# Patent

## Title
Load torque estimation apparatus, image forming apparatus, load torque estimation method and non-transitory computer-readable information recording medium

## Abstract

A load torque estimation apparatus inputs a controlling value for controlling the electric motor and an actually measured value of a rotational speed of the electric motor to a model to estimate load torque of the electric motor; and derives a mechanical time constant of the electric motor corresponding to the load torque estimated by the estimation part. The load torque estimation apparatus updates the mechanical time constant included in the model by using the mechanical time constant corresponding to the load torque estimated at an (n−1)th control period (where n denotes an integer greater than or equal to 2) and estimates the load torque of the electric motor at an nth control period by inputting the controlling value and the actually measured value acquired at the nth control period to the model acquired through the updating.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a load torque estimation apparatus, an image forming apparatus, a load torque estimation method and a non-transitory computer-readable information recording medium.
2. Description of the Related Art
In the related art, a technology is known to estimate load torque of an electric motor in a real-time manner. For example, Japanese Laid-Open Patent Application No. 2008-137450 (Patent Reference No. 1) discloses a technology of determining a control model for an electric motor that is a control target and estimating the load torque of the electric motor by using a voltage value (controlling value) for controlling the electric motor and the rotational speed (actually measured value) of the electric motor.
SUMMARY OF THE INVENTION
According to one aspect of the present invention, a load torque estimation apparatus for estimating load torque of an electric motor includes an estimation part configured to input a controlling value for controlling the electric motor and an actually measured value of a rotational speed of the electric motor to a model to estimate load torque of the electric motor; and a derivation part configured to derive a mechanical time constant of the electric motor corresponding to the load torque estimated by the estimation part. The estimation part is configured to update the mechanical time constant included in the model by using the mechanical time constant corresponding to the load torque estimated at an (n−1)th control period (where n denotes an integer greater than or equal to 2) and estimate the load torque of the electric motor at an nth control period by inputting the controlling value and the actually measured value acquired at the nth control period to the model acquired through the updating.
Other objects, features and advantages of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a hardware configuration of a load torque estimation apparatus according to an embodiment;
FIG. 2 is a functional configuration diagram illustrating functions implemented as a result of a load torque estimation program being executed;
FIG. 3 is a block diagram for controlling an electric motor and estimating load torque;
FIGS. 4A and 4B illustrate motor nominal models;
FIG. 5 illustrates a method of measuring a mechanical time constant of an electric motor;
FIG. 6 illustrates a method of measuring an electrical time constant of an electric motor;
FIG. 7 illustrates relationships of the rotational speed with the mechanical time constant and the electrical time constant of an electric motor;
FIG. 8 is a flowchart illustrating a flow of a load torque estimation process;
FIG. 9 illustrates a method of measuring a mechanical time constant of an electric motor;
FIG. 10 illustrates a method of measuring an electrical time constant of an electric motor;
FIG. 11 illustrates relationships of the load torque with the mechanical time constant and the electrical time constant of an electric motor;
FIG. 12 is a flowchart illustrating a flow of a load torque estimation process;
FIG. 13 illustrates an internal configuration of an image forming apparatus; and
FIG. 14 illustrates a driving and conveyance mechanism in an intermediate transfer unit of an image forming apparatus in a magnified manner.



DETAILED DESCRIPTION OF THE EMBODIMENTS
In a case of determining a control model to estimate load torque as disclosed in Patent Reference No. 1, it may be impossible to estimate load torque correctly when a state of a control target changes. This is because characteristics of the control target may vary according to a change in the state of the control target, and as a result, the control model may have different characteristics from those of the determined control model.
The embodiments of the present invention have been devised in consideration of the problem and an object of the embodiments is to improve accuracy in an estimation of load torque of an electric motor.
Below, using the accompanying drawings, the embodiments of the present invention will be described. Note that as for parts/elements having substantially identical functional configurations, the same reference numerals are provided and duplicate description are omitted.
First Embodiment
Load Torque Estimation Apparatus
First, a hardware configuration of a load torque estimation apparatus according to the present embodiment will be described. FIG. 1 illustrates a hardware configuration of a load torque estimation apparatus 100 according to the present embodiment.
As illustrated in FIG. 1, the load torque estimation apparatus 100 includes a Central Processing Unit (CPU) 101, a Read-Only Memory (ROM) 102, a Random Access Memory (RAM) 103 and a storage device 104. The load torque estimation apparatus 100 further includes a display part 105, an input part 106 and an interface part 107. The respective devices/parts in the load torque estimation apparatus 100 are mutually connected by a bus 108.
The CPU 101 executes a load torque estimation program 110 stored in the storage device 104.
The ROM 102 is a nonvolatile memory. The ROM 102 stores various programs and data necessary for the CPU 101 to execute the load torque estimation program 110. Specifically, the ROM 102 stores boot programs such as a Basic Input/Output System (BIOS), an Extensible Firmware Interface (EFI) and so forth.
The RAM 103 is a main storage device such as a Dynamic Random Access Memory (DRAM), a Static Random Access Memory (SRAM) or so. The RAM 103 functions as a work area to which the load torque estimation program 110 is expanded when it is executed by the CPU 101.
The storage device 104 stores the load torque estimation program 110. The display part 105 displays a screen page for a user to input a control target value(s) (a target rotational speed and/or a target position), a screen page for showing a detection result (actually measured value) of the rotational speed of the electric motor 130 and/or a detection result (actually measured value) of position information of the electric motor 130. Further, the display part 105 displays a screen page for showing an estimated (calculated) value of load torque.
The input part 106 is an operating device for a user to perform various input operations (operations of inputting a control target value and so forth) to the load torque estimation apparatus 100 and includes, for example, a mouse, a keyboard, and/or the like.
The interface part 107 transmits a controlling value for controlling the electric motor 130 that is a control target to a motor driving apparatus 120. Also, the interface part 107 receives, from a position/rotational speed detection part 140 via the motor driving apparatus 120, information (the actually measured value of the rotational speed or the actually measured value of the position information) that indicates a state of the electric motor 130 that is the control target.
The motor driving apparatus 120 drives the electric motor 130 based on the controlling value transmitted from the interface part 107. Also, the motor driving apparatus 120 receives the detection signal that is output by the position/rotational speed detection part 140 and transmits the detection signal as the actually measured value of the rotational speed or the actually measured value of the position information to the interface part 107.
The position/rotational speed detection part 140 is provided to the electric motor 130 and outputs the detection signal (a signal indicating the rotational speed or a signal indicating a position). In the present embodiment, the position/rotational speed detection part 140 can be, for example, a two-phase encoder or a single-phase photodetector. Also, the position/rotational speed detection part 140 can be a magnetic sensor such as a Frequency Generator (FG) sensor, a Hall element sensor or so.
<Functional Configuration of Load Torque Estimation Program>
Next, functions implemented from execution of the load torque estimation program 110 will be described. FIG. 2 is a functional configuration diagram illustrating functions implemented as a result of the load torque estimation program 110 being executed.
In FIG. 2, a target rotational speed input part 201 or a target position input part 202 acquires a control target value (a target rotational speed or a target position) that is input by the user using the input part 106 and inputs the control target value to a control part 200.
An actually measured value input part 204 acquires the actually measured value of the rotational speed or the actually measured value of the position information of the electric motor 130, received via the interface part 107, and inputs the acquired actually measured value to the control part 200.
The control part 200 calculates a controlling value (voltage value) for controlling the electric motor 130 based on the control target value (the target rotational speed or the target position) that is thus input and the actually measured value of the rotational speed or the actually measured value of the position information that is thus input also.
A controlling value output part 205 transmits the controlling value (voltage value) thus calculated by the control part 200 to the motor driving apparatus 120 via the interface part 107.
An estimation part 206 has a rotational speed estimation part 210 and a torque estimation part 211. The rotational speed estimation part 210 generates a motor nominal model that is a control model calculating an estimated value of the rotational speed of the electric motor 130 based on the controlling value (voltage value) that is output by the control part 200. Also, the estimation part 206 calculates an estimated value of the rotational speed using the motor nominal model.
The torque estimation part 211 generates a torque estimation model that is a control model calculating an estimated value of load torque of the electric motor 130 based on the estimated value of the rotational speed calculated based on the motor nominal model and the actually measured value of the rotational speed acquired via the control part 200. Also, the torque estimation part 211 calculates an estimated value of load torque of the electric motor 130 using the torque estimation model.
A derivation part 207 derives a mechanical time constant and an electrical time constant depending on the rotational speed, using an approximation formula or a table that is previously prepared, based on the actually measured value of the rotational speed transmitted from the estimation part 206. Also, the derivation part 207 inputs the thus derived mechanical time constant and electrical time constant to the estimation part 206. Note that the approximation formula or the table prescribes relationships of the rotational speed with the mechanical time constant and the electrical time constant.
The rotational speed estimation part 210 and the torque estimation part 211 in the estimation part 206 update the motor nominal model and the torque estimation model, respectively, based on the mechanical time constant and the electrical time constant that are input from the derivation part 207. Note that details of the estimation part 206 will be described later.
An estimated torque output part 203 outputs an estimated value of load torque calculated by the torque estimation part 211 of the estimation part 206. Note that a destination to which the estimated value is output can be the storage device 104 or the display part 105. Alternatively, the estimated value can be output to an external apparatus via the interface part 107.
<Description of Block Diagram>
Next, a block diagram will be described for controlling the rotational speed or the position of an electric motor and estimating the load torque of the electric motor. FIG. 3 is a block diagram for controlling the rotational speed or the position of the electric motor 130 and estimating the load torque of the electric motor 130.
As shown in FIG. 3, the control part 200 outputs the controlling value (voltage value Vct1) based on the control target value (the target rotational speed ωtgt or the target position xtgt) and the actually measured value (the actually measured value ωdet of the rotational speed or the actually measured value xdet of the rotational position) that is fed back.
The electric motor 130 generates a predetermined rotational torque T based on the controlling value (voltage value Vct1) that is output by the control part 200. In contrast thereto, the electric motor 130 receives load torque τ and therefore, the electric motor 130 rotates at a rotational speed according to the difference between the rotational torque T and the load torque τ.
The position/rotational speed detection part 140 detects the rotational speed of the electric motor 130 and feeds the rotational speed back as the actually measured value ωdet of the rotational speed to the control part 200.
Alternatively, the position/rotational speed detection part 140 calculates position information based on the detected rotational speed (or directly detects the position information) and feeds the position information back as the actually measured value xdet of the position information to the control part 200.
Thus, by carrying out feedback control based on the actually measured value ωdet of the rotational speed or the actually measured value xdet of the position information, the electric motor 130 is controlled to the target rotational speed ωtgt or the target position xtgt.
In parallel with the control of the rotational speed or the control of the position of the electric motor 130, the estimation part 206 successively calculates an estimated value τe of load torque.
Specifically, the rotational speed estimation part 210 acquires the controlling value (voltage value Vct1) that is output by the control part 200 and calculates an estimated value ωe of the rotational speed of the electric motor 130 based on the motor nominal model P(s).
Further, the estimation part 206 acquires the actually measured value ωdet of the rotational speed detected by the position/rotational speed detection part 140, calculates the difference between the estimated value ωe and the actually measured value ωdet of the rotational speed and inputs the calculated difference value to the torque estimation part 211.
The torque estimation part 211 calculates an estimated value τe of load torque from the input difference value using the torque estimation model Tq(s).
The torque estimation model Tq(s) can be expressed as follows:




  
    
      
        
          Tq
          ⁡
          
            (
            s
            )
          
        
        =
        
          
            
              
                
                  P
                  
                    -
                    1
                  
                
                ⁡
                
                  (
                  s
                  )
                
              
              ⁢
              
                F
                ⁡
                
                  (
                  s
                  )
                
              
            
            
              R
              +
              sL
            
          
          ×
          Kt
        
      
    
    
      
        (
        
          FORMULA
          ⁢
          
            
          
          ⁢
          1
        
        )
      
    
  




P−1(s) denotes the reciprocal of the motor nominal model P(s). F(s) denotes a transfer function of a low-pass filter and can be expressed as follows when P(s) is an nth-order transfer function:




  
    
      
        
          F
          ⁡
          
            (
            s
            )
          
        
        =
        
          1
          
            
              (
              
                s
                
                  
                    f
                    ×
                    2
                    ⁢
                    π
                  
                  +
                  1
                
              
              )
            
            n
          
        
      
    
    
      
        (
        
          FORMULA
          ⁢
          
            
          
          ⁢
          2
        
        )
      
    
  




R denotes the coil resistance of the electric motor 130; L denotes the coil inductance of the electric motor 130; and Kt denotes the torque constant. f denotes a band frequency.
A procedure of calculating an estimated value τe of load torque by inputting the difference value between the estimated value ωe and the actually measured value ωdet of the rotational speed to the torque estimation part 211 will now be briefly described.
In the above-mentioned FORMULA 1, first the difference value between the estimated value ωe and the actually measured value ωdet of the rotational speed is multiplied by P−1(s)F(s) and thus, an estimated value (here, referred to as Ve) of the voltage required for driving the electric motor 130 for the load torque τ is calculated.
Further, by multiplying the thus calculated estimated value Ve of the voltage by 1/(R+sL), an estimated value (here, referred to as Ie) of the current required for driving the electric motor 130 for the load torque τ is calculated. By multiplying the thus calculated estimated value Ie of the current by the torque constant Kt, it is possible to calculate an estimated value τe corresponding to the load torque τ.
Thus, it can be seen that by multiplying the difference value between the estimated value ωe and the actually measured value ωdet of the rotational speed by the torque estimation model Tq(s) shown in FORMULA 1, the estimated value τe of the load torque is calculated.
Note that the controlling value (voltage value Vct1) and the actually measured value (the actually measured value ωdet of the rotational speed) are output every control period of the control part 200. Therefore, in the estimation part 206, it is possible to calculate the estimated value τe of the load torque every control period of the control part 200.
<Motor Nominal Model>
Next, details of the motor nominal model P(s) will be described. Generally speaking, an electric motor can be expressed by a block diagram shown in FIG. 4A.
In FIG. 4A, Vct1 denotes the controlling value (voltage value) that is output by the control part 200; R denotes the coil resistance of the electric motor 130; L denotes the coil inductance of the electric motor 130; and Kt denotes the torque constant. J denotes the inertia and Ke denotes the back electromotive force constant.
Note that the “closed loop” block diagram shown in FIG. 4A can be rewritten into the “open loop” block diagram shown in FIG. 4B.
That is, the motor nominal model P(s) can be expressed as follows:




  
    
      
        
          P
          ⁡
          
            (
            s
            )
          
        
        =
        
          
            
              
                ω
                _
              
              e
            
            
              V
              ctl
            
          
          =
          
            
              1
              Ke
            
            ×
            
              1
              
                (
                
                  
                    TmTes
                    2
                  
                  +
                  Tms
                  +
                  1
                
                )
              
            
          
        
      
    
    
      
        (
        
          FORMULA
          ⁢
          
            
          
          ⁢
          3
        
        )
      
    
  




Tm denotes a mechanical time constant, and can be expressed by the following formula:




  
    
      
        Tm
        =
        
          JR
          KtKe
        
      
    
    
      
        (
        
          FORMULA
          ⁢
          
            
          
          ⁢
          4
        
        )
      
    
  




J denotes the inertia, Kt denotes the torque constant and Ke denotes the back electromotive force constant.
Te denotes an electrical time constant, and can be expressed by the following formula:




  
    
      
        Te
        =
        
          L
          R
        
      
    
    
      
        (
        
          FORMULA
          ⁢
          
            
          
          ⁢
          5
        
        )
      
    
  




L denotes the coil inductance of the electric motor 130 and R denotes the coil resistance of the electric motor 130.
Thus, the motor nominal model P(s) required for acquiring an estimated value τe of load torque includes the mechanical time constant and the electrical time constant.
The applicant of the present patent application focused attention to relationships of the rotational speed with the mechanical time constant and the electrical time constant of an electric motor when analyzing the cause of a fact that an error in an estimated value of load torque calculated according to the related art becomes greater along with a change in the state of the electric motor that is the control target.
This is because, when calculating an estimated value of load torque according to the related art, the mechanical time constant and the electrical time constant of an electric motor are assumed as being fixed and predetermined constants are substituted for the mechanical time constant and the electrical time constant of the electric motor regardless of the rotational speed.
In contrast thereto, the applicant acquired the mechanical time constant and the electrical time constant of an electric motor for various rotational speeds experimentally. As a result, it was found out that the mechanical time constant and the electrical time constant of an electric motor vary according to the rotational speed.
Below, relationships of the rotational speed with the mechanical time constant and the electrical time constant of an electric motor will be described and a process of calculating an estimated value of load torque while updating the mechanical time constant and the electrical time constant of the electric motor according to the rotational speed will be described.
<Relationships of Rotational Speed with Mechanical Time Constant and Electrical Time Constant of Electric Motor>
First, relationships of the rotational speed ωdet with the mechanical time constant Tm and the electrical time constant Te of the electric motor 130 will be described using FIGS. 5-7.
FIG. 5 illustrates how to experimentally acquire the relationships between the rotational speed ωdet and the mechanical time constant Tm of the electric motor 130. In FIG. 5, a graph (a-1) illustrates a step input of a voltage V500 such that the rotational speed becomes 500 rpm. A graph (b-1) of FIG. 5 illustrates a temporal change of the actually measured value ωdet of the rotational speed of the electric motor 130 when the step input of the voltage V500 is given to the electric motor 130.
As can be seen from the graph (b-1) of FIG. 5, it is possible to derive the mechanical time constant Tm500 at a time of 500 rpm in the rotational speed by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
Similarly, a graph (a-2) of FIG. 5 illustrates a step input of a voltage V1000 such that the rotational speed becomes 1000 rpm. A graph (b-2) of FIG. 5 illustrates a temporal change of the actually measured value ωdet of the rotational speed of the electric motor 130 when the step input of the voltage V1000 is given to the electric motor 130.
As can be seen from the graph (b-2) of FIG. 5, it is possible to derive the mechanical time constant Tm1000 at a time of 1000 rpm in the rotational speed by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
Similarly, a graph (a-3) of FIG. 5 illustrates a step input of a voltage V3000 such that the rotational speed becomes 3000 rpm. A graph (b-3) of FIG. 5 illustrates a temporal change of the actually measured value ωdet of the rotational speed of the electric motor 130 when the step input of the voltage V3000 is given to the electric motor 130.
As can be seen from the graph (b-3) of FIG. 5, it is possible to derive the mechanical time constant Tm3000 at a time of 3000 rpm in the rotational speed by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
The graph of Tm in FIG. 7 is the thus acquired mechanical time constants at respective rotational speeds. In FIG. 7, the abscissa axis denotes the rotational speed of the electric motor 130 and the ordinate axis denotes the values acquired from standardizing the respective values of the mechanical time constant.
On the other hand, FIG. 6 illustrates how to experimentally acquire the relationships between the rotational speed ωdet and the electrical time constant Te of the electric motor 130. In FIG. 6, a graph (a-1) illustrates a step input of a voltage V500 such that the rotational speed becomes 500 rpm. A graph (b-1) of FIG. 6 illustrates a temporal change of the actually measured value Idet of the current flowing through the coil of the electric motor 130 when the step input of the voltage V500 is given to the electric motor 130.
As can be seen from the graph (b-1) of FIG. 6, it is possible to derive the electrical time constant Te500 at a time of 500 rpm in the rotational speed by acquiring a time required for the actually measured value Idet of the current to reach 63.2% of the displacement.
Similarly, a graph (a-2) of FIG. 6 illustrates a step input of a voltage V1000 such that the rotational speed becomes 1000 rpm. A graph (b-2) of FIG. 6 illustrates a temporal change of the actually measured value Idet of the current flowing through the coil of the electric motor 130 when the step input of the voltage V1000 is given to the electric motor 130.
As can be seen from the graph (b-2) of FIG. 6, it is possible to derive the electrical time constant Te1000 at a time of 1000 rpm in the rotational speed by acquiring a time required for the actually measured value Idet of the current to reach 63.2% of the displacement.
Similarly, a graph (a-3) of FIG. 6 illustrates a step input of a voltage V3000 such that the rotational speed becomes 3000 rpm. A graph (b-3) of FIG. 6 illustrates a temporal change of the actually measured value Idet of the current flowing through the coil of the electric motor 130 when the step input of the voltage V3000 is given to the electric motor 130.
As can be seen from the graph (b-3) of FIG. 6, it is possible to derive the electrical time constant Te3000 at a time of 3000 rpm in the rotational speed by acquiring a time required for the actually measured value Idet of the current to reach 63.2% of the displacement.
The graph of Te in FIG. 7 is the thus acquired electrical time constants at respective rotational speeds. In FIG. 7, the abscissa axis denotes the rotational speed of the electric motor 130 and the ordinate axis denotes the values acquired from standardizing the respective values of the electrical time constant.
Thus, the mechanical time constant Tm and the electrical time constant Te of the electric motor 130 vary depending on the rotational speed. Therefore, in the load torque estimation apparatus 100, when the motor nominal model P(s) is used to calculate an estimated value ωe of the rotational speed, the mechanical time constant Tm and the electrical time constant Te are successively updated according to the actually measured value (ωdet) of the rotational speed of the electric motor 130 acquired at the time of calculation.
Specifically, based on the graph of FIG. 7, Tm and Te are approximated in forms of Nth-order formulas as functions of the rotational speed, respectively. Then, the mechanical time constant Tm and the electrical time constant Te are calculated by substituting the actually measured value of the rotational speed of the electric motor 130 acquired at the time of calculation in these approximation formulas. Then, the thus calculated mechanical time constant Tm and the electrical time constant Te are used to generate (or update) the motor nominal model P(s) and the generated (or updated) motor nominal model P(s) is used to calculate the estimated value ωe of the rotational speed.
Note that the mechanical time constant Tm and the electrical time constant Te can be expressed by the following formulas when being expressed by primary expressions, for example.

Tm=Am×ωdet+Bm (where Am and Bm are constants, respectively)

Te=Ae×ωdet+Be (where Ae and Be are constants, respectively)

Note that the approximation formulas are not limited to such primary expressions.
Note that the method of deriving the mechanical time constant Tm and the electrical time constant Te is not limited to such a method of using approximation formulas as those mentioned above. For example, it is also possible to employ a method of deriving, at a time of calculation, the mechanical time constant Tm and the electrical time constant Te corresponding to the rotational speed closest to the actually measured value ωdet of the rotational speed of the electric motor 130 according to a table which is previously prepared according to the graph of FIG. 7.
Note that in the above description, the above-mentioned approximation formulas or table are/is prepared based on FIG. 7 illustrating the mechanical time constants and the electrical time constants for the range from 0 rpm to 3000 rpm in the rotational speed. However, embodiments of the present invention are not limited thereto. For example, it is also possible to prepare such approximation formulas or a table using a result acquired from an experiment carried out for a broader range of the rotational speed.
<Process According to Load Torque Estimation Program>
Next, a flow of a load torque estimation process according to the load torque estimation program 110 of calculating an estimated value of load torque while updating the mechanical time constant and the electrical time constant of an electric motor according to its rotational speed will be described. FIG. 8 is a flowchart illustrating a flow of a load torque estimation process according to the load torque estimation program 110.
When the load torque estimation program 110 is executed, the actually measured value input part 204 acquires the actually measured value ωdet1 of the rotational speed at a timing T1 in Step S801.
In Step S802, the derivation part 207 derives the mechanical time constant and the electrical time constant corresponding to the actually measured value ωdet1 of the rotational speed based on the approximation formulas. Here, the mechanical time constant Tm_ωdet1 and the electrical time constant Te_ωdet1 are derived.
In Step S803, the rotational speed estimation part 210 generates the motor nominal model P(s)1 based on the mechanical time constant Tm_ωdet1 and the electrical time constant Te_ωdet1. Further, the torque estimation part 211 generates the torque estimation model Tq(s)1.
In Step S804, the estimation part 206 acquires the controlling value (voltage value Vct11) that is output by the control part 200 at the timing T1. Further, the rotational speed estimation part 210 calculates the estimated value ωe1 of the rotational speed by multiplying the motor nominal model P(s)1 generated in Step S803 by the controlling value (voltage value Vct11).
In Step S805, the estimation part 206 calculates the difference value between the actually measured value ωdet1 of the rotational speed acquired in Step S801 and the estimated value ωe1 of the rotational speed calculated in Step S804.
Further, the torque estimation part 211 calculates the estimated value τe1 of the load torque by multiplying the torque estimation model Tq(s)1 generated in Step S803 by the thus calculated difference value.
When calculation of the estimated value τe1 of the load torque is finished in Step S805, waiting is carried out for the next control period. In the next control period, again the process starting from Step S801 is executed.
That is, at a timing T2, the actually measured value ωdet2 of the rotational speed is acquired (Step S801) and the mechanical time constant Tm_ωdet2 and the electrical time constant Te_ωdet2 are derived (Step S802). Further, the motor nominal model P(s)2 and the torque estimation model Tq(s)2 are generated (Step S803), the estimated value ωe2 of the rotational speed is calculated (Step S804) and the estimated value τe2 of the load torque is calculated (Step S805).
Thereafter, also in the further next control period, the same process is repeated. Thus, for every control period, the mechanical time constant and the electrical time constant are calculated according to the actually measured value of the rotational speed, and the estimated value of the load torque is calculated. As a result, it is possible to reduce the errors in the estimated values of the load torque regardless of the rotational speeds.
<Summary of Embodiment>
As can be seen from the above description, in the load torque estimation apparatus according to the present embodiment, a model of an electric motor that is a control target is determined. Then, using a controlling value (voltage value) for controlling the electric motor and the actually measured value of the rotational speed of the electric motor, the load torque of the electric motor is estimated.
When determining the model of the electric motor, attention is focused on the fact that the mechanical time constant and the electrical time constant vary depending on the rotational speed of the electric motor, and the mechanical time constant and the electrical time constant are derived based on the actually measured value of the rotational speed.
The mechanical time constant and the electrical time constant at each rotational speed are acquired by an experiment and are approximated by Nth-order approximation formulas or are stored in a form of a table previously.
The mechanical time constant and the electrical time constant are derived every control period based on the approximation formulas or the table, and the mechanical time constant and the electrical time constant included in the model are updated every control period.
For every control period, an estimated value of the load torque is calculated using the model thus updated.
Thereby, it is possible to avoid an increase in an error of an estimated value of load torque due to a rotational speed of an electric motor which may occur in the related art. As a result, it is possible to improve accuracy in an estimation of load torque of an electric motor.
Second Embodiment
In the first embodiment, attention is focused on relationships of the rotational speed with the mechanical time constant and the electrical time constant of the electric motor 130 as the control target for a case where the determined control model varies due to a change in the state of the electric motor 130 as the control target.
However, a state of the electric motor as the control target is not limited to the rotational speed and, for example, the load torque can also be used instead.
Therefore, concerning the present embodiment, relationships of the mechanical time constant and the electrical time constant with load torque of an electric motor will be described and a process of calculating an estimated value of load torque while updating the mechanical time constant and the electrical time constant of the electric motor according to the load torque will be described.
Note that because the hardware configuration, the functional configuration, the block diagram and the motor nominal model in the present embodiment are the same as those in the above-mentioned first embodiment, duplicate description thereof is omitted here.
<Relationships of Load Torque with Mechanical Time Constant and Electrical Time Constant of Electric Motor>
First, relationships of the load torque τdet with the mechanical time constant Tm and the electrical time constant Te of the electric motor 130 will be described using FIGS. 9-11.
FIG. 9 illustrates how to experimentally acquire the relationships between the load torque Tdet and the mechanical time constant Tm of the electric motor 130. In FIG. 9, a graph (a-1) illustrates a step input of a voltage V1 such that the electric motor 130 comes to have a predetermined rotational speed ωp in a state where load torque=0.01 [Nm] is applied to the electric motor 130. A graph (b-1) of FIG. 9 illustrates a temporal change of the actually measured value ωdet of the rotational speed of the electric motor 130 when the step input of the voltage V1 is given to the electric motor 130 in the state where load torque=0.01 [Nm] is applied to the electric motor 130.
As can be seen from the graph (b-1) of FIG. 9, it is possible to derive the mechanical time constant Tm1 at a time of load torque=0.01 [Nm] by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
Similarly, a graph (a-2) of FIG. 9 illustrates a step input of a voltage V2 such that the electric motor 130 comes to have the predetermined rotational speed ωp in a state where load torque=0.02 [Nm] is applied to the electric motor 130. A graph (b-2) of FIG. 9 illustrates a temporal change of the actually measured value ωdet of the rotational speed of the electric motor 130 when the step input of the voltage V2 is given to the electric motor 130 in the state where load torque=0.02 [Nm] is applied to the electric motor 130.
As can be seen from the graph (b-2) of FIG. 9, it is possible to derive the mechanical time constant Tm2 at a time of load torque=0.02 [Nm] by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
Similarly, a graph (a-3) of FIG. 9 illustrates a step input of a voltage V6 such that the electric motor 130 comes to have the predetermined rotational speed ωp in a state where load torque=0.06 [Nm] is applied to the electric motor 130. A graph (b-3) of FIG. 9 illustrates a temporal change of the actually measured value ωdet of the rotational speed of the electric motor 130 when the step input of the voltage V6 is given to the electric motor 130 in the state where load torque=0.06 [Nm] is applied to the electric motor 130.
As can be seen from the graph (b-3) of FIG. 9, it is possible to derive the mechanical time constant Tm6 at a time of load torque=0.06 [Nm] by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
The graph of Tm in FIG. 11 is the thus acquired mechanical time constants for respective values of the load torque. In FIG. 11, the abscissa axis denotes the load torque applied to the electric motor 130 and the ordinate axis denotes the values acquired from standardizing the respective values of the mechanical time constant.
On the other hand, FIG. 10 illustrates how to experimentally acquire the relationships between the load torque τdet and the electrical time constant Te of the electric motor 130. In FIG. 10, a graph (a-1) illustrates a step input of a voltage V1 such that the electric motor 130 comes to have a predetermined rotational speed in a state where load torque=0.01 [Nm] is applied to the electric motor 130. A graph (b-1) of FIG. 10 illustrates a temporal change of the actually measured value Idet of the current flowing through the coil of the electric motor 130 when the step input of the voltage V1 is given to the electric motor 130 in the state where load torque=0.01 [Nm] is applied to the electric motor 130.
As can be seen from the graph (b-1) of FIG. 10, it is possible to derive the electrical time constant Te1 at a time of load torque=0.01 [Nm] by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
Similarly, a graph (a-2) of FIG. 10 illustrates a step input of a voltage V2 such that the electric motor 130 comes to have the predetermined rotational speed in a state where load torque=0.02 [Nm] is applied to the electric motor 130. A graph (b-2) of FIG. 10 illustrates a temporal change of the actually measured value Idet of the current flowing through the coil of the electric motor 130 when the step input of the voltage V2 is given to the electric motor 130 in the state where load torque=0.02 [Nm] is applied to the electric motor 130.
As can be seen from the graph (b-2) of FIG. 10, it is possible to derive the electrical time constant Tee at a time of load torque=0.02 [Nm] by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
Similarly, a graph (a-3) of FIG. 10 illustrates a step input of a voltage V6 such that the electric motor 130 comes to have the predetermined rotational speed in a state where load torque=0.06 [Nm] is applied to the electric motor 130. A graph (b-3) of FIG. 10 illustrates a temporal change of the actually measured value Idet of the current flowing through the coil of the electric motor 130 when the step input of the voltage V6 is given to the electric motor 130 in the state where load torque=0.06 [Nm] is applied to the electric motor 130.
As can be seen from the graph (b-3) of FIG. 10, it is possible to derive the electrical time constant Te6 at a time of load torque=0.06 [Nm] by acquiring a time required for the actually measured value ωdet of the rotational speed to reach 63.2% of the displacement.
The graph of Te in FIG. 11 is the thus acquired electrical time constants for respective values of the load torque. In FIG. 11, the abscissa axis denotes the load torque applied to the electric motor 130 and the ordinate axis denotes the values acquired from standardizing the respective values of the electrical time constant.
Thus, the mechanical time constant Tm and the electrical time constant Te of the electric motor 130 vary depending on the load torque. Therefore, in the load torque estimation apparatus 100 according to the present embodiment, when the motor nominal model P(s) is used to calculate an estimated value ωe of the rotational speed, the mechanical time constant Tm and the electrical time constant Te are successively updated according to the estimated value of the load torque of the electric motor 130 acquired at the time of previous calculation.
Specifically, based on the graph of FIG. 11, Tm and Te are approximated in forms of Nth-order formulas as functions of load torque, respectively. Then, the mechanical time constant Tm and the electrical time constant Te are calculated by substituting the estimated value of the load torque of the electric motor 130 acquired at the time of previous calculation in these approximation formulas. Then, the thus calculated mechanical time constant Tm and the electrical time constant Te are used to generate (or update) the motor nominal model P(s) and the generated (or updated) motor nominal model P(s) is used to calculate the estimated value ωe of the rotational speed.
Note that the mechanical time constant Tm and the electrical time constant Te can be expressed by the following formulas when being expressed by primary expressions, for example.

Tm=Cm×τe+Dm (where Cm and Dm are constants, respectively)

Te=Ce×τe+De (where Ce and De are constants, respectively)

Note that the approximation formulas are not limited to such primary expressions.
Note that the method of deriving the mechanical time constant Tm and the electrical time constant Te is not limited to such a method of using approximation formulas as those mentioned above. For example, it is also possible to employ a method of deriving, at a time of calculation, the mechanical time constant Tm and the electrical time constant Te corresponding to the load torque closest to the estimated value τe of the load torque of the electric motor 130 according to a table which is previously prepared according to the graph of FIG. 11.
Note that in the above description, the above-mentioned approximation formulas or table are/is prepared based on FIG. 11 illustrating the mechanical time constants and the electrical time constants for the range from 0 [Nm] to 0.06 [Nm] in the load torque. However, embodiments of the present invention are not limited thereto. For example, it is also possible to prepare such approximation formulas or a table using a result acquired from an experiment carried out for a broader range of the load torque.
<Process According to Load Torque Estimation Program>
Next, a flow of a load torque estimation process according to the load torque estimation program 110 of calculating an estimated value of load torque while updating the mechanical time constant and the electrical time constant of an electric motor according to its load torque will be described. FIG. 12 is a flowchart illustrating a flow of a load torque estimation process according to the load torque estimation program 110.
When the load torque estimation program 110 is executed, the estimation part 206 acquires the controlling value (Vct11) and the actually measured value ωdet1 of the rotational speed at a timing T1 in Step S1201.
In Step S1102, the previous estimated value of the load torque is acquired. Note that since there is no previous estimated value of the load torque here, a predetermined initial value Te0 is acquired.
In Step S1203, the derivation part 207 derives the mechanical time constant and the electrical time constant corresponding to the estimated value (here, the initial value τe0) of the load torque acquired in Step S1202 based on the approximation formulas. Here, the mechanical time constant Tm_τe0 and the electrical time constant Te_τe0 are derived.
In Step S1204, the rotational speed estimation part 210 generates the motor nominal model P(s)1 based on the mechanical time constant Tm_τe0 and the electrical time constant Te_τe0. Further, the torque estimation part 211 generates the torque estimation model Tq(s)1.
In Step S1205, the rotational speed estimation part 210 calculates the estimated value ωe1 of the rotational speed by multiplying the motor nominal model P(s)1 generated in Step S1204 by the controlling value (voltage value Vct11).
In Step S1206, the estimation part 206 calculates the difference value between the actually measured value ωdet1 of the rotational speed acquired in Step S1201 and the estimated value ωe1 of the rotational speed calculated in Step S1205.
Further, the torque estimation part 211 calculates the estimated value τe1 of load torque by multiplying the torque estimation model Tq(s)1 generated in Step S1204 by the thus calculated difference value.
When calculation of the estimated value τe1 of the load torque is finished in Step S1206, waiting is carried out for the next control period. In the next control period, again the process starting from Step S1201 is executed.
That is, after the controlling value (voltage value Vct12) and the actually measured value ωdet2 of the rotational speed at a timing T2 are acquired (Step S1201), the previous estimated value τe1 of the load torque is acquired (Step S1202). Further, the mechanical time constant Tm_ωdet1 and the electrical time constant Te_ωdet1 are derived based on the previous estimated value τe1 of the load torque (Step S1203). Further, the motor nominal model P(s)2 and the torque estimation model Tq(s)2 are generated (Step S1204), the estimated value ωe2 of the rotational speed is calculated (Step S1205) and the estimated value τe2 of load torque is calculated (Step S1206).
Thereafter, also in the further next control period, the same process is repeated. Thus, for every control period, the mechanical time constant and the electrical time constant are calculated according to the previous estimated value of the load torque, and the current estimated value of load torque is calculated. As a result, it is possible to reduce the errors in the estimated values of load torque regardless of the magnitudes of load torque.
<Summary of Embodiment>
As can be seen from the above description, in the load torque estimation apparatus according to the present embodiment, a model of an electric motor that is a control target is determined. Then, using a controlling value (voltage value) for controlling the electric motor and the actually measured value of the rotational speed of the electric motor, the load torque of the electric motor is estimated.
When determining the model of the electric motor, attention is focused on the fact that the mechanical time constant and the electrical time constant vary depending on the load torque of the electric motor, and the mechanical time constant and the electrical time constant are derived based on the estimated value of the load torque calculated at the (n−1)th control period (where n denotes an integer greater than or equal to 2).
The mechanical time constant and the electrical time constant at each value of the load torque are previously acquired by an experiment and are approximated by Nth-order approximation formulas or are stored in a form of a table.
The mechanical time constant and the electrical time constant are derived at the nth control period based on the approximation formulas or the table, and the mechanical time constant and the electrical time constant included in the model are updated.
By inputting the controlling value (voltage value) and the actually measured value of the rotational speed of the electric motor acquired at the nth control period to the model acquired through the updating, the estimated value of the load torque at the nth control period is acquired.
Thereby, it is possible to avoid an increase in an error of an estimated value of load torque due to the magnitude of load torque of an electric motor which may occur in the related art. As a result, it is possible to improve accuracy in an estimation of load torque of an electric motor.
Third Embodiment
According to the first and second embodiments, the rotational speed and the load torque are used as the changing states of the electric motor that is the control target. Then, experiments are carried out for the rotational speed and the load torque separately and the relationships of the rotational speed with the mechanical time constant and the electrical time constant and the relationships of the load torque with the mechanical time constant and the electrical time constant are acquired, respectively. Then, for the acquired relationships, the approximation formulas or the tables are prepared, respectively.
However, the present invention is not limited thereto. It is also possible to prepare approximation formulas or a table for variations of the mechanical time constant and the electrical time constant in consideration of both influences of the rotational speed and the load torque.
More specifically, experiments are carried out for various combinations of respective values of the rotational speed and respective values of the load torque, and thus, the mechanical time constants and the electrical time constants are acquired. Then, for every control period, using the actually measured value of the rotational speed and the previous estimated value of the load torque, the mechanical time constant and the electrical time constant are derived.
Thereby, it is possible to calculate an estimated value of load torque with higher accuracy.
Fourth Embodiment
In the first and second embodiments, the mechanical time constant and the electrical time constant are derived every control period. However, the present invention is not limited thereto. As shown in FIGS. 7 and 11, when the changes in the mechanical time constant and the changes in the electrical time constant along with the changes in the rotational speed or the load torque are compared, it is seen that the changes in the mechanical time constant along with the changes in the rotational speed or the load torque are greater than the changes in the electrical time constant along with the changes in the rotational speed or the load torque.
Therefore, it is possible that only the mechanical time constant is derived every control period and a predetermined value is previously substituted for the electrical time constant.
Fifth Embodiment
In the first and second embodiments, the actually measured value of the rotational speed is fed back and thus the control part 200 carries out feedback control such that the electric motor 130 is rotated at the target rotational speed. Alternatively, the actually measured value of the position information is fed back and thus the control part 200 carries out feedback control such that the electric motor 130 is rotated to the target position.
However, in the present invention, control carried out by the control part 200 is not limited thereto. For example, it is also possible to carry out speed feedforward control for a target rotational speed or position feedforward control for a target position.
Sixth Embodiment
In the above-mentioned first to fifth embodiments, a target apparatus/machine or so to which the load torque estimation apparatus 100 is applied is not explicitly mentioned. The load torque estimation apparatus 100 according to any one of the above-mentioned first to fifth embodiments can be applied to, for example, an image forming apparatus in which a drive motor driving and rotating a drive roller is provided. It is also possible to apply the load torque estimation apparatus 100 according to any one of the above-mentioned first to third embodiments to an automobile, a robot, an amusement machine or so.
FIG. 13 illustrates the internal configuration of an image forming apparatus 1300 which is one example of an apparatus, a machine or so to which the load torque estimation apparatus 100 is applied. As shown in FIG. 13, the image forming apparatus 1300 includes an intermediate transfer unit 1310, an optical writing unit 1320, a scanner 1330, an automatic document feeder 1340 and a paper feeding device 1350.
FIG. 14 illustrates a driving and conveyance mechanism in the intermediate transfer unit 1310 of the image forming apparatus 1300 in a magnifying manner. As shown in FIG. 14, the driving and conveyance mechanism of the intermediate transfer unit 1310 has an intermediate transfer belt 1409 as an intermediate transfer member, photosensitive drums 1401-1404 as image carrying members, primary transfer rollers 1405-1408 as primary transfer members and a drive roller 1410. The driving and conveyance mechanism of the intermediate transfer unit 1310 further has a secondary transfer facing roller 1411, a secondary transfer roller 1412, a tension roller 1413, a driven roller 1414 and so forth. Note that the drive roller 1410 is driven and rotated by a drive motor which is a driving part.
As a defective image caused by the driving and conveyance mechanism of the intermediate transfer unit 1310 in the image forming apparatus 1300, there may be an image having a banding phenomenon of periodically or randomly generating band-like density variations. In particular, a phenomenon called shock jitter is known of generating a band-like density variation in a specific timing due to a shock occurring when the front or rear edge of a recording medium 1415 passes through the driving and conveyance mechanism, two types of driving and conveyance mechanisms come into contact with one another or are removed from one another, or so.
As a countermeasure for such a banding phenomenon caused by shock jitter, a method is known of reducing a variation in the rotational speed of the drive roller 1410 occurring due to a load variation when the front or rear edge of a recording medium 1415 passes through the secondary transfer area. According to this method, control is carried out such that even if a load varies, the drive roller 1410 is rotated at a fixed rotational speed.
By applying the load torque estimation apparatus 100 according to any one of the above-mentioned embodiments to a process of controlling the drive motor driving and rotating the drive roller 1410 and changing the motor nominal model, it is possible to carry out a control voltage/load torque estimation with high precision in response to a load torque variation. Then, by feeding back the estimated control voltage, it is possible to reduce an influence of a load torque variation due to shock jitter.
According to the embodiments of the present invention, it is possible to improve accuracy in an estimation of load torque of an electric motor.
Note that the present invention is not limited to the configurations shown above. It is possible to combine any other element(s) to any configuration described above concerning the above-mentioned embodiments, for example. In this regard, it is possible to make any change without departing from the scope of the present invention and it is possible to determine the change appropriately depending on a particular applied form.
Thus, the load torque estimation apparatuses, the image forming apparatuses, the load torque estimation methods and the non-transitory computer-readable information recording mediums have been described by the embodiments. However, the present invention is not limited to the specifically disclosed embodiments, and any other variations and modifications may be made without departing from the scope of the present invention.
The present application is based on and claims the benefit of priority of Japanese Priority Application No. 2013-191151 filed Sep. 13, 2013 and Japanese Priority Application No. 2014-153609 filed Jul. 29, 2014, the entire contents of which are hereby incorporated herein by reference.

## Claims

1. A load torque estimation apparatus configured to estimate load torque of an electric motor, the load torque estimation apparatus comprising:
a processor and a memory, the memory containing instructions that, when executed by the processor, configures the processor to,
input, to a model, a controlling value for controlling the electric motor and a rotational speed of the electric motor, and
estimate load torque of the electric motor based on the model by,
deriving an electrical time constant of the electric motor corresponding to the load torque at a first control period,
updating the electrical time constant included in the model based on the electrical time constant corresponding to the load torque estimated at the first control period, and
estimating the load torque of the electric motor at a second control period subsequent to the first control period by inputting the controlling value and the rotational speed acquired at the second control period to the model acquired through the updating of the electrical time constant.

2. The load torque estimation apparatus as claimed in claim 1, wherein the processor is configured to,
derive a mechanical time constant of the electric motor corresponding to the load torque at the first control period,
update the mechanical time constant included in the model based on the mechanical time constant corresponding to the load torque estimated at the first control period, and
estimate the load torque of the electric motor at the second control period subsequent to the first control period by inputting the controlling value and the rotational speed acquired at the second control period to the model acquired through the updating of electrical time constant and the mechanical time constant.

3. The load torque estimation apparatus as claimed in claim 2, wherein the processor is configured to,
derive the electrical time constant of the electric motor corresponding to the load torque estimated at the first control period using an approximation formula or a table prescribing relationships between the load torque and the electrical time constant of the electric motor, and
derive the mechanical time constant of the electric motor corresponding to the load torque estimated at the first control period using an approximation formula or a table prescribing relationships between the load torque and the mechanical time constant of the electric motor.

4. The load torque estimation apparatus as claimed in claim 1, wherein the processor is configured to acquire the rotational speed of the electric motor based on an output of a two-phase encoder or an output of a magnetic sensor provided to the electric motor.

5. An image forming apparatus comprising:
the load torque estimation apparatus claimed in claim 1.

6. The load torque estimation apparatus of claim 1, wherein the electrical time constant is based on one or more of an inductance of a coil of the electric motor and a resistance of the coil of the electric motor.

7. The load torque estimation apparatus as claimed in claim 1, wherein the rotational speed of the electric motor input to the load torque estimation apparatus is determined by measuring an actual rotational speed of the electric motor.

8. A method of estimating load torque of an electric motor in a load torque estimation apparatus configured to estimate load torque of an electric motor, the method comprising:
inputting a controlling value for controlling the electric motor and a rotational speed of the electric motor to a model; and
estimating load torque of the electric motor based on the model by,
deriving an electrical time constant of the electric motor corresponding to the load torque at a first control period,
updating the electrical time constant included in the model based on the electrical time constant corresponding to the load torque estimated at the first control period, and
estimating the load torque of the electric motor at a second control period subsequent to the first control period by inputting the controlling value and the rotational speed acquired at the second control period to the model acquired through the updating of the electrical time constant.

9. The method claim 8, wherein the electrical time constant is based on one or more of an inductance of a coil of the electric motor and a resistance of the coil of the electric motor.

10. The method as claimed in claim 8, wherein the rotational speed of the electric motor input to the load torque estimation apparatus is determined by measuring an actual rotational speed of the electric motor.

11. A load torque estimation apparatus configured to estimate load torque of an electric motor, the load torque estimation apparatus comprising:
a processor and a memory, the memory containing instructions that, when executed by the processor, configures the processor to,
input, to a model, a controlling value for controlling the electric motor and a rotational speed of the electric motor, and
estimate load torque of the electric motor based on the model,
derive an electrical time constant of the electric motor corresponding to the load torque of the electric motor at a first control period,
update the electrical time constant included in the model based on the rotational speed of the electric motor at a second control period subsequent to the first control period, and
re-estimate the load torque based on the updated model.

12. The load torque estimation apparatus of claim 11, wherein the processor is configured to update a mechanical time constant included in the model based on the rotational speed of the electric motor.

13. The load torque estimation apparatus of claim 11, wherein the processor is configured to update the electrical time constant based on an approximation formulate or table prescribing relationships between the load torque and the electrical time constant of the electric motor.

14. The load torque estimation apparatus of claim 11, wherein the processor is configured to acquire the rotational speed of the electric motor based on an output of a two-phase encoder or an output of a magnetic sensor provided to the electric motor.

15. An image forming apparatus comprising;
the load torque estimation apparatus claimed in claim 11.

16. The load torque estimation apparatus of claim 11, wherein the electrical time constant is based on one or more of an inductance of a coil of the electric motor and a resistance of the coil of the electric motor.

17. The load torque estimation apparatus as claimed in claim 11, wherein the processor is further configured to derive the electrical time constant of the electric motor corresponding to the estimated load torque thereof.

18. The load torque estimation apparatus as claimed in claim 11, wherein the rotational speed of the electric motor input to the load torque estimation apparatus is determined by measuring an actual rotational speed of the electric motor.