A Lyapunov Stability Analysis of Modified HOSM Controllers Using a PID-Sliding Surface Applied to an ABS Laboratory Setup

Abstract

The antilock braking system (ABS) is a mechatronic system that helps a driver maintain the maneuverability of a vehicle while braking by preventing wheel lock-ups. However, the design of high-performance controllers for this type of system is complicated because of its highly nonlinear dynamics. The problem becomes even more difficult to resolve when uncertainties in the parameters appear in its dynamics. In this paper, an ABS laboratory setup mimicking a quarter car model is considered. A modified high-order sliding mode (HOSM) controller using a proportional-integral-differential (PID) control as a sliding surface was designed. This controller provides a reference value of a tire slip. The proposed controller uses a tracking error to define the slip surface through the PID controller structure, and the modified HOSM controller holds the system on the previously designed slip surface. The closed-loop system stability has been proven in the sense of Lyapunov. Finally, the ABS laboratory setup allows for experimentally checking the performance of the modified HOSM controller using a PID-sliding surface, showing a considerable increase in the efficiency of the control system compared with a PID-like controller.