Patent Publication Number: US-11383759-B2

Title: Motor control apparatus

Description:
INCORPORATION BY REFERENCE 
     The disclosure of Japanese Patent Application No. 2018-144000 filed on Jul. 31, 2018 including the specification, drawings and abstract, is incorporated herein by reference in its entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to a control apparatus for an electric motor for steering angle control. 
     2. Description of Related Art 
     In automated driving and assisted driving using an electric power steering system (EPS), a steer-by-wire system, a rear-wheel steering system, or other systems, the steered angle of steered wheels is controlled by an electric motor. In this type of motor control, angle feedback control is used that controls the motor torque of the electric motor, in accordance with the deviation between a target steered angle and an actual steered angle. In the angle feedback control, PID control is generally used. Specifically, a target torque is calculated by multiplying a term of the deviation between the target steered angle and the actual steered angle, an integral term of the deviation, and a differential term of the deviation, by a proportional gain, an integral gain, and a differential gain, respectively, and then adding these terms. Then, the electric motor is controlled such that the motor torque becomes equal to the target torque (see Japanese Patent Application Publication No. 2004-256076 and WO 2014/162769 Pamphlet). 
     The PID control described above is a linear control algorithm. Therefore, variations in non-linear disturbance torque, such as road surface load torque (disturbance torque on the rack shaft side), friction torque of a steering system, and steering torque (disturbance torque on the steering side), cause a decrease or variation in angle control accuracy. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a motor control apparatus capable of reducing the influence of disturbance torque on angle control performance, and performing angle control with high accuracy. 
     According to an aspect of the present invention, there is provided a motor control apparatus that controls driving of an electric motor for steering angle control, the motor control apparatus including: a manual steering command value generation unit that generates a manual steering command value, using a steering torque; a summed angle command value calculation unit that calculates a summed angle command value, by adding the manual steering command value to an automatic steering command value; and a control unit that performs angle control of the electric motor, based on the summed angle command value; wherein the control unit includes a basic torque command value calculation unit that calculates a basic torque command value, based on the summed angle command value, a disturbance torque estimation unit that estimates a disturbance torque other than a motor torque of the electric motor applied to an object driven by the electric motor, and a disturbance torque compensation unit that corrects the basic torque command value, based on the disturbance torque; and the manual steering command value generation unit uses an estimated torque calculated based on the disturbance torque, when generating the manual steering command value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and further features and advantages of the invention will become apparent from the following description of example embodiments with reference to the accompanying drawings, wherein like numerals are used to represent like elements and wherein: 
         FIG. 1  is a schematic diagram illustrating the general configuration of an electric power steering system to which a motor control apparatus according to an embodiment of the present invention is applied; 
         FIG. 2  is a block diagram illustrating the electrical configuration of a motor control ECU; 
         FIG. 3  is a block diagram illustrating the configuration of a manual steering command value generation unit; 
         FIG. 4  is a graph illustrating an example setting of an assist torque command value T ac  with respect to a steering torque T d ; 
         FIG. 5  is a schematic diagram illustrating an example of a reference EPS model used in a command value setting unit; 
         FIG. 6  is a block diagram illustrating the configuration of an angle control unit; 
         FIG. 7  is a schematic diagram illustrating an example of the configuration of a physical model of the electric power steering system; 
         FIG. 8  is a block diagram illustrating the configuration of a disturbance torque estimation unit; and 
         FIG. 9  is a schematic diagram illustrating the configuration of a torque control unit. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.  FIG. 1  is a schematic diagram illustrating the general configuration of an electric power steering system to which a motor control apparatus according to an embodiment of the present invention is applied. An electric power steering system  1  includes a steering wheel  2 , a steering operation mechanism  4 , and a steering assist mechanism  5 . The steering wheel  2  is a steering member for steering the vehicle. The steering operation mechanism  4  steers steered wheels  3  in conjunction with rotation of the steering wheel  2 . The steering assist mechanism  5  assists the driver in steering. The steering wheel  2  and the steering operation mechanism  4  are mechanically coupled to each other via a steering shaft  6  and an intermediate shaft  7 . 
     The steering shaft  6  includes an input shaft  8  coupled to the steering wheel  2 , and an output shaft  9  coupled to the intermediate shaft  7 , The input shaft  8  and the output shaft  9  are relatively rotatably coupled to each other via a torsion bar  10 . A torque sensor  12  is disposed near the torsion bar  10 . The torque sensor  12  detects a steering torque (torsion bar torque) T d  applied to the steering wheel  2 , based on the amount of relative rotational displacement between the input shaft  8  and the output shaft  9 . In the present embodiment, the torque sensor  12  detects the steering torque T d  for steering to the right as a positive value, and detects the steering torque T d  for steering to the left as a negative value. The greater the absolute value of the steering torque T d  is, the greater the magnitude of the steering torque T d  is. 
     The steering operation mechanism  4  is a rack-and-pinion mechanism including a pinion shaft  13  and a rack shaft  14  that serves as a steered shaft. The steered wheels  3  are coupled to the opposite ends of the rack shaft  14  via tie rods  15  and knuckle arms (not illustrated). The pinion shaft  13  is coupled to the intermediate shaft  7 . The pinion shaft  13  is configured to rotate in conjunction with steering of the steering wheel  2 . A pinion  16  is coupled to the distal end of the pinion shaft  13 . 
     The rack shaft  14  extends linearly in the lateral direction of the vehicle. A rack  17  that meshes with the pinion  16  is formed at an axially intermediate portion of the rack shaft  14 . The pinion  16  and the rack  17  convert rotation of the pinion shaft  13  into axial movement of the rack shaft  14 . The steered wheels  3  can be steered by moving the rack shaft  14  in the axial direction. 
     When the steering wheel  2  is operated (rotated), the rotation is transmitted to the pinion shaft  13  via the steering shaft  6  and the intermediate shaft  7 . Then, the pinion  16  and the rack  17  convert rotation of the pinion shaft  13  into axial movement of the rack shaft  14 . Thus, the steered wheels  3  are steered. The steering assist mechanism  5  includes an electric motor  18  and a reducer  19 . The electric motor  18  generates a steering assist force (assist torque). The reducer  19  amplifies an output torque of the electric motor  18 , and transmits the amplified torque to the steering operation mechanism  4 . The reducer  19  is a worm gear mechanism including a worm gear  20  and a worm wheel  21  that meshes with the worm gear  20 . The reducer  19  is housed in a gear housing  22  serving as a transmission mechanism housing. In the following, the reduction ratio (gear ratio) of the reducer  19  may be represented by N. The reduction ratio N is defined as a ratio ωwg/ωww of an angular velocity ωwg of the worm gear  20  to an angular velocity www of the worm wheel  21 . 
     The worm gear  20  is rotationally driven by the electric motor  18 . The worm wheel  21  is coupled to the output shaft  9  so as to be rotatable therewith. When the worm gear  20  is rotationally driven by the electric motor  18 , the worm wheel  21  is rotationally driven. Thus, a motor torque is applied to the steering shaft  6 , and the steering shaft  6  (output shaft  9 ) is rotated. The rotation of the steering shaft  6  is transmitted to the pinion shaft  13  via the intermediate shaft  7 . The rotation of the pinion shaft  13  is converted into axial movement of the rack shaft  14 . Thus, the steered wheels  3  are steered. That is, the electric motor  18  rotationally drives the worm gear  20 , and thereby can assist in steering and steer the steered wheels  3 . The electric motor  18  is provided with a rotation angle sensor  23  that detects a rotation angle of the electric motor  18 . 
     The torque applied to the output shaft  9  (an example of an object driven by the electric motor  18 ) includes a motor torque of the electric motor  18 , and a disturbance torque other than the motor torque. A disturbance torque T lc  other than the motor torque includes the steering torque T d , a road surface load torque (road surface reaction force torque) T rl , and a friction torque T f . The steering torque T d  is torque applied to the output shaft  9  from the steering wheel  2  side, by the force applied to the steering wheel  2  by the driver, the force generated by inertia of steering, and so on. 
     The road surface load torque T rl  is torque applied to the output shaft  9  via the rack shaft  14  from the steered wheels  3  side, by the self-aligning torque generated by the tire, the force generated by the suspension and tire wheel alignment, the friction force of a rack-and-pinion mechanism. 
     The friction torque T f  is friction torque applied to the output shaft  9  (the object driven by the electric motor  18 ) and not included in the steering torque T d  or the road surface load torque T rl , The friction torque T f  includes at least the friction torque generated between the electric motor  18  and the output shaft  9 . In the present embodiment, the friction torque T f  mainly includes the friction torque generated by the reducer  19  (friction torque generated between the worm wheel  21  and the worm gear  20 ). 
     The vehicle is equipped with a charge-coupled device (CCD) camera  25 , a global positioning system (GPS)  26 , a radar  27 , and a map information memory  28 . The CCD camera  25  takes a picture of the road ahead in the traveling direction of the vehicle. The GPS  26  detects the position of the vehicle. The radar  27  detects the road shape and an obstacle. The map information memory  28  stores map information. The CCD camera  25 , the GPS  26 , the radar  27 , and the map information memory  28  are connected to a higher-level electronic control unit (ECU)  201  for performing assisted driving control and automated driving control. The higher-level ECU  201  performs surrounding environment recognition, own vehicle position estimation, route planning, and so on, based on the information obtained by the CCD camera  25 , the GPS  26 , and the radar  27 , and the map information. Then, the higher-level ECU  201  determines control target values for steering and a drive actuator. 
     In the present embodiment, the higher-level ECU  201  sets an automatic steering command value θ adac  for automatic steering. In the present embodiment, the automatic steering control is, for example, control for causing the vehicle to travel along the target trajectory. The automatic steering command value θ adac  is a target value of the steering angle for causing the vehicle to automatically travel along the target trajectory. The processing for setting such an automatic steering command value θ adac  is well known and, therefore, will not be described herein in detail. 
     The automatic steering command value θ adac  set by the higher-level ECU  201  is transmitted to the motor control ECU  202  via an in-vehicle network. The steering torque T d  detected by the torque sensor  12  and an output signal of the rotation angle sensor  23  are input to the motor control ECU  202 . The motor control ECU  202  controls the electric motor  18 , based on these input signals and the information provided from the higher-level ECU  201 , 
       FIG. 2  is a block diagram illustrating the electrical configuration of the motor control ECU  202 . 
     The motor control ECU  202  includes a microcomputer  40 , a drive circuit (inverter circuit)  31 , and a current detection circuit  32 . The drive circuit  31  is controlled by the microcomputer  40 , and supplies power to the electric motor  18 . The current detection circuit  32  detects a current flowing through the electric motor  18  (hereinafter referred to as a “motor current I”). 
     The microcomputer  40  includes a CPU and memories (a ROM, a RAM, a non-volatile memory, and the like). The microcomputer  40  executes predetermined programs to serve as a plurality of function processing units. The plurality of function processing units include a manual steering command value generation unit  41 , a summed angle command value calculation unit  42 , and a control unit  43 . The manual steering command value generation unit  41  is provided to set, when the driver operates the steering wheel  2 , a steering angle (more correctly, a rotation angle θ of the output shaft  9 ) corresponding to the steering wheel operation as a manual steering command value θ mdac . The manual steering command value generation unit  41  generates the manual steering command value θ mdac , using the steering torque T d  detected by the torque sensor  12  and a disturbance torque estimation value {circumflex over (T)} lc  transmitted from an angle control unit  44  (described below) of the control unit  43 . 
     The summed angle command value calculation unit  42  calculates a summed angle command value θ acmd  by adding the manual steeling command value θ mdac  to the automatic steering command value θ adac  set by the higher-level ECU  201 . 
     The control unit  43  performs angle control of the electric motor  18 , based on the summed angle command value θ acmd . More specifically, the control unit  43  controls driving of the drive circuit  31  such that the steering angle θ (the rotation angle θ of the output shaft  9 ) approaches the summed angle command value θ acmd . 
     The control unit  43  includes the angle control unit  44  and a torque control unit (current control unit)  45 . The angle control unit  44  calculates a motor torque command value T m  as the target value of the motor torque of the electric motor  18 , based on the summed angle command value θ acmd . The torque control unit  45  drives the drive circuit  31  such that the motor torque of the electric motor  18  approaches the motor torque command value T m .  FIG. 3  is a block diagram illustrating the configuration of the manual steering command value generation unit  41 . 
     The manual steering command value generation unit  41  includes an assist torque command value setting unit  51  and a command value setting unit  52 . The assist torque command value setting unit  51  sets an assist torque command value T ac  as the target value of the assist torque required for manual operation. The assist torque command value setting unit Si sets the assist torque command value T ac , based on the steering torque T d  detected by the torque sensor  12 .  FIG. 4  illustrates an example setting of the assist torque command value T ac  with respect to the steering torque T d . 
     The assist torque command value T ac  is set to a positive value when a steering assist force for steering to the left needs to be generated from the electric motor  18 , and is set to a negative value when a steering assist force for steering to the right needs to be generated from the electric motor  18 , The assist torque command value T ac  is positive when the steering torque T d  has a positive value, and negative when the steering torque T d  has a negative value. The assist torque command value T ac  is set such that its absolute value increases as the absolute value of the steering torque T d  increases. 
     The assist torque command value setting unit  51  may calculate the assist torque command value T ac , by multiplying the steering torque T d  by a predetermined constant. Referring back to  FIG. 3 , the command value setting unit  52  sets the manual steering command value θ mdac , based on the steering torque T d , the assist torque command value T ac , and the disturbance torque estimation value {circumflex over (T)} lc  calculated by a disturbance torque estimation unit  64  (described below) (see  FIG. 6 ) of the angle control unit  44 . 
     The disturbance torque estimation value {circumflex over (T)} lc  calculated by the disturbance torque estimation unit  64  is the estimated value of the disturbance torque other than the motor torque applied to the object (output shaft  9 ) driven by the electric motor  18 , The disturbance torque estimation value {circumflex over (T)} lc  includes the steering torque T d , the road surface load torque T rl , and the friction torque T f . The command value setting unit  52  basically sets the manual steering command value θ mdac , using a reference EPS model of  FIG. 5 . 
     The reference EPS model is a single inertia model including a lower column. The lower column corresponds to the output shaft  9  and the worm wheel  21 . In  FIG. 5 , J c  represents the inertia of the lower column; θ c  represents the rotation angle of the lower column; and T d  represents the steering torque. The lower column receives the steering torque T d , a torque N·T m  applied from the electric motor  18  to the output shaft  9 , and the road surface load torque T rl . 
     The equation of motion of the reference EPS model is represented by the following Expression (1).
 
 J   c   ·d   2 θ c   /dt   2   =T   d   +N·T   m   +T   rl   (1)
 
     In the present embodiment, the command value setting unit  52  uses the disturbance torque estimation value {circumflex over (T)} lc  calculated by the disturbance torque estimation unit  64  (see  FIGS. 3 and 6 ), as the road surface load torque T rl  of  FIG. 5  (T rl  in Expression (1)). In this case, the equation of motion of the reference EPS model is represented by the following Expression (2).
 
 J   c   ·d   2 θ c   /dt   2   =T   d   +N·T   m   +{circumflex over (T)}   rl   (2)
 
     The command value setting unit  52  solves the differential equation of Expression (2) by assigning the steering torque T d  detected by the torque sensor  12  to T d  and assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  to N·T m , and thereby calculates the rotation angle θ c  of the lower column. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . 
       FIG. 6  is a block diagram illustrating the configuration of the angle control unit  44 . The angle control unit  44  calculates the motor torque command value T m  based on the summed angle command value θ acmd . The angle control unit  44  includes a low-pass filter (LPF)  61 , a feedback control unit  62 , a feedforward control unit  63 , the disturbance torque estimation unit  64 , a torque addition unit  65 , a disturbance torque compensation unit  66 , a first reduction ratio division unit  67 , a reduction ratio multiplication unit  68 , a rotation angle calculation unit  69 , and a second reduction ratio division unit  70 . 
     The reduction ratio multiplication unit  68  multiplies the motor torque command value T m  calculated by the first reduction ratio division unit  67  by a reduction ratio N of the reducer  19 . Thus, the motor torque command value T m  is converted into a steering torque command value T cmd  (=N·T m ) applied to the output shaft  9  (worm wheel  21 ). The rotation angle calculation unit  69  calculates a rotor rotation angle θ m  of the electric motor  18 , based on the output signal of the rotation angle sensor  23 . The second reduction ratio division unit  70  divides the rotor rotation angle θ m  calculated by the rotation angle calculation unit  69  by the reduction ratio N. Thus, the rotor rotation angle θ m  is converted into a rotation angle (actual steering angle) θ of the output shaft  9 . 
     The low-pass filter  61  performs low-pass filtering on the summed angle command value θ acmd . A summed angle command value θ cmd  resulting from low-pass filtering is transmitted to the feedback control unit  62  and the feed forward control unit  63 . The feedback control unit  62  is provided to bring a steering angle estimation value {circumflex over (θ)} calculated by the disturbance torque estimation unit  64  closer to the summed angle command value θ cmd  resulting from the low-pass filtering. The feedback control unit  62  includes an angle deviation calculation unit  62 A and a PD control unit  62 B. The angle deviation calculation unit  62 A calculates a deviation Δθ (=θ cmd −{circumflex over (θ)}) between the summed angle command value θ cmd  and the steering angle estimation value {circumflex over (θ)}. The angle deviation calculation unit  62 A may calculate a deviation (θ cmd −{circumflex over (θ)}) between the summed angle command value θ cmd  and the actual steering angle θ calculated by the second reduction ratio division unit  70 , as the angle deviation Δθ. 
     The PD control unit  62 B performs a PD operation (proportional differential operation) on the angle deviation Δθ calculated by the angle deviation calculation unit  62 A. Thus, a feedback control torque T fb  is calculated. The feedback control torque T fb  is transmitted to the torque addition unit  65 . The feedforward control unit  63  is provided to compensate for delay in responsiveness due to the inertia of the electric power steering system  1 , and improve control responsiveness. The feedforward control unit  63  includes an angular acceleration calculation unit  63 A and an inertia multiplication unit  63 B. The angular acceleration calculation unit  63 A calculates a target angular acceleration d 2 θ cmd /dt 2  by differentiating the summed angle command value θ cmd  twice. 
     The inertia multiplication unit  63 B multiplies the target angular acceleration d 2 θ cmd /dt 2  calculated by the angular acceleration calculation unit  63 A, by an inertia J of the electric power steering system  1 . Thus, a feedforward control torque T ff  (=J·d 2 θ cmd /dt 2 ) is calculated. The inertia J is calculated from, for example, a physical model (described below) (see  FIG. 7 ) of the electric power steering system  1 . The feedforward control torque T ff  is transmitted to the torque addition unit  65 , as an inertia compensation value. 
     The torque addition unit  65  adds the feedforward control torque T ff  to the feedback control torque T fb . Thus, a basic torque command value (T fb , T ff ) is calculated. 
     The disturbance torque estimation unit  64  is provided to estimate a non-linear torque (disturbance torque: torque other than the motor torque) generated as a disturbance in a plant (the object controlled by the electric motor  18 ). The disturbance torque estimation unit  64  estimates the disturbance torque (disturbance load) T lc , the steering angle θ, and a steering angle differential value (angular velocity) dθ/dt, based on the steering torque command value T cmd  (=N·T m ) that is input to the plant and the actual steering angle θ that is output from the plant. The estimated values of the disturbance torque T lc , the steering angle θ, and the steering angle differential value (angular velocity) dθ/dt are represented by {circumflex over (T)} lc , {circumflex over (θ)}, and d{circumflex over (θ)}/dt. The disturbance torque estimation unit  64  will be described in detail below. 
     The disturbance torque estimation value {circumflex over (T)} lc  calculated by the disturbance torque estimation unit  64  is transmitted to the command value setting unit  52  (see  FIG. 3 ) of the manual steering command value generation unit  41 , and is also transmitted to the disturbance torque compensation unit  66  as a disturbance torque compensation value. The steering angle estimation value {circumflex over (θ)} calculated by the disturbance torque estimation unit  64  is transmitted to the angle deviation calculation unit  62 A. The disturbance torque compensation unit  66  subtracts the disturbance torque estimation value {circumflex over (T)} lc  from the basic torque command value (T fb +T ff ). Thus, the steering torque command value T cmd  (=T fb +T ff −{circumflex over (T)} lc ) is calculated. In this manner, the steering torque command value (the torque command value for the output shaft  9 ) for which the disturbance torque is compensated is obtained. 
     The steering torque command value T cmd  is transmitted to the first reduction ratio division unit  67 . The first reduction ratio division unit  67  divides the steering torque command value T cmd  by the reduction ratio N. Thus, the motor torque command value T m  is calculated. The motor torque command value T m  is transmitted to the torque control unit  45  (see  FIG. 2 ). The disturbance torque estimation unit  64  will now be described in detail. The disturbance torque estimation unit  64  includes, for example, a disturbance observer that estimates the disturbance torque T lc , the steering angle θ, and the angular velocity dθ/dt, using the physical model  101  of the electric power steering system  1  of  FIG. 7 . 
     The physical model  101  includes a plant (an example of an object driven by a motor)  102  including the output shaft  9  and the worm wheel  21  fixed to the output shaft  9 . The plant  102  receives the steering torque T d  from the steering wheel  2  via the torsion bar  10 , and receives the road surface load torque T rl  from the steered wheels  3  side. Further, the plant  102  receives the steering torque command value T cmd  (=N·T m ) via the worm gear  20 . The plant  102  also receives the friction torque T f  due to the friction between the worm wheel  21  and the worm gear  20 . 
     When the inertia of the plant  102  is represented by J, the motion equation of the inertia of the physical model  101  is represented by the following Expression (3).
 
 J{umlaut over (θ)}=N·T   m   +T   lc  
 
 T   lc   =T   d   +T   rl   +T   f   (3)
 
     Here, d 2 θ/dt 2  represents the angular acceleration of the plant  102 . N represents the reduction ratio of the reducer  19 . T lc  represents the disturbance torque applied to the plant  102  other than the motor torque. In the present embodiment, the disturbance torque T lc  is represented as the sum of the steering torque T d , the road surface load torque T rl , and the friction torque T f . In reality, however, the disturbance torque T lc  includes torque other than these torques. 
     The state equation for the physical model  101  of  FIG. 7  is represented by the following Expression (4). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             x 
                             . 
                           
                           = 
                           
                             Ax 
                             + 
                             
                               
                                 B 
                                 1 
                               
                               ⁢ 
                               
                                 u 
                                 1 
                               
                             
                             + 
                             
                               
                                 B 
                                 2 
                               
                               ⁢ 
                               
                                 u 
                                 2 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           y 
                           = 
                           
                             Cx 
                             + 
                             
                               Du 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     In the above Expression (4), x represents a state variable vector. In the above Expression (4), u 1  represents a known input vector. In the above Expression (4), u 2  represents an unknown input vector. In the above Expression (4), y represents an output vector (measured value). In the above Expression (4), A represents a system matrix. In the above Expression (4), B 1  represents a first input matrix. In the above Expression (4), B 2  represents a second input matrix. In the above Expression (4), C represents an output matrix. In the above Expression (4), D represents a feedthrough matrix. 
     The above state equation is extended to a system including the unknown input vector u 2  as one of the states. The state equation of an extended system (extended state equation) is represented by the following Expression (5). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               x 
                               . 
                             
                             e 
                           
                           = 
                           
                             
                               
                                 A 
                                 e 
                               
                               ⁢ 
                               
                                 x 
                                 e 
                               
                             
                             + 
                             
                               
                                 B 
                                 e 
                               
                               ⁢ 
                               
                                 u 
                                 1 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           y 
                           = 
                           
                             
                               C 
                               e 
                             
                             ⁢ 
                             
                               x 
                               e 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     In the above Expression (5), x e  represents a state variable vector of the extended system, and is represented by the following Expression (6). 
     
       
         
           
             
               
                 
                   
                     x 
                     e 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           x 
                         
                       
                       
                         
                           
                             u 
                             2 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In the above Expression (5), A e  represents a system matrix of the extended system. In the above Expression (5), B e  represents a known input matrix of the extended system. In the above Expression (5), C e  represents an output matrix of the extended system. 
     A disturbance observer (extended state observer) represented by the following Expression (7) is constructed from the extended state equation of the above Expression (5). 
     
       
         
           
             
               
                 
                   { 
                   
                     
                       
                         
                           
                             
                               
                                 x 
                                 ^ 
                               
                               . 
                             
                             e 
                           
                           = 
                           
                             
                               
                                 A 
                                 e 
                               
                               ⁢ 
                               
                                 
                                   x 
                                   ^ 
                                 
                                 e 
                               
                             
                             + 
                             
                               
                                 B 
                                 e 
                               
                               ⁢ 
                               
                                 u 
                                 1 
                               
                             
                             + 
                             
                               L 
                               ⁡ 
                               
                                 ( 
                                 
                                   y 
                                   - 
                                   
                                     y 
                                     ^ 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             y 
                             ^ 
                           
                           = 
                           
                             
                               C 
                               e 
                             
                             ⁢ 
                             
                               
                                 x 
                                 ^ 
                               
                               e 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     In Expression (7), {circumflex over (x)} e , represents the estimated value of x e . L represents an observer gain. Further, ŷ represents the estimated value of y. Here, {circumflex over (x)} e  is represented by the following Expression (8). 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       ^ 
                     
                     e 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             θ 
                             ^ 
                           
                         
                       
                       
                         
                           
                             
                               θ 
                               ^ 
                             
                             . 
                           
                         
                       
                       
                         
                           
                             
                               T 
                               ^ 
                             
                             lc 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In Expression (8), {circumflex over (θ)} is the estimated value of θ, and {circumflex over (T)} lc  is the estimated value of T lc . The disturbance torque estimation unit  64  calculates the state variable vector {circumflex over (x)} e  based on the equation of the above Expression (7). 
       FIG. 8  is a block diagram illustrating the configuration of the disturbance torque estimation unit  64 . The disturbance torque estimation unit  64  includes an input vector input unit  81 , an output matrix multiplication unit  82 , a first addition unit  83 , a gain multiplication unit  84 , an input matrix multiplication unit  85 , a system matrix multiplication unit  86 , a second addition unit  87 , an integration unit  88 , and a state variable vector output unit  89 . The steering torque command value T cmd  (=N·T m ) calculated by the reduction ratio multiplication unit  68  (see  FIG. 6 ) is transmitted to the input vector input unit  81 . The input vector input unit  81  outputs an input vector u 1 . 
     The output of the integration unit  88  is the state variable vector {circumflex over (x)} e  (see the above Expression (8)). When starting a calculation, the initial value is given as the state variable vector {circumflex over (x)} e . The initial value of the state variable vector {circumflex over (x)} e  is, for example, 0. The system matrix multiplication unit  86  multiplies the state variable vector {circumflex over (x)} e  by the system matrix A e . The output matrix multiplication unit  82  multiplies the state variable vector {circumflex over (x)} e  by the output matrix C e . 
     The first addition unit  83  subtracts an output (C e ·{circumflex over (x)} e ) of the output matrix multiplication unit  82  from the output vector (measured value) y as the actual steering angle θ calculated by the second reduction ratio division unit  70  (see  FIG. 6 ). That is, the first addition unit  83  calculates the difference (y−ŷ) between the output vector y and the output vector estimation value ŷ (=C e ·{circumflex over (x)} e ). The gain multiplication unit  84  multiplies the output (y−ŷ) of the first addition unit  83  by the observer gain L (see the above Expression (7)). 
     The input matrix multiplication unit  85  multiplies the input vector u 1  output from the input vector input unit  81  by the input matrix B e . The second addition unit  87  adds the output (B e ·u 1 ) of the input matrix multiplication unit  85 , the output (A e ·{circumflex over (x)} e ) of the system matrix multiplication unit  86 , and the output (L(y−ŷ)) of the gain multiplication unit  84 . Thus, a differential value d{circumflex over (x)} e /dt of the state variable vector is calculated. The integration unit  88  integrates the output (d{circumflex over (x)} e /dt) of the output of the second addition unit  87 , Thus, the state variable vector {circumflex over (x)} e  is calculated. The state variable vector output unit  89  calculates the disturbance torque estimation value {circumflex over (T)} lc , the steering angle estimation value {circumflex over (θ)}, and the angular velocity estimation value d{circumflex over (θ)}/dt based on the state variable vector {circumflex over (x)} e . 
     Unlike the extended state observer described above, a general disturbance observer includes an inverse model of the plant and a low-pass filter. The motion equation of the plant is represented by Expression (3) as described above. Accordingly, the inverse model of the plant is represented by the following Expression (9).
 
 T   lc   =J{umlaut over (θ)}−N·T   m   (9)
 
     The input to a typical disturbance observer is J·d 2 θ/dt 2  and N·T m , and is greatly affected by noise of the rotation angle sensor  23  because the second-order differential value of the actual steering angle θ is used. Meanwhile, the extended state observer described above estimates the disturbance torque based on integration, and therefore the influence of the noise due to differential can be reduced. 
     A typical disturbance observer including an inverse model of a plant and a low-pass filter may be used as the disturbance torque estimation unit  64 .  FIG. 9  is a schematic diagram illustrating the configuration of the torque control unit  45 . The torque control unit  45  (see  FIG. 2 ) includes a motor current command value calculation unit  91 , a current deviation calculation unit  92 , a PI control unit  93 , and a pulse width modulation (PWM) control unit  94 . 
     The motor current command value calculation unit  91  divides the motor torque command value T m  calculated by the angle control unit  44  (see  FIG. 2 ) by a torque constant K t  of the electric motor  18 . Thus, a motor current command value I cmd  is calculated. The current deviation calculation unit  92  calculates a deviation ΔI (=I cmd −I) between the motor current command value I cmd  obtained by the motor current command value calculation unit  91  and the motor current I detected by the current detection circuit  32 . 
     The PI control unit  93  performs a proportional integral (PI) operation on the current deviation ΔI calculated by the current deviation calculation unit  92 . Thus, a drive command value for bringing the motor current I flowing through the electric motor  18  closer to the motor current command value I cmd  is generated. The PWM control unit  94  generates a PWM control signal of a duty ratio corresponding to the drive command value, and supplies the PWM control signal to the drive circuit  31 . Thus, power corresponding to the drive command value is supplied to the electric motor  18 . 
     In the above embodiment, the summed angle command value θ acmd  is calculated by adding the manual steering command value θ mdac  to the automatic steering command value θ adac , and the electric motor  18  is controlled based on the summed angle command value θ acmd . Therefore, it is possible to achieve cooperative control that allows manual steering while performing steering control based mainly on automatic steering control, without switching between manual steering control and automatic steering control. Also, it is possible to seamlessly shift between manual steering control and automatic steering control, thereby not giving a sense of discomfort to the driver when steering manually. 
     In the above embodiment, the basic torque command value (T fb +T ff ) is calculated based on the summed angle command value θ acmd , and the basic torque command value (T fb +T ff ) is corrected by the disturbance torque estimation value {circumflex over (T)} lc  calculated by the disturbance torque estimation unit  64 . Therefore, it is possible to reduce the influence of the disturbance torque on the angle control performance. This makes it possible to perform angle control with high accuracy. 
     In the above embodiment, the manual steering command value θ mdac  is set using the disturbance torque estimation value {circumflex over (T)} lc  calculated by the disturbance torque estimation unit  64  and including the road surface load torque T rl . Therefore, it is possible to provide a steering feeling corresponding to the actual road surface conditions during manual steering. Hereinafter, modifications of the command value setting unit  52  (see  FIG. 3 ) of the manual steering command value generation unit  41  will be described. In a first modification, the command value setting unit  52  uses the value ({circumflex over (T)} lc −T d ) obtained by subtracting the steering torque T d  from the disturbance torque estimation value {circumflex over (T)} lc  (≈T d +T rl +T f ), as the road surface load torque T rl  (T rl  in the above Expression (1)) of  FIG. 5 . 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (10). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               J 
                               c 
                             
                             · 
                             
                               d 
                               2 
                             
                           
                           ⁢ 
                           
                             θ 
                             c 
                           
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             2 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             d 
                           
                           + 
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             ( 
                             
                               
                                 
                                   T 
                                   ^ 
                                 
                                 lc 
                               
                               - 
                               
                                 T 
                                 d 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             
                               T 
                               ^ 
                             
                             lc 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The command value setting unit  52  solves the differential equation of Expression (10), by assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . 
     In the first modification, the manual steering command value θ mdac  is set using the value ({circumflex over (T)} lc −T d ) obtained by subtracting the steering torque T d  from the disturbance torque estimation value {circumflex over (T)} lc . Therefore, it is possible to prevent the steering torque T d  included in the disturbance torque estimation value {circumflex over (T)} lc  from being used for setting the manual steering command value θ mdac . Thus, it is possible to more effectively provide a steering feeling corresponding to the actual road surface conditions during manual steering. In a second modification, the command value setting unit  52  uses the value ({circumflex over (T)} lc −T d −T f ) obtained by subtracting the steering torque T d  and the friction torque T f  from the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . The friction torque T f  can be estimated using, for example, a friction model that estimates friction generated in the reducer  19 . 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (11). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               J 
                               c 
                             
                             · 
                             
                               d 
                               2 
                             
                           
                           ⁢ 
                           
                             θ 
                             c 
                           
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             2 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             d 
                           
                           + 
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             ( 
                             
                               
                                 
                                   T 
                                   ^ 
                                 
                                 lc 
                               
                               - 
                               
                                 T 
                                 d 
                               
                               - 
                               
                                 T 
                                 f 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             
                               T 
                               ^ 
                             
                             lc 
                           
                           - 
                           
                             T 
                             f 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The command value setting unit  52  solves the differential equation of Expression (11), by assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . 
     In the second modification, the manual steering command value θ mdac  is set using the value ({circumflex over (T)} lc −T d −T f ) obtained by subtracting the steering torque T d  and the friction torque T f  from the disturbance torque estimation value {circumflex over (T)} lc . Therefore, it is possible to prevent the steering torque T d  and the friction torque T f  included in the disturbance torque estimation value {circumflex over (T)} lc  from being used for setting the manual steering command value θ mdac . Thus, it is possible to more effectively provide a steering feeling corresponding to the actual road surface conditions during manual steering. In a third modification, the command value setting unit  52  uses the sum (T vsd +{circumflex over (T)} lc ) of a virtual spring-damper load T vsd  and the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . 
     The virtual spring-damper load T vsd  is represented by the following Expression (12), using a spring constant k and a viscous damping coefficient c.
 
 T   vsd   =−k·θ   c   −c ( dθ/dt )  (12)
 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (13).
 
 J   c   ·d   2 θ c   /dt   2   =T   d   +N·T   m   +{−k·θ   c   −c ( dθ   c   /dt )} {circumflex over (T)}   lc   (13)
 
     Predetermined values obtained in advance through experiments and analyses are set as the spring constant k and the viscous damping coefficient c. The same applies to fourth to tenth modifications. The command value setting unit  52  solves the differential equation of Expression (13), by assigning the steering torque T d  detected by the torque sensor  12  to T d  and assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . 
     In the third modification, since the disturbance torque estimation value {circumflex over (T)} lc  is used for setting the manual steering command value θ mdac , it is possible to provide a steering feeling corresponding to the actual road surface conditions during manual steering. Further, in the third modification, the virtual spring-damper load T vsd  is used for setting the manual steering command value θ mdac . Therefore, a reaction force is generated that brings the manual steering command value θ mdac  back to zero when steering manually. Thus, even in the case where a manual operation is performed during automatic steering, the steering angle θ easily follows the automatic steering command value θ adac  when the manual operation is stopped. In a fourth modification, the command value setting unit  52  uses the sum {T vsd +({circumflex over (T)} lc −T d )} of the virtual spring-damper load T vsd  and the value ({circumflex over (T)} lc −T d ) obtained by subtracting the steering torque T d  from the disturbance torque estimation value {circumflex over (T)} lc  as the road surface load torque T rl  of  FIG. 5 . 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (14). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               J 
                               c 
                             
                             · 
                             
                               d 
                               2 
                             
                           
                           ⁢ 
                           
                             θ 
                             c 
                           
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             2 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             d 
                           
                           + 
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                           
                             ( 
                             
                               
                                 
                                   T 
                                   ^ 
                                 
                                 lc 
                               
                               - 
                               
                                 T 
                                 d 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                           
                             
                               T 
                               ^ 
                             
                             lc 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     The command value setting unit  52  solves the differential equation of Expression (14), by assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . In the fourth modification, the same effects as those of the third modification can be obtained. 
     In a fifth modification, the command value setting unit  52  uses the sum {T vsd +({circumflex over (T)} lc −T d −T f )} of the virtual spring-damper load T vsd  and the value ({circumflex over (T)} lc −T d −T f ) obtained by subtracting the steering torque T d  and the friction torque T f  from the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . The friction torque T f  can be estimated using, for example, a friction model that estimates friction generated in the reducer  19 . 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (15). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               J 
                               c 
                             
                             · 
                             
                               d 
                               2 
                             
                           
                           ⁢ 
                           
                             θ 
                             c 
                           
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             2 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             d 
                           
                           + 
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 T 
                                 ^ 
                               
                               lc 
                             
                             - 
                             
                               T 
                               d 
                             
                             - 
                             
                               T 
                               f 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                           
                             
                               T 
                               ^ 
                             
                             lc 
                           
                           + 
                           
                             T 
                             f 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The command value setting unit  52  solves the differential equation of Expression (15), by assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . In the fifth modification, the same effects as those of the third modification can be obtained. 
     The disturbance torque estimation value {circumflex over (T)} lc  calculated by the disturbance torque estimation unit  64  (see  FIG. 6 ) includes the road surface load torque T rl . The road surface load torque T rl  includes a steady component (self-aligning torque) for bringing the steering angle back to a neutral position (straight driving position), and variation components such as road surface disturbance torque (for example, disturbance torque due to rocks on the road, and irregularities of the road surface) and friction torque of the rack-and-pinion mechanism. The steady component is the low-frequency component of the road surface load torque T rl  included in the disturbance torque estimation value {circumflex over (T)} lc , and the variation component is a high-frequency component of the road surface load torque T rl . 
     In a sixth modification, the command value setting unit  52  uses the sum {T vsd +HPF ({circumflex over (T)} lc )} of the virtual spring-damper load T vsd  and the high-frequency component HPF ({circumflex over (T)} lc ) of the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . The high-frequency component HPF ({circumflex over (T)} lc ) of the disturbance torque estimation value {circumflex over (T)} lc  can be obtained by extracting only the frequency component with a frequency higher than a predetermined frequency from the frequency components of the disturbance torque estimation value {circumflex over (T)} lc , using a high-pass filter. 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (16).
 
 J   c   ·d   2 θ c   /dt   2   =T   d   +N·T   m   +{−k·θ   c   −c ( dθ   c   /dt )}+ HPF ( {circumflex over (T)}   lc )  (16)
 
     The command value setting unit  52  solves the differential equation of Expression (16), by assigning the steering torque T d  detected by the torque sensor  12  to T d  and assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . 
     In the sixth modification, the virtual spring-damper load T vsd  is used for setting the manual steering command value θ mdac . Therefore, a reaction force is generated that brings the manual steering command value θ mdac  back to zero when steering manually. Meanwhile, the low-frequency component (steady component) of the disturbance torque estimation value {circumflex over (T)} lc  is not used for setting the manual steering command value θ mdac . Therefore, as compared to the third to fifth modifications described above, the reaction force that brings the steering angle to the neutral position (straight driving position) when steering manually is reduced. Thus, even in the case where a manual operation is performed during automatic steering, the steering angle more easily follows the automatic steering command value θ adac  when the manual operation is stopped. 
     Further, in the sixth modification, the high-frequency component HPF ({circumflex over (T)} lc ) of the disturbance torque estimation value {circumflex over (T)} lc  is used for setting the manual steering command value θ mdac . Thus, the road surface disturbance torque and the friction torque of the rack-and-pinion mechanism are used for setting the manual steering command value θ mdac , so that it is possible to provide a steering feeling corresponding to the actual road surface conditions during manual steering. In a seventh modification, the command value setting unit  52  uses the sum {T vsd +HPF ({circumflex over (T)} lc −T d )} of the virtual spring-damper load T vsd  and the high-frequency component HPF ({circumflex over (T)} lc −T d ) of the value ({circumflex over (T)} lc −T d ) obtained by subtracting the steering torque T d  from the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . HPF ({circumflex over (T)} lc −T d ) can be obtained by extracting only the frequency component with a frequency higher than a predetermined frequency from the frequency components of ({circumflex over (T)} lc −T d ), using a high-pass filter. 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (17).
 
 J   c   ·d   2 θ c   /dt   2   =T   d   +N·T   m   +{−k·θ   c   −c ( dθ   c   /dt )}+ HPF ( {circumflex over (T)}   lc   −T   d )  (17)
 
     The command value setting unit  52  solves the differential equation of Expression (17), by assigning the steering torque T d  detected by the torque sensor  12  to T d  and assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . In the seventh modification, the same effects as those of the sixth modification can be obtained. 
     In an eighth modification, the command value setting unit  52  uses the sum {T vsd +HPF ({circumflex over (T)} lc −T d −T f )} of the virtual spring-damper load T vsd  and the high-frequency component HPF ({circumflex over (T)} lc −T d −T f ) of the value ({circumflex over (T)} lc −T d −T f ) obtained by subtracting the steering torque T d  and the friction torque T f  from the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . 
     The friction torque T f  can be estimated using, for example, a friction model that estimates friction generated in the reducer  19 . HPF ({circumflex over (T)} lc −T d −T f ) can be obtained by extracting only the frequency component with a frequency higher than a predetermined frequency from the frequency components of ({circumflex over (T)} lc −T d −T f ), using a high-pass filter. In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (18).
 
 J   c   ·d   2 θ c   /dt   2   =T   d   +T   m   +{−k·θ   c   −c ( dθ   c   /dt )}+ HPF ( {circumflex over (T)}   lc   −T   d   −T   f )   (18)
 
     The command value setting unit  52  solves the differential equation of Expression (18), by assigning the steering torque T d  detected by the torque sensor  12  to T d  and assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . In the eighth modification, the same effects as those of the sixth modification can be obtained. 
     In a ninth modification, the command value setting unit  52  uses the sum {T vsd +HPF ({circumflex over (T)} lc )−T d } of the virtual spring-damper load T vsd  and the value {HPF ({circumflex over (T)} lc )−T d } obtained by subtracting the steering torque T d  from the high-frequency component HPF ({circumflex over (T)} lc ) of the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (19). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               J 
                               c 
                             
                             · 
                             
                               d 
                               2 
                             
                           
                           ⁢ 
                           
                             θ 
                             c 
                           
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             2 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             d 
                           
                           + 
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           { 
                           
                             
                               HPF 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     T 
                                     ^ 
                                   
                                   lc 
                                 
                                 ) 
                               
                             
                             - 
                             
                               T 
                               d 
                             
                           
                           } 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                           
                             HPF 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   T 
                                   ^ 
                                 
                                 lc 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     The command value setting unit  52  solves the differential equation of Expression (19), by assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . In the ninth modification, the same effects as those of the sixth modification can be obtained. 
     In a tenth modification, the command value setting unit  52  uses the sum {T vsd +HPF ({circumflex over (T)} lc )−T d −T f } of the virtual spring-damper load T vsd  and the value {HPF ({circumflex over (T)} lc )−T d −T f } obtained by subtracting the steering torque T d  and the friction torque T f  from the high-frequency component HPF ({circumflex over (T)} lc ) of the disturbance torque estimation value {circumflex over (T)} lc , as the road surface load torque T rl  of  FIG. 5 . The friction torque T f  can be estimated using, for example, a friction model that estimates friction generated in the reducer  19 . 
     In this case, the equation of motion of the reference EPS model of  FIG. 5  is represented by the following Expression (20). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               J 
                               c 
                             
                             · 
                             
                               d 
                               2 
                             
                           
                           ⁢ 
                           
                             θ 
                             c 
                           
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             t 
                             2 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             T 
                             d 
                           
                           + 
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           { 
                           
                             
                               HPF 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     T 
                                     ^ 
                                   
                                   lc 
                                 
                                 ) 
                               
                             
                             - 
                             
                               T 
                               d 
                             
                             - 
                             
                               T 
                               f 
                             
                           
                           } 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             N 
                             · 
                             
                               T 
                               m 
                             
                           
                           + 
                           
                             { 
                             
                               
                                 
                                   - 
                                   k 
                                 
                                 · 
                                 
                                   θ 
                                   c 
                                 
                               
                               - 
                               
                                 c 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       θ 
                                       c 
                                     
                                     ⁢ 
                                     
                                       / 
                                     
                                     ⁢ 
                                     d 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             } 
                           
                           + 
                           
                             HPF 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   T 
                                   ^ 
                                 
                                 lc 
                               
                               ) 
                             
                           
                           - 
                           
                             T 
                             f 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     The command value setting unit  52  solves the differential equation of Expression (20), by assigning the assist torque command value T ac  set by the assist torque command value setting unit  51  (see  FIG. 3 ) to N·T m . Thus, the rotation angle θ c  of the lower column is calculated. Then, the command value setting unit  52  sets the obtained rotation angle θ c  of the lower column as the manual steering command value θ mdac . In the tenth modification, the same effects as those of the sixth modification can be obtained. 
     In the case where any of the first modification to the tenth modification is used, when a determination is made that the driver is not holding the steering wheel  2 , each of a steering torque T tb , the torque N·T m  applied from the electric motor  18  to the output shaft  9 , and an estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  may be set to zero. 
     The estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  is {circumflex over (T)} lc  of the above Expression (13), ({circumflex over (T)} lc −T d ) of the above Expression (14), ({circumflex over (T)} lc −T d −T f ) of the above Expression (15), HPF ({circumflex over (T)} lc ) of the above Expression (16), HPF ({circumflex over (T)} lc −T d ) of the above Expression (17), HPF ({circumflex over (T)} lc −T d −T f ) of the above Expression (18), {HPF ({circumflex over (T)} lc −T d } of the above Expression (19), or {HPF ({circumflex over (T)} lc )−T d −T f } of the above Expression (20). 
     Specifically, as indicated by the long dashed short dashed line in  FIGS. 2 and 3 , a hands-on/off determination unit  48  is provided that determines whether the driver is holding the steering wheel  2  (hands-on) or not holding the steering wheel  2  (hands-off). The hands-on/off determination unit  48  may be one that determines whether the hands are on the steering wheel  2  based on an output signal of a touch sensor provided on the steering wheel  2 , or may be one that determines whether the hands are on the steering wheel  2  based on an image captured by a camera provided in the vehicle. Note that the hands-on/off determination unit  48  is not limited to those described above, and may be any unit that can determine whether the hands are on the steering wheel  2 . 
     A hands-on/off determination signal output from the hands-on/off determination unit  48  is transmitted to the command value setting unit  52 . When the hands-on/off determination unit  48  determines that the driver is holding the steering wheel  2 , the command value setting unit  52  calculates the manual steering command value θ mdac , using the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc . That is, the command value setting unit  52  calculates the manual steering command value θ mdac  (=θ c ) based on any of the above Expressions (13) to (20). 
     On the other hand, when the hands-on/off determination unit  48  determines that the driver is not holding the steering wheel  2 , the command value setting unit  52  solves the differential equation by assigning zero to each of the steering torque T tb , N·T m , and the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  in any of the above Expressions (13) to (20). Thus, the manual steering command value θ mdac  (=θ c ) is calculated. In this modification, when the driver is not manually steering, the steering torque T tb  that is input to the manual steering command value generation unit  41  is set to substantially zero. Also, the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  is set to zero for calculation of the manual steering command value θ mdac . Thus, it is possible to prevent the manual steering command value θ mdac  from being set based on disturbance other than the driver torque when the driver is not manually steering. 
     In the other modifications described above, when a determination is made that the driver is not holding the steering wheel  2 , each of the steering torque T tb , the torque N·T m  applied from the electric motor  18  to the output shaft  9 , and the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  is set to zero. However, when a determination is made that the driver is not holding the steering wheel  2 , only the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  out of the steering torque T tb , the torque N·T m  applied from the electric motor  18  to the output shaft  9 , and the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  may be set to zero, or the steering torque T tb  and the estimated torque based on the disturbance torque estimation value {circumflex over (T)} lc  may be set to zero. 
     While an embodiment of the present invention has been described above, the present invention may be practiced in other embodiments. For example, although the angle control unit  44  (see  FIG. 6 ) includes the feedforward control unit  63  in the above embodiments, the feedforward control unit  63  may be omitted. In this case, the feedback control torque T fb  calculated by the feedback control unit  62  is used as the basic torque command value. 
     In the above embodiments, the disturbance torque estimation unit  64  calculates the disturbance torque estimation value {circumflex over (T)} lc , based on the motor torque command value T m  and the rotation angle θ of the plant. However, a motor torque acquisition unit that acquires a motor torque generated by the electric motor  18  may be provided, and the motor torque acquired by the motor torque acquisition unit may be used in place of the motor torque command value T m . In the above embodiments, the present invention is applied to motor control of a column assist type EPS. However, the present invention may be applied to motor control of EPS other than those of the column assist types. The present invention may be applied to controlling an electric motor for steering angle control of a steer-by-wire system. 
     Further, various modifications can be made to the present invention within the scope of the appended claims.