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Figure 2. (a) Autonomous EPS system positioning in the vehicle CAD model. (b) EPS positioning in the actual vehicle: 1—BLDC motor; 2—HTD belt; 3—Support structure; 4—Ball screw; 5—Clevises; 6—Steering column.

Figure 2 (a) Autonomous EPS system positioning in the vehicle CAD model. (b) EPS positioning in the actual vehicle: 1—BLDC motor; 2—HTD belt; 3—Support structure; 4—Ball screw; 5—Clevises; 6—Steering column.

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Figure 3. Dynamic model of the studied system. For performance assessment and control tuning purposes, the system is modeled by following a linear lumped-parameter approach. The developed model is schematized in Figure 3. The model includes the motor and its controller along with the dynamic model of the autonomous steering system.
Figure 3. Dynamic model of the studied system. For performance assessment and control tuning purposes, the system is modeled by following a linear lumped-parameter approach. The developed model is schematized in Figure 3. The model includes the motor and its controller along with the dynamic model of the autonomous steering system.
Table 1. Electric motor model parameters. 3.2. Mechanical System The mechanical dynamics of the steering actuator are described through a 3-DOF system, in which friction is modeled as viscous damping and constant gear ratios are used. For the ball screw, a viscous damper with coefficient gs is introduced. The ball screw transmission ratio is Tgs. The same approach is used to model the belt drive connecting the motor shaft with the ball screw nut. Damping coefficient 6g and transmission ratio Tg are used. Furthermore, the belt stiffness is accounted for through the coefficient kg. The steering column is modeled by considering it as a torsion bar with torsional stiffness kr and damping coefficient Brg. The rack and pinion mechanism of the steering system of the vehicle is represented by the constant gear ratio Tp that is equal to the C-factor of the rack. The ratio Tr considers the ratio between the wheel steering angle dw and the linear displacement of the rack xr. It was experimentally determined based on the acquisitions from the on-vehicle sensor data. The term Bsw models the friction of the steering wheel. The equations of motion are obtained through the Lagrangian approach with the motor Relevant parameters from the motor manufacturer are reported in Table 1.
Table 1. Electric motor model parameters. 3.2. Mechanical System The mechanical dynamics of the steering actuator are described through a 3-DOF system, in which friction is modeled as viscous damping and constant gear ratios are used. For the ball screw, a viscous damper with coefficient gs is introduced. The ball screw transmission ratio is Tgs. The same approach is used to model the belt drive connecting the motor shaft with the ball screw nut. Damping coefficient 6g and transmission ratio Tg are used. Furthermore, the belt stiffness is accounted for through the coefficient kg. The steering column is modeled by considering it as a torsion bar with torsional stiffness kr and damping coefficient Brg. The rack and pinion mechanism of the steering system of the vehicle is represented by the constant gear ratio Tp that is equal to the C-factor of the rack. The ratio Tr considers the ratio between the wheel steering angle dw and the linear displacement of the rack xr. It was experimentally determined based on the acquisitions from the on-vehicle sensor data. The term Bsw models the friction of the steering wheel. The equations of motion are obtained through the Lagrangian approach with the motor Relevant parameters from the motor manufacturer are reported in Table 1.
Table 2. Dynamic model parameters. 3.3. Electric Motor Control The adopted control strategy for the BLDC motor has been designed and modeled »ased on the EPOS 4 controller architecture [24]. The most suitable operating mode for the 1utonomous steering actuator is the cyclic synchronous position mode provided by the ZPOS 4 ECU. As presented in Figure 4, the reference steering angle (dsw ref) is computed by he trajectory planning algorithm implemented in dSPACE™. The reference is compared vith the signal acquired by the steering wheel encoder sensor. Then, it is converted to a notor target position that is passed to the EPOS motor controller. Thus, the EPOS performs he position control loop and provides the current set to the inner (cascade) current control oop, which in turn will yield motion on the motor shaft. A full description of the model transmission ratios and known masses and inertia are provided in Table 2. The missing parameters, i.e., the ball screw inertia Jgs, the steering wheel inertia Jsy, the wheel inertia Jw, the belt damping fz, the belt stiffness kg, the damping of the ball screw Bgs, the damping of the steering wheel Bsy, the damping of the steering column 7, and the stiffness of the steering column krz, are identified through the grey-box model parameters estimation optimization process described in Section 4.3.
Table 2. Dynamic model parameters. 3.3. Electric Motor Control The adopted control strategy for the BLDC motor has been designed and modeled »ased on the EPOS 4 controller architecture [24]. The most suitable operating mode for the 1utonomous steering actuator is the cyclic synchronous position mode provided by the ZPOS 4 ECU. As presented in Figure 4, the reference steering angle (dsw ref) is computed by he trajectory planning algorithm implemented in dSPACE™. The reference is compared vith the signal acquired by the steering wheel encoder sensor. Then, it is converted to a notor target position that is passed to the EPOS motor controller. Thus, the EPOS performs he position control loop and provides the current set to the inner (cascade) current control oop, which in turn will yield motion on the motor shaft. A full description of the model transmission ratios and known masses and inertia are provided in Table 2. The missing parameters, i.e., the ball screw inertia Jgs, the steering wheel inertia Jsy, the wheel inertia Jw, the belt damping fz, the belt stiffness kg, the damping of the ball screw Bgs, the damping of the steering wheel Bsy, the damping of the steering column 7, and the stiffness of the steering column krz, are identified through the grey-box model parameters estimation optimization process described in Section 4.3.
Table 3. Electric motor controller parameters. 4. Results and Discussion 4.1. Testbed Setup The parameters used for implementing the electric motor control are reported in Table 3.
Table 3. Electric motor controller parameters. 4. Results and Discussion 4.1. Testbed Setup The parameters used for implementing the electric motor control are reported in Table 3.
Figure 4. Electric motor control block diagram. The acceleration feedforward (FF,) accounts for the inertia of the system and its coefficient is determined bv
Figure 4. Electric motor control block diagram. The acceleration feedforward (FF,) accounts for the inertia of the system and its coefficient is determined bv
Figure 5. Autonomous steering actuator testbed setup block scheme. sensor mounted ECU in real-tim CAN to the PC and to acquire t on the s he data o teering rack and to provide the reference profile to the actuator e at a sampling frequency of 100 Hz. All the systems are connected via to both provide the enabling and configurations messages to the system f encoder sensor steering angle and steering profile from the TI microcontroller and the values of actual current and the actual position of the electric motor provided from the EPOS controller. Figure 5 schematizes the overall layout of the actuator testbed installed in the ac tual vehicle.
Figure 5. Autonomous steering actuator testbed setup block scheme. sensor mounted ECU in real-tim CAN to the PC and to acquire t on the s he data o teering rack and to provide the reference profile to the actuator e at a sampling frequency of 100 Hz. All the systems are connected via to both provide the enabling and configurations messages to the system f encoder sensor steering angle and steering profile from the TI microcontroller and the values of actual current and the actual position of the electric motor provided from the EPOS controller. Figure 5 schematizes the overall layout of the actuator testbed installed in the ac tual vehicle.
Figure 6. Sine-sweep steering maneuver—suspended vehicle, 0-10 Hz, amplitude 10 degrees. (a) Reference steering wheel position and measured response by the steering encoder. (b) Measured motor current and position.
Figure 6. Sine-sweep steering maneuver—suspended vehicle, 0-10 Hz, amplitude 10 degrees. (a) Reference steering wheel position and measured response by the steering encoder. (b) Measured motor current and position.
Figure 7. Sine-sweep steering maneuver—stationary vehicle on the ground, dry asphalt, 0-10 Hz, amplitude 10 degrees. (a) Reference steering wheel position and measured response by the steering encoder. (b) Measured motor current and position. Figure 7. Sine-sweep steering maneuver—stationary vehicle on the ground, dry asphalt, 0-10 Hz,
Figure 7. Sine-sweep steering maneuver—stationary vehicle on the ground, dry asphalt, 0-10 Hz, amplitude 10 degrees. (a) Reference steering wheel position and measured response by the steering encoder. (b) Measured motor current and position. Figure 7. Sine-sweep steering maneuver—stationary vehicle on the ground, dry asphalt, 0-10 Hz,
Table 4. Identified parameters.
Table 4. Identified parameters.
Figure 8. Experimental frequency response function of the closed loop system: suspended vehicle (blue) and vehicle on the ground (orange).
Figure 8. Experimental frequency response function of the closed loop system: suspended vehicle (blue) and vehicle on the ground (orange).
Figure 9. Steering wheel position behavior during the performed sine-sweep maneuver for validating the system identifica- tion: target position (black, dash-dotted) vs. measured position (blue, solid) vs. identified model response (orange, solid).
Figure 9. Steering wheel position behavior during the performed sine-sweep maneuver for validating the system identifica- tion: target position (black, dash-dotted) vs. measured position (blue, solid) vs. identified model response (orange, solid).
Figure 10. Autonomous driving test. (a) Steering wheel position measured by the encoder sensor (orange, solid) vs. target position generated by the MPC strategy devoted to autonomous driving (blue, solid). (b) Spatial coordinates (X,Y) of the race track related to the performed autonomous driving test.
Figure 10. Autonomous driving test. (a) Steering wheel position measured by the encoder sensor (orange, solid) vs. target position generated by the MPC strategy devoted to autonomous driving (blue, solid). (b) Spatial coordinates (X,Y) of the race track related to the performed autonomous driving test.
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