Feedback linearization of ABS with time delay input using adaptive sliding mode control

Abstract

In many proposed controllers of anti-lock braking system, there exist a lot of control methods such as backstepping, gain-scheduling, sliding mode control, robust PID control, and complex control. However, in those solutions, the time delay input is not considered in modeling the anti-lock braking system. In practice, there exists the time delay on the input caused by the communication of sensors and the response time of the actuator. Thus, in this thesis, we adopt the time delay input in modeling the anti-lock braking system. Using the linear transformation based on the reduction method suggested by Kwon, we compensate the time delay with feedback linearization and adaptive sliding mode control. Applying the feedback linearization, the exact cancelation does not take place because of time delay input. We regard the remained term by feedback linearization as uncertainty in a viewpoint of the design of the controller. The uncertainties appeared by feedback linearization is confirmed that the norm of the uncertainties is bounded, and then we design the adaptive sliding mode controller as adapting the value of the uncertainties. The upper bound of the uncertainties is not fixed about the parameters of the anti-lock braking system. We do not know the upper bound of the uncertainties exactly, using the adaptive controller, we adapt the value of the upper bound. Then, the adaption value is used in the switching controller gain of the sliding mode controller. In the design process of anti-lock braking system controller, we need full states, vehicle velocity and angular velocity of the wheel, but the measurable output is just wheel angular velocity. Thus we have to design the observer for estimating the vehicle velocity. In this situation, a sliding mode observer for the nonlinear model of anti-lock braking system is proposed. In the design process, we make the sliding mode observer based on Lyapunov techniques. Finally, we simulate the designe...