 
     The third command signal generation unit  76  outputs the third torque control input ib 3  as the third torque current command signal i 3 , when the third excitation torque input d 3  is not generated. The third command signal generation unit  76  outputs, as the third torque current command signal i 3 , the third torque control input ib 3  on which the third excitation torque input d 3  is superimposed, when the third excitation torque input d 3  is generated. 
     As described, above, the dynamometer control device  7  performs excitation control by appropriately superimposing the first excitation torque input d 1  while performing torque current control using the base torque command signal ib 1  with regard to the first dynamometer  21 , when an input/output characteristic of the testing system S is estimated. Further, the dynamometer control device  7  performs excitation control by appropriately superimposing the excitation torque inputs d 2  and d 3  while performing speed control using the speed detection signals w 2  and w 3  with regard to the second and third dynamometers  22  and  23 , when an input/output characteristic of the testing system S is estimated. 
     Returning to  FIG. 1 , by controlling each of the dynamometers  21  to  23  by the dynamometer control device  7  as described above, the estimation device  8  estimates a transfer function matrix Gti representing a mechanical characteristic (hereinafter, the characteristic is also referred to as a “torque command—shaft torque characteristic”) from each of the torque current command signals i 1  to i 3  to each of the shaft torque detection signals t 1  to t 3 , a transfer function matrix Gwi representing a mechanical characteristic (hereinafter, the characteristic is also referred to as a “torque command—rotation speed characteristic”) from each of the torque current command signals i 1  to i 3  to each of the speed detection signals w 1  to w 3 , and a transfer function matrix C representing an input/output characteristic (hereinafter, also referred to as a “control circuit characteristic”) of the speed control device  73  from each of the speed detection signals w 2  and w 3  to each of the torque control inputs ib 2  and ib 3 . 
     First, the transfer function matrix Gti representing a torque command—shaft torque characteristic is represented by a 3×3 matrix configured by a total of nine independent components, as indicated in the following Equation (1). In the following Equation (1), for example, a transfer function Gt 1 _i 1  which is a component in the first column and first row of the matrix Gti represents a mechanical characteristic of the first shaft torque detection signal t 1  to the first torque current command signal i 1 . Further, a transfer function Gt 1 _i 2  which is a component in the second column and first row of the matrix Gti represents a mechanical characteristic of the first shaft torque detection signal t 1  to the second torque current command signal i 2 . The same also applies to other components, and a description thereof is omitted. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
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                   = 
                   
                     
                       Gti 
                       · 
                       
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                                 ⁢ 
                                 
                                     
                                 
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                         ( 
                         
                           
                             
                               
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                                 ⁢ 
                                 
                                     
                                 
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                               Gt1_i2 
                             
                             
                               Gt1_i3 
                             
                           
                           
                             
                               Gt2_i1 
                             
                             
                               Gt2_i2 
                             
                             
                               Gt2_i3 
                             
                           
                           
                             
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                         ) 
                       
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     Furthermore, the transfer function matrix Gwi representing a torque command—rotation speed characteristic is represented by a 3×3 matrix configured by a total of nine independent components, as indicated in the following Equation (2). In the following Equation (2), for example, a transfer function Gw 1 _i 1  which is a component in the first column and first row of the matrix Gwi represents a transfer function of a mechanical characteristic of the first speed detection signal w 1  to the first torque current command signal i 1 . Further, a transfer function Gw 1 _i 2  which is a component in the second column and first row of the matrix Gwi represents a transfer function of a mechanical characteristic of the first speed detection signal w 1  to the second torque current command signal i 2 . The same also applies to other components, and a description thereof is omitted. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
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                       · 
                       
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                                 ⁢ 
                                 
                                     
                                 
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                       · 
                       
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     Furthermore, in the dynamometer control device  7  as illustrated in  FIG. 2 , an input/output characteristic from the speed detection signals w 1  to w 3  and the excitation torque inputs d 1  to d 3  which are inputs to the dynamometer control device  7 , to the torque current command signals i 1  to i 3  which are inputs to the dynamometer control device  7  is represented by the following Equation (3) by use of a 3×3 unit matrix, and a transfer function matrix C representing a control circuit characteristic of the speed control device  73 . In addition, in the calculation in the estimation device  8 , a frequency characteristic when excitation is made by use of the excitation torque inputs d 1  to d 3  is measured, so that the base torque command signal ib 1 , the average speed command signal w_av, and the difference speed command signal dw which do not temporally change can be negligible, as indicated in the following Equation (3). Further, in the speed control device  73 , the two torque control inputs ib 2  and ib 3  are generated using the two speed detection signals w 2  and w 3 , so that the transfer function matrix C thereof is substantially represented by a 2×2 matrix as indicated in the following Equation (3). In the following Equation (3), for example, a transfer function C 22  which is a component in the second column and second row of the matrix C represents a transfer function of the second torque control input ib 2  to the second speed detection signal w 2  in, the speed control device  73 . Further, a transfer function C 23  which is a component in the third column and second row of the matrix C represents a transfer function of the second torque control input ib 2  to the third speed detection signal w 3  in the speed control device  73 . The same also applies to other components, and a description thereof is omitted. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     Example 1 
     Next, an input/output characteristic estimation method in Example 1 using the, testing system as above is described. The input/output characteristic estimation method in Example 1 estimates a transfer function from the second torque current command signal i 2  or the third torque current command signal i 3  to the second shaft torque detection signal t 2  or the third shaft torque detection signal t 3  (i.e., in the matrix Gti in Equation (1), four transfer functions including the component Gt 2 _i 2  in the second column and second row, the component Gt 2 _i 3  in the third column and second row, the component Gt 3 _i 2  in the second column and third row, and the component Gt 3 _i 3  in the third column and third row), and a transfer function from the second torque current command signal i 2  or the third torque current command signal i 3  to the second speed detection signal w 2  or the third speed detection signal w 3  (i.e., in the transfer function matrix Gwi in Equation (2), four transfer functions including the component Gw 2 _i 2  in the second column and second row, the component Gw 2 _i 3  in the third column and second row, the component Gw 3 _i 2  in the second column and third row, and the component Gw 3 _i 3  in the third column and third row). 
       FIG. 3  is a flowchart illustrating a specific calculation procedure for estimating an input/output characteristic by the input/output characteristic estimation method in Example 1. In S 1 , control of the first to third dynamometers using the dynamometer control device illustrated in  FIG. 2  is started. In other words, the first dynamometer performs torque current control using the base torque command signal ib 1 , and the second and third dynamometers perform speed control using the speed detection signals w 2 , w 3 , and others. In addition, each of the excitation torque inputs d 1  to d 3  is assumed to be 0. 
     In S 2 , the dynamometer control device sets operating points of the first to third dynamometers to operating points predetermined for measurement of an input/output characteristic. More specifically, while keeping all the excitation torque inputs d 1  to d 3  at 0, the dynamometer control device keeps the base torque command signal ib 1  constant at a predetermined given value, keeps the average speed command signal w_av constant at a predetermined given value, and sets the difference speed command signal dw at 0. 
     In S 3 , while maintaining the base torque command signal, the average speed command signal, and the difference speed command signal at the operating points in S 2 , the dynamometer control device generates the second excitation torque input d 2  varying at a predetermined excitation frequency, superimposes the second excitation torque input d 2  on the second torque control input ib 2 , and vibrates the second torque current command signal i 2 . In addition, in this instance, each of the other excitation torque inputs d 1  and d 3  is assumed to be 0. 
     In S 4 , the estimation device measures the second excitation torque input d 2 , the second torque current command signal i 2 , the second shaft torque detection signal t 2 , the second speed detection signal w 2 , the third torque current command signal i 3 , the third shaft torque detection signal t 3 , and the third speed detection signal w 3 . 
     In S 5 , the estimation device measures six frequency responses i 2 d 2 , t 2 d 2 , w 2 d 2 , i 3 d 2 , t 3 d 2 , and w 3 d 2  as indicated in the following Equations (4-1) to (4-6), by calculating ratios between the second excitation torque input d 2  measured in S 4  and the other output signals i 2 , t 2 , w 2 , i 3 , t 3 , and w 3 . Here, i 2 d 2  represents a frequency response of the second torque current command signal i 2  to the second excitation torque input d 2  input to the second dynamometer  22 , t 2 d 2  represents a frequency response of the second shaft torque detection signal t 2  to the input d 2 , w 2 d 2  represents a frequency response of the second-speed detection signal w 2  to the input d 2 , i 3 d 2  represents a frequency response of the third torque current command signal i 3  to the input d 2 , t 3 d 2  represents a frequency response of the third shaft torque detection signal t 3  to the input d 2 , and w 3 d 2  represents a frequency response of the third speed detection signal w 3  to the input d 2 .
 
 i 2 d 2= i 2/ d 2  (4-1)
 
 t 2 d 2= t 2/ d 2  (4-2)
 
 w 2 d 2= w 2/ d 2  (4-3)
 
 i 3 d 2= i 3/ d 2  (4-4)
 
 t 3 d 2= t 3/ d 2  (4-5)
 
 w 3 d 2= w 3/ d 2  (4-6)
 
     In S 6 , the estimation device determines whether or not measurement of the six frequency responses i 2 d 2  and others is completed within a predetermined frequency region. When the determination in S 6  is NO, the estimation device returns to S 3 , changes the excitation frequency of the second excitation torque input d 2 , and then again executes the processing of S 4  and S 5 . When the determination in S 6  is YES, the estimation device shifts to S 7 . 
     In S 7 , while maintaining the base torque command signal, the average speed command signal, and the difference speed command signal at the operating points in S 2 , the dynamometer control device generates the third excitation torque input d 3  varying at a predetermined excitation frequency, superimposes the third excitation torque input d 3  on the third torque control input ib 3 , and vibrates the third torque current command signal i 3 . In addition, in this instance, each of the other excitation torque inputs d 1  and d 2  is assumed to be 0. 
     In S 8 , the estimation device measures the third excitation torque input d 3 , the second torque current command signal i 2 , the second shaft torque detection signal t 2 , the second speed detection signal w 2 , the third torque current command signal i 3 , the third shaft torque detection signal t 3 , and the third speed detection signal w 3 . 
     In S 9 , the estimation device measures six frequency responses i 2 d 3 , t 2 d 3 , w 2 d 3 , i 3 d 3 , t 3 d 3 , and w 3 d 3  as indicated in the following Equations (5-1) to (5-6), by calculating ratios between the third excitation torque input d 3  measured in S 8  and the other output signals i 2 , t 2 , w 2 , i 3 , t 3 , and w 3 . Here, i 2 d 3  represents a frequency response of the second torque current command signal i 2  to the third excitation torque input d 3  input to the third dynamometer  23 , t 2 d 3  represents a frequency response of the second shaft torque detection signal t 2  to the input d 3 , w 2 d 3  represents a frequency response of the second speed detection signal w 2  to the input d 3 , i 3 d 3  represents a frequency response of the third torque current command signal i 3  to the input d 3 , t 3 d 3  represents a frequency response of the third shaft torque detection signal t 3  to the input d 3 , and w 3 d 3  represents a frequency response of the third speed detection signal w 3  to the input d 3 .
 
 i 2 d 3= i 2/ d 3  (5-1)
 
 t 2 d 3= t 2/ d 3  (5-2)
 
 w 2 d 3= w 2/ d 3  (5-3)
 
 i 3 d 3= i 3/ d 3  (5-4)
 
 t 3 d 3= t 3/ d 3  (5-5)
 
 w 3 d 3= w 3/ d 3  (5-6)
 
     In S 10 , the estimation device determines whether or not measurement of the six frequency responses i 2 d 3  and others is completed within a predetermined frequency region. When the determination in S 10  is NO, the estimation device returns to S 7 , changes the excitation frequency of the third excitation torque input d 3 , and then again executes the processing of S 8  and S 9 . When the determination in S 10  is YES, the estimation device shifts to S 11 . 
     In S 11 , the estimation device calculates four pairs of transfer functions Gt 2 _i 2 , Gt 2 _i 3 , Gt 3 _i 2 , and Gt 3 _i 3  by using the eight pairs of frequency responses i 2 d 2 , t 2 d 2 , i 2 d 3 , t 2 d 3 ,  13 d 2 , t 3 d 2 , i 3 d 3 , and t 3 d 3  measured by the processing described above, and finishes this processing. More specifically, the transfer functions Gt 2 _i 2  and others are calculated by inputting the above-described frequency responses i 2 d 2  and others to the following Equations (6-1) to (6-4) derived on the basis of the above Equations (1) to (3). Gt 2 _i 2  in the following Equation (6-1) represents a transfer function from the second torque current command signal i 2  to the second shaft torque detection signal t 2 , Gt 2 _i 3  in the following Equation (6-2) represents a transfer function from the third torque current command signal i 3  to the second shaft torque detection signal t 2 , Gt 3 _i 2  in the following Equation (6-3) represents a transfer function from the second torque current command, signal i 2  to the third shaft torque detection signal t 3 , and Gt 3 _i 3 .in the following Equation (6-4) represents a transfer function from the third torque current command signal i 3  to the third. shaft torque detection signal t 3 . 
     
       
         
           
             
               
                 
                   Gt2_i2 
                   = 
                   
                     
                       
                         
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                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   Gt2_i3 
                   = 
                   
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           t 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           t 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   Gt3_i2 
                   = 
                   
                     
                       
                         
                           - 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           t 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           t 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   Gt3_i3 
                   = 
                   
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           t 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           t 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     In S 12 , the estimation device calculates four transfer functions Gw 2 _i 2 , Gw 2 _i 3 , Gw 3 _i 2 , and Gw 3 _i 3  by using the eight pairs of frequency responses i 2 d 2 , w 2 d 2 , i 2 d 3 , w 2 d 3 , i 3 d 2 , w 3 d 2 , i 3 d 3 , and w 3 d 3  measured by the processing described above. More specifically, the transfer functions Gw 2 _i 2  and others are calculated by inputting the above-described frequency responses i 2 d 2  and others to the following Equations (7-1) to (7-4) derived on the basis of the above Equations (1) to (3). Gw 2 _i 2  in the following Equation (7-1) represents a transfer function from the second torque current command signal i 2  to the second speed detection signal w 2 , Gw 2 _i 3  in the following Equation (7-2) represents a transfer function from the third torque current command signal i 3  to the second speed detection signal w 2 , Gw 3 _i 2  in the following Equation (7-3) represents a transfer function from the second torque current command signal i 2  to the third speed detection signal w 3 , and Gw 3 _i 3  in the following Equation (7-4) represents a transfer function from the third torque current command signal i 3  to the third speed detection signal w 3 . 
     
       
         
           
             
               
                 
                   Gw2_i2 
                   = 
                   
                     
                       
                         
                           - 
                           i 
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   Gw2_i3 
                   = 
                   
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
             
               
                 
                   Gw3_i2 
                   = 
                   
                     
                       
                         
                           - 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
             
               
                 
                   Gw3_i3 
                   = 
                   
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           i 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
       FIGS. 4A to 4H  are graphs each illustrating an estimation result by the estimation device in Example 1. More specifically,  FIG. 4A  illustrates a Bode diagram of the transfer function Gt 2 _i 2  estimated by Equation (6-1),  FIG. 4B  illustrates a Bode diagram of the transfer function Gt 3 _i 2  estimated by Equation (6-3),  FIG. 4C  illustrates a Bode diagram of the transfer function Gw 2 _i 2  estimated by Equation (7-1),  FIG. 4D  illustrates a Bode diagram of the transfer function Gw 3 _i 2  estimated by Equation (7-3),  FIG. 4E  illustrates a Bode diagram of the transfer function Gt 2 _i 3  estimated by Equation (6-2),  FIG. 4F  illustrates a Bode diagram of the transfer function Gt 3 _i 3  estimated by Equation (6-4),  FIG. 4G  illustrates a Bode diagram of the transfer function Gw 2 _i 3  estimated by Equation (7-2), and  FIG. 4H  illustrates a Bode diagram of the transfer function Gw 2 _i 3  estimated by Equation (7-4). Further, in each of the diagrams, a thin full line indicates a true mechanical characteristic, and a broken line indicates an estimation result by the input/output characteristic estimation method in Example 1. 
     Moreover, each thick solid line in each of the diagrams indicates an estimation result by a conventional input/output characteristic estimation method. Here, the conventional input/output characteristic estimation method refers to a method which simply measures a response to an excitation torque input. More specifically, the thick solid line in  FIG. 4A  is a response (i.e., t 2 d 2  in Equation (4-2)) of the shaft torque detection signal t 2  when the second excitation torque input d 2  is input to the second dynamometer, the thick solid line in  FIG. 4B  is a response (i.e., t 3 d 2  in Equation (4-5)) of the third shaft torque detection signal t 3  when the excitation torque input d 2  is input to the second dynamometer, the thick solid line in  FIG. 4C  is a response (i.e., w 2 d 2  in Equation (4-3)) of the second speed detection signal w 2  when the second excitation torque input d 2  is input to the second dynamometer, the thick solid line in  FIG. 4D  is a response (i.e., w 3 d 2  in Equation (4-6)) of the third speed detection signal w 3  when the second excitation torque input d 2  is input to the second dynamometer, the thick solid line in  FIG. 4E  is a response (i.e., t 2 d 3  in Equation (5-2)) of the shaft torque detection signal t 2  when the excitation torque input d 3  is input to the third dynamometer, the thick solid line in  FIG. 4F  is a response (i.e., t 3 d 3  in Equation (5-5)) of the third shaft torque detection signal t 3  when the excitation torque input d 3  is input to the third dynamometer, the thick solid line in  FIG. 4G  is a response (i.e., w 2 d 3  in Equation (5-3)) of the second speed detection signal w 2  when the excitation torque input d 3  is input to the third dynamometer, and the thick solid line in  FIG. 4H  is a response (i.e., w 3 d 3  in Equation (5-6)) of the third speed detection signal w 3  when the excitation torque input d 3  is input to the third dynamometer. 
     As illustrated in  FIGS. 4A to 4H , a true mechanical characteristic cannot be obtained by merely measuring a response to an excitation torque input with regard to a mechanical characteristic to be obtained, as in the conventional input/output characteristic estimation method. This is because a test piece includes a plurality of shafts, and each shaft is controlled by the speed control device and subjected to a characteristic of this speed control device In contrast, the input/output characteristic estimation device in Example 1 estimates one transfer function by combining a plurality of responses obtained when a plurality of dynamometers connected to a test piece are excitation-controlled, and can thereby estimate an input/output characteristic of a testing system with accuracy while removing a characteristic of the speed control device, as illustrated in  FIGS. 4A to 4H . 
     In addition, in the processing in  FIG. 3 , it is not necessary, in estimating each transfer function, to measure a response when the first excitation torque input d 1  is input to the first dynamometer. Thus, in performing the input/output characteristic estimation method in Example 1, an actual engine may be connected to the first shaft S 1  of the test piece W, without connecting the first dynamometer  21  thereto. 
     Example 2 
     Next, an input/output characteristic estimation method for a testing system in Example 2 is described. The input/output characteristic estimation method in Example 2 estimates transfer functions from two input signals (the second speed detection signal w 2  or the third speed detection signal w 3 ) to the second torque current command signal i 2  or the third torque current command signal i 3  in the speed control device  73  in  FIG. 2  (i.e., in the transfer function matrix C in Equation (3), four transfer functions including the component C 22  in the second column and second row, the component C 23  in the third column and second row, the component C 32  in the second column and third row, and the component C 33  in the third column and third row. 
       FIG. 5  is a flowchart illustrating a specific calculation procedure for estimating an input/output characteristic by the input/output characteristic estimation method in Example 2. In S 21 , control of the first to third dynamometers using the dynamometer control device in  FIG. 2  is started, as in S 1  of  FIG. 3 . In S 22 , the dynamometer control device sets operating points of the first to third dynamometers to operating points predetermined for measurement of an input/output characteristic, as in S 2  of  FIG. 3 . In S 23 , the dynamometer control device generates the second excitation torque input d 2 , superimposes the second excitation torque input d 2  on the second torque control input ib 2 , and vibrates the second torque current command signal i 2 , as in S 3  of  FIG. 3 . 
     In S 24 , the estimation device measures the second excitation torque input d 2 , the second torque current command signal i 2 , the second speed detection signal w 2 , the third torque current command signal i 3 , and the third speed detection signal w 3 . 
     In S 25 , the estimation device measures four frequency responses i 2 d 2 , w 2 d 2 , i 3 d 2 , and w 3 d 2  as indicated in the following Equations (8-1) to (8-4), by calculating ratios between the second excitation torque input d 2  measured in S 24  and the other output signals i 2 , w 2 , i 3 , and w 3 .
 
 i 2 d 2= i 2/ d 2  (8-1)
 
 w 2 d 2= w 2/ d 2  (8-2)
 
 i 3 d 2= i 3/ d 2  (8-3)
 
 w 3 d 2= w 3/ d 2  (8-4)
 
     In S 26 , the estimation device determines whether or not measurement of the four frequency responses i 2 d 2  and others is completed within a predetermined frequency region. When the determination in S 26  is NO, the estimation device returns to S 23 , changes the excitation frequency of the second excitation torque input d 2 , and then again executes the processing of S 24  and S 25 . When the determination in S 26  is YES, the estimation device shifts to S 27 . In S 27 , the dynamometer control device generates the third excitation torque input d 3 , superimposes the third excitation torque input d 3  on the third torque control input ib 3 , and vibrates the third torque current command signal i 3 , as in S 7  of  FIG. 3 . 
     In S 28 , the estimation device measures the third excitation torque input d 3 , the second torque current command signal i 2 , the second speed detection signal w 2 , the third torque current command signal i 3 , and the third speed detection signal w 3 . 
     In S 29 , the estimation device measures four frequency responses i 2 d 2 , w 2 d 3 , i 3 d 3 ,. and w 3 d 3  as indicated in the following Equations (9-1) to (9-4), by calculating ratios between the third excitation torque input d 3  measured in S 28  and the other output signals i 2 , w 2 , i 3 , and w 3 .
 
 i 2 d 3= i 2/ d 3  (9-1)
 
 w 2 d 3= w 2/ d 3  (9-2)
 
 i 3 d 3= i 3/ d 3  (9-3)
 
 w 3 d 3= w 3/ d 3  (9-4)
 
     In S 30 , the estimation device determines whether or not measurement of, the four frequency responses i 2 d 3  and others is completed within a predetermined frequency region. When the determination in S 30  is, NO, the estimation device returns to S 37 , changes the excitation frequency of the third excitation torque input d 3 , and then again executes, the processing of, S 28  and S 29 . When the determination in S 30  is YES, the estimation device shifts to S 31 . 
     In S 31 , the estimation device calculates four transfer functions C 22 , C 23 , C 32 , and C 33  by using the eight pairs of frequency responses i 2 d 2 , w 2 d 2 , i 3 d 2 , w 3 d 2 , i 2 d 3 , w 2 d 3 , i 3 d 3 , and w 3 d 3  measured by the processing described above. More specifically, the transfer functions C 22  and others are calculated by inputting the above-described frequency responses i 2 d 2  and others to the following Equations (10-1) to (10-4) derived on the basis of the above Equations (1) to (3). C 22  in the following Equation (10-1) represents a transfer function from the second speed detection signal w 2  to the second torque current command signal i 2  (or the second torque control input ib 2 ), C 23  in the following Equation (10-2) represents a transfer function from the third speed detection signal w 3  to the second torque current command signal i 2  (or the second torque control input ib 2 ), C 32  in the following Equation (10-3) represents a transfer function from the second speed detection signal w 2  to the third torque current command signal i 3  (or the third torque control input ib 3 ), and C 33  in the following Equation (10-4) represents a transfer function from the third speed detection signal w 3  to the-third torque current command signal i 3  (or the third torque control input ib 3 ). 
     
       
         
           
             
               
                 
                   
                     C 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   = 
                   
                     
                       
                         w 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         w 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         w 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     10 
                     ⁢ 
                     
                       - 
                     
                     ⁢ 
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     C 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   = 
                   
                     
                       
                         w 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                       + 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       - 
                       
                         i 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                       
                     
                     
                       
                         
                           - 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           3 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                       + 
                       
                         w 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           2 
                           · 
                           w 
                         
                         ⁢ 
                         
                             
                         
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     In addition, in the processing in  FIG. 5 , it is not necessary, in estimating each transfer function, to measure a response when the first excitation torque input d 1  is input to the first dynamometer. Thus, in performing the input/output characteristic estimation method in Example 2, an actual engine may be connected to the first shaft S 1  of the test piece W, without connecting the first dynamometer  21  thereto, as in Example 1. 
     According to the input/output characteristic estimation method in Example 2 as above, frequency responses (i 2 d 2 , w 2 d 2 , and others) to the excitation torque input d 2  when the second dynamometer is excitation-controlled by the excitation torque input d 2  are measured in the processing of S 23  to S 25 , and frequency responses (i 2 d 3 , w 2 d 3 , and others) to the excitation torque input d 3  when the third dynamometer is excitation-controlled by the excitation torque input d 3  are measured in the processing of S 27  to S 29 . Further, in the processing of S 31 , a transfer function from the input signal (w 2  or w 3 ) to the output signal (i 2  or i 3 ) in the speed control device which controls speeds of the second and third dynamometers is estimated by using a plurality of frequency responses measured in the excitation control. In this way, in the input/output characteristic estimation method in Example 2, a transfer function representing an input/output characteristic of a speed control device is estimated by combining the frequency response when the second dynamometer is excitation-controlled by the input d 2  with the frequency response when the third dynamometer different from the second dynamometer is excitation-controlled by the input d 3 . Thereby, it is possible to estimate the transfer function with accuracy in a state where the speed control device is actually operated. In addition, an actual speed control device is configured by combining various control circuits. Thus, it may be difficult to operate only a particular control circuit and then estimate an input/output characteristic thereof, or it may take time. In the input/output characteristic estimation method in Example 2, an input/output characteristic of a speed control device can be estimated in a state where the, speed control device is actually operated. Therefore, the input/output characteristic can be estimated with ease and in a short time. 
     Example 3 
     Next, an input/output characteristic estimation method for a testing system in Example 3 is described. In the input/output characteristic estimation method in-Example 3, all the transfer functions indicated in the., above Equations (1) to (3) are estimated. 
       FIGS. 6A to 6B  are flowcharts illustrating a specific calculation procedure for estimating an input/output characteristic by the input/output characteristic estimation method in Example 3. In addition, processing of S 51  to S 62  is the same as the processing of S 1  to S 12  in  FIG. 3 , and processing of S 63  is the same as the processing of S 31  in  FIG. 5 . Therefore, a detailed description thereof is omitted. 
     In S 64 , while maintaining the base torque command signal, the average speed command signal, and the difference speed command signal at the operating points in S 52 , the dynamometer control device generates the first excitation torque input d 1  varying at a predetermined excitation frequency, superimposes the first excitation torque input d 1  on the base torque command signal ib 1 , and vibrates the first torque current command signal i 1 . In addition, in this instance, each of the other excitation torque inputs d 2  and d 3  is assumed to be 0. 
     In S 65 , the estimation device measures the first excitation torque input d 1 , the first shaft torque detection signal t 1 , the first speed detection signal w 1 , the second shaft torque detection signal t 2 , the second speed detection signal w 2 , the third shaft torque detection signal t 3 , and the third speed detection signal w 3 . 
     In S 66 , the estimation device measures six frequency responses t 1 d 1 , w 1 d 1 , t 2 d 1 , w 2 d 1 , t 3 d 1 , and w 3 d 1  as indicated in the following Equations (11-1) to (11-6), by calculating ratios between the first excitation torque input d 1  measured in S 65  and the other output signals t 1 , w 1 , t 2 , w 2 , t 3 , and w 3 . Here, t 1 d 1  represents a frequency response of the first shaft torque detection signal t 1  to the first excitation torque input d 1  input to the first dynamometer  21 , w 1 d 1  represents a frequency response of the first speed detection signal w 1  to the input d 1 , t 2 d 1  represents a frequency response of the second shaft torque detection signal t 2  to the input d 1 , w 2 d 1  represents a frequency response of the second speed detection signal w 2  to the input d 1 , t 3 d 1  represents a frequency response of the third shaft torque detection signal t 3  to the input d 1 , and w 3 d 1  represents a frequency response of the third speed detection signal w 3  to the input d 1 .
 
 t 1 d 1= t 1/ d 1  (11-1)
 
 w 1 d 1= w 1/ d 1  (11-2)
 
 t 2 d 1= t 2/ d 1  (11-3)
 
 w 2 d 1= w 2/ d 1  (11-4)
 
 t 3 d 1= t 3/ d 1  (11-5)
 
 w 3 d 1= w 3/ d 1  (11-6)
 
     In S 67 , the estimation device determines whether or not measurement of the six frequency responses t 1 d 1  and others is completed within a predetermined frequency region. When the determination in S 67  is NO, the estimation device returns to S 64 , changes the excitation frequency of the first excitation torque input d 1 , and then again executes the processing of S 65  and S 66 . When the determination in S 67  is YES, the estimation device shifts to S 68 . 
     In S 68 , the estimation device calculates five pairs of transfer functions Gt 1 _i 1 , Gt 1 _i 2 , Gt 1 _i 3 , Gt 2 _i 1 , and Gt 3 _i 1  by using the six pairs of frequency responses t 1 d 1 , w 1 d 1 , t 2 d 1 , w 2 d 1 , t 3 d 1 , and w 3 d 1  measured in S 66 , and twelve pairs of transfer functions (see S 61  to  63 ) calculated on the basis of the frequency responses measured by excitation control (see S 53  to  55 ) for the second dynamometer and excitation control (see S 57  to  59 ) for the third dynamometer. More. specifically, Gt 1 _i 1  and others are calculated by inputting, to the following Equations (12-1) to (12-5) derived on the basis of the above Equations (1) to (3), the frequency responses t 1 d 1  and others to the first excitation torque input d 1  measured in S 66 , the frequency responses t 1 d 2  and others to the excitation torque inputs d 2  and d 3  measured in S 55  and S 59 , and the transfer functions Gw 2 _i 2 , C 22 , and others calculated in S 61  to S 63  on the basis of the frequency responses t 1 d 2  and others.
 
 Gt 1_ i 1= t 1 d 1− C 22· t 1 d 2· w 2 d 1+ C 22 2   ·Gw 2_ i 2· t 1 d 2· w 2 d 1+ C 22· C 32· Gw 2_ i 3· t 1 d 2· w 2 d 1+ C 22· C 23· Gw 3_ i 2· t 1 d 2· w 2 d 1+ C 23· C 32 ·Gw 3_ i 3· t 1 d 2· w 2 d 1− C 32· t 1 d 3· w 2 d 1+ C 22 ·C 32 ·Gw 2_ i 2· t 1 d 3 ·w 2 d 1+ C 32 2   ·Gw 2_ i 3· t 1 d 3· w 2 d 1+ C 22· C 33 ·Gw 3_ i 2· t 1 d 3· w 2 d 1+ C 32· C 33 ·Gw 3_ i 3· t 1 d 3· w 2 d 1− C 23· t 1 d 2· w 3 d 1+ C 22 ·C 23 ·Gw 2_ i 2· t 1 d 2· w 3 d 1+ C 22· C 33· Gw 2_ i 3· t 1 d 2· w 3 d 1+ C 23 2   ·Gw 3_ i 2· t 1 d 2· w 3 d 1+ C 23· C 33· Gw 3_ i 3· t 1 d 2· w 3 d 1− C 33· t 1 d 3· w 3 d 1+ C 23· C 32· Gw 2_ i 2· t 1 d 3· w 3 d 1+ C 32· C 33· Gw 2_ i 3· t 1 d 3· w 3 d 1+ C 23· C 33· Gw 3_ i 2· t 1 d 3· w 3 d 1+ C 33 2   ·Gw 3_ i 3 ·t 1 d 3· w 3 d 1  (12-1)
 
 Gt 1_ i 2= t 1 d 2− C 22 ·Gw 2_ i 2· t 1 d 2− C 23· Gw 3_ i 2· t 1 d 2− C 32 ·Gw 2_ i 2 ·t 1 d 3− C 33· Gw 3_ i 2· t 1 d 3  (12-2)
 
 Gt 1_ i 3= t 1 d 3− C 22 ·Gw 2_ i 3· t 1 d 2− C 23· Gw 3_ i 3· t 1 d 2− C 32 ·Gw 2_ i 3· t 1 d 3− C 33· Gw 3_ i 3· t 1 d 3  (12-3)
 
 Gt 2_ i 1= t 2 d 1− C 22 ·Gt 2_ i 2· w 2 d 1− C 32· Gt 2_ i 3· w 2 d 1− C 23· Gt 2_ i 2· w 3 d 1− C 33· Gt 2_ i 3· w 3 d 1  (12-4)
 
 Gt 3_ i 1= t 3 d 1− C 22· Gt 3_ i 2· w 2 d 1− C 32· Gt 3_ i 3· w 2 d 1− C 23· Gt 3_ i 2· w 3 d 1− C 33· Gt 3_ i 3· w 3 d 1  (12-5)
 
     In S 69 , the estimation device calculates five pairs of transfer functions Gw 1 _i 1 , Gw 1 _i 2 , Gw 1 _i 3 , Gw 2 _i 1 , and Gw 3 _i 1  by using the six pairs of frequency responses t 1 d 1 , w 1 d 1 , t 2 d 1 , w 2 d 1 , t 3 d 1 , and w 3 d 1  measured in S 66 , and twelve pairs of transfer functions (see S 61  to  63 ) calculated on the basis of the frequency responses measured by excitation control (see S 53  to  55 ) for the second dynamometer and excitation control (see S 57  to  59 ) for the third dynamometer, and finishes this processing. More specifically, the transfer functions Gw 1 _i 1  and others are calculated by inputting, to the following Equations (13-1) to (13-5) derived on the basis of the above Equations (1) to (3), the frequency responses t 1 d 1  and others to the first excitation torque input d 1  measured in S 66 , the frequency responses t 1 d 2  and others to the excitation torque inputs d 2  and d 3  measured in S 55  and S 59 , and the transfer functions Gw 2 _i 2 , C 22 , and others calculated in S 61  to S 63  on the basis of the frequency responses t 1 d 2  and others.
 
 Gw 1_ i 1 =w 1 d 1− C 22· w 1 d 2· w 2 d 1+ C 22 2   ·Gw 2_ i 2· w 1 d 2· w 2 d 1+ C 22· C 32· Gw 2_ i 3· w 1 d 2· w 2 d 1+ C 22· C 23 ·Gw 3_ i 2· w 1 d 2· w 2 d 1+ C 23· C 32· Gw 3_ i 3· w 1 d 2· w 2 d 1− C 32· w 1 d 3· w 2 d 1+ C 22· C 32· Gw 2_ i 2· w 1 d 3· w 2 d 1+ C 32 2   ·Gw 2_ i 3· w 1 d 3· w 2 d 1+ C 22· C 33· Gw 3_ i 2· w 1 d 3· w 2 d 1+ C 32· C 33· Gw 3_ i 3· w 1 d 3· w 2 d 1− C 23 ·w 1 d 2· w 3 d 1+ C 22· C 23· Gw 2_ i 2· w 1 d 2· w 3 d 1+ C 22· C 33· Gw 2_ i 3· w 1 d 2· w 3 d 1+ C 23 2   ·Gw 3_ i 2· w 1 d 2· w 3 d 1+ C 23· C 33· Gw 3_ i 3· w 1 d 2· w 3 d 1− C 33 ·w 1 d 3· w 3 d 1+ C 23· C 32· Gw 2_ i 2· w 1 d 3· w 3 d 1+ C 32· C 33· Gw 2_ i 3· w 1 d 3· w 3 d 1+ C 23· C 33· Gw 3_ i 2· w 1 d 3· w 3 d 1+ C 33 2   ·Gw 3_ i 3· w 1 d 3· w 3 d 1  (13-1)
 
 Gw 1_ i 2= w 1 d 2− C 22· Gw 2_ i 2· w 1 d 2− C 23· Gw 3_ i 2· w 1 d 2− C 32· Gw 2_ i 2· w 1 d 3− C 33· Gw 3_ i 2· w 1 d 3  (13-2)
 
 Gw 1_ i 3= w 1 d 3− C 22· Gw 2_ i 3· w 1 d 2− C 23· Gw 3_ i 3· w 1 d 2− C 32· Gw 2_ i 3· w 1 d 3− C 33· Gw 3_ i 3· w 1 d 3  (13-3)
 
 Gw 2_ i 1= w 2 d 1− C 22· Gw 2_ i 2· w 2 d 1− C 32· Gw 2_ i 3· w 2 d 1− C 23· Gw 2_ i 2· w 3 d 1− C 33· Gw 2_ i 3· w 3 d 1  (13-4)
 
 Gw 3_ i 1= w 3 d 1− C 22· Gw 3_ i 2· w 2 d 1− C 32· Gw 3_ i 3· w 2 d 1− C 23· Gw 3_ i 2· w 3 d 1− C 33· Gw 3_ i 3· w 3 d 1  (13-5)
 
       FIGS. 7A to 7J  are graphs each illustrating an estimation result by the input/output characteristic estimation method in 
     Example 3 
     More specifically,  FIG. 7A  illustrates a Bode diagram of the transfer function Gt 1 _i 1  estimated by Equation (12-1),  FIG. 7B  illustrates a Bode diagram of the transfer function Gt 2 _it estimated by Equation (12-4),  FIG. 7C  illustrates a Bode diagram of the transfer function Gt 3 _i 1  estimated by Equation (12-5),  FIG. 7D  illustrates a Bode diagram of the transfer function Gw 1 _i 1  estimated by Equation (13-1),  FIG. 7E  illustrates a Bode diagram of the transfer function Gw 2 _i 1  estimated by Equation (13-4),  FIG. 7F  illustrates a Bode diagram of the transfer function Gw 3 _i 1  estimated by Equation (13-5),  FIG. 7G  illustrates a Bode diagram of the transfer function Gt 1 _i 2  estimated by Equation (12-2),  FIG. 7H  illustrates a Bode diagram of the transfer function Gt 1 _i 3  estimated by Equation (12-3),  FIG. 7I  illustrates a Bode diagram of the transfer function Gw 1 _i 2  estimated by Equation (13-2), and  FIG. 7J  illustrates a Bode diagram of the transfer function Gw 1 _i 3  estimated by Equation (13-3). Further, in each of the diagrams, a thin full line indicates a true mechanical characteristic, and a broken line indicates an estimation result by the input/output characteristic estimation method in Example 1. 
     Moreover, each thick solid line in each of the diagrams indicates an estimation result by a conventional input/output characteristic estimation method. More specifically, the thick solid line in  FIG. 7A  is a response (i.e., t 1 d 1  in Equation (11-1)) of the first shaft torque detection signal t 1  when the excitation torque input d 1  is input to the first dynamometer, the thick solid line in  FIG. 7B  is a response (i.e., t 2 d 1  in Equation (11-3)) of the second shaft torque detection signal t 2  when the excitation torque input d 1  is input to the first dynamometer, the thick solid line in  FIG. 7C  is a response (i.e., t 3 d 1  in Equation (11-5)) of the first shaft torque detection signal t 1  when the excitation torque input d 3  is input to the third dynamometer, the thick solid line in  FIG. 7D  is a response (i.e., w 1 d 1  in Equation (11-2)) of the first speed detection signal w 1  when the excitation torque input dl is input to the first dynamometer, the thick solid line in  FIG. 7E  is a response (i.e., w 2 d 1  in Equation (11-4)) of the second speed detection signal w 2  when the excitation torque input d 1  is input to the first dynamometer, the thick solid line in  FIG. 7F  is a response (i.e., w 3 d 1  in Equation (11-6)) of the third speed detection signal w 3  when the excitation torque input d 1  is input to the first dynamometer, the thick solid line in  FIG. 7G  is a response of the first shaft torque detection signal t 1  when the excitation torque input d 2  is input to the second dynamometer, the thick solid line in  FIG. 7H  is a response of the first shaft torque detection signal t 1  when the excitation torque input d 3  is input to the third dynamometer, the thick solid line in  FIG. 7I  is a response of the first speed detection signal w 1  when the excitation torque input d 2  is input to the second dynamometer, and the thick solid line in  FIG. 7J  is a response of the first speed detection signal w 1  when the excitation torque input d 3  is input to the third dynamometer. 
     As illustrated in  FIGS. 7A to 7J , a conventional input/output characteristic estimation device is subjected to a characteristic of a speed control device, and cannot obtain a true mechanical characteristic. In contrast, the input/output characteristic estimation method in Example 3 estimates one transfer function by combining a plurality of responses obtained when a plurality of dynamometers connected to a test piece are excitation-controlled, and can thereby estimate an input/output characteristic of a testing system with accuracy while removing a characteristic of the speed control device, as illustrated in  FIGS. 7A to 7J . 
     EXPLANATION OF REFERENCE NUMERALS 
     S . . . testing system 
     W . . . test piece 
     S 1  . . . first shaft 
     S 2  . . . second shaft 
     S 3  . . . third shaft 
       21  . . . first dynamometer 
       22  . . . second dynamometer 
       23  . . . third dynamometer 
       51  . . . first rotation speed detector 
       52  . . . second rotation speed detector 
       53  . . . third rotation speed detector 
       61  . . . first shaft torque detector 
       62  . . . second shaft torque detector 
       63  . . . third shaft torque detector 
       7  . . . dynamometer control device 
       72  . . . excitation torque generation unit 
       73  . . . speed control device 
       8  . . . estimation device