 (32) is solved in each control cycle, and a series of control increments is obtained in the control horizon.
Energies 2021, 14, 671 9 of 18 The first element of the series of control increments obtained above is taken as the actual control increment of the system, and the sum of this increment and the control amount at the previous moment is applied to the current system, as follows: The system executes this control amount until the next moment. At the new moment, the system re-predicts the output of the next horizon based on the state information and obtains a new control increment sequence through the optimization process. Solving repeatedly in this way completes the goal of system rolling optimization control.

Simulation Results and Analyses
To verify the effectiveness of the designed controller, simulations of step-steering input and double-lane change maneuvers were performed in the MATLAB/Simulink environment. By comparing the results of tilt control, zero-roll-angle control, and passive suspension, the advantages of the proposed active tilt control, which actively tilts the vehicle body to the turning direction, were analyzed. In the legend in the following figures, θ = θ des represents the proposed tilt model predictive control, θ = 0 represents the model predictive control for zero-roll-angle control, which uses a zero roll angle as the control target, and PS represents an uncontrolled passive suspension vehicle. The parameters of the vehicle model are listed in Table 1.  The parameters and constraints of the vehicle tilt model predictive control and the zero-roll-angle control controller were set as follows: T s = 0.02s, N p = 25, Nc = 15, ρ = 1000, Q = diag(10 6, 10 6 ), R = diag(10 −4, 10 −4 ),

Step-Steering Input Maneuver
The vehicle was operated on a class B road at a speed of 80 km/h [31]. The way to produce a random road roughness profile is to let the white noise pass a shaping filter [32]. The step-steering input maneuver was performed at 5 s, and the front-wheel steering angle reached a final value of δ = 1 • at 10 s. The front-wheel steering angle is shown in Figure 3. Figures 4 and 5 show the response curves of the centrifugal and gravity moments, respectively. Under steady-state conditions, the centrifugal moment of the vehicle under tilt control was approximately 1800 Nm, which was slightly larger than the values of 1650 Nm under zero-roll-angle control and 1600 Nm under the passive suspension. For the gravity moment, the passive suspension was 700 Nm, and the gravity moment of the vehicle under tilt control was 1800 Nm, which was exactly equal to the centrifugal moment. Hence, when the vehicle body was actively inclined in the turning direction, the gravity moment generated due to the shift of the CG could completely offset the moment generated by the centrifugal force during the steady state of the turning.

Step-Steering Input Maneuver
The vehicle was operated on a class B road at a speed of 80 km/h [31]. The way to produce a random road roughness profile is to let the white noise pass a shaping filter [32]. The step-steering input maneuver was performed at 5 s, and the front-wheel steering angle reached a final value of 1    at 10 s. The front-wheel steering angle is shown in Figure 3.     Nm under zero-roll-angle control and 1600 Nm under the passive suspension. For the gravity moment, the passive suspension was 700 Nm, and the gravity moment of the vehicle under tilt control was 1800 Nm, which was exactly equal to the centrifugal moment. Hence, when the vehicle body was actively inclined in the turning direction, the gravity moment generated due to the shift of the CG could completely offset the moment generated by the centrifugal force during the steady state of the turning.    Nm under zero-roll-angle control and 1600 Nm under the passive suspension. For the gravity moment, the passive suspension was 700 Nm, and the gravity moment of the vehicle under tilt control was 1800 Nm, which was exactly equal to the centrifugal moment. Hence, when the vehicle body was actively inclined in the turning direction, the gravity moment generated due to the shift of the CG could completely offset the moment generated by the centrifugal force during the steady state of the turning.     Figure 6 shows the response curves of the vehicle's body roll angle. Tilt control and zero-roll-angle control could better track the desired tilt angle and zero, respectively. However, the vehicle's body tilt angle under the active tilt control was opposite to that of the passive suspension, and it tilted inward by 15°.  The steady-state value with the passive suspension was 3.3 m/s 2, while that under zeroroll-angle control was 2.45 m/s 2, which was lower than that of the passive suspension. With the gradual increase in the control force of the active suspension, the occupant's perceived lateral acceleration of tilt control initially fluctuated, with a peak value of approxi-   Figure 7 shows the response curve of the occupant's perceived lateral acceleration. The steady-state value with the passive suspension was 3.3 m/s 2, while that under zero-rollangle control was 2.45 m/s 2, which was lower than that of the passive suspension. With the gradual increase in the control force of the active suspension, the occupant's perceived lateral acceleration of tilt control initially fluctuated, with a peak value of approximately 0.15 m/s 2, and then gradually approached zero. Compared with the other two methods, tilt control greatly improved the ride comfort.  Figure 7 shows the response curve of the occupant's perceived lateral acceleration. The steady-state value with the passive suspension was 3.3 m/s 2, while that under zeroroll-angle control was 2.45 m/s 2, which was lower than that of the passive suspension. With the gradual increase in the control force of the active suspension, the occupant's perceived lateral acceleration of tilt control initially fluctuated, with a peak value of approximately 0.15 m/s 2, and then gradually approached zero. Compared with the other two methods, tilt control greatly improved the ride comfort. The response curves of the LTR of the vehicle are shown in Figure 8. The LTR value of the passive suspension system was 0.21, whereas the LTR value under zero-roll-angle control was 0.15. The variation of the LTR under tilt control was the same as that of the occupant's perceived lateral acceleration. As the control force of the active suspension gradually increased to the steady-state amplitude, the LTR value initially had a peak value of approximately 0.012, and then eventually approached a stable value of 0.0045. Therefore, the LTR value under tilt control was greatly reduced compared with zero-roll-angle control and the passive suspension, which significantly reduced the possibility of vehicle rollover and was able to effectively improve the vehicle's curve negotiating speed. The response curves of the LTR of the vehicle are shown in Figure 8. The LTR value of the passive suspension system was 0.21, whereas the LTR value under zero-roll-angle control was 0.15. The variation of the LTR under tilt control was the same as that of the occupant's perceived lateral acceleration. As the control force of the active suspension gradually increased to the steady-state amplitude, the LTR value initially had a peak value of approximately 0.012, and then eventually approached a stable value of 0.0045. Therefore, the LTR value under tilt control was greatly reduced compared with zero-roll-angle control and the passive suspension, which significantly reduced the possibility of vehicle rollover and was able to effectively improve the vehicle's curve negotiating speed.  Figure 9 shows the control force response curve of the left suspension. Due to space limitations, the control force response curve of the right suspension was omitted, whose amplitude was opposite to that of the left suspension. The steady-state amplitude of the single-side suspension control force under tilt control was 4650 N, while the amplitude of the single-side suspension control force under zero-roll-angle control was 1320 N. The control force on each side of the suspension was supplied by two suspension actuators, that is, each actuator provided half the control force on each side; thus, the control force of the active suspension was within an acceptable range.  Figure 9 shows the control force response curve of the left suspension. Due to space limitations, the control force response curve of the right suspension was omitted, whose amplitude was opposite to that of the left suspension. The steady-state amplitude of the single-side suspension control force under tilt control was 4650 N, while the amplitude of the single-side suspension control force under zero-roll-angle control was 1320 N. The control force on each side of the suspension was supplied by two suspension actuators, that is, each actuator provided half the control force on each side; thus, the control force of the active suspension was within an acceptable range.
limitations, the control force response curve of the right suspension was omitted, whose amplitude was opposite to that of the left suspension. The steady-state amplitude of the single-side suspension control force under tilt control was 4650 N, while the amplitude of the single-side suspension control force under zero-roll-angle control was 1320 N. The control force on each side of the suspension was supplied by two suspension actuators, that is, each actuator provided half the control force on each side; thus, the control force of the active suspension was within an acceptable range. The time response curve of the vehicle yaw rate is shown in Figure 10. "Desired" in the figure represents the desired yaw rate. The y