Quarter car active suspension system: Minimum time controller design using singular perturbation method

Abstract

Suspension systems have been widely applied to vehicles. Every vehicle moving on the randomly profiled road is exposed to vibration and shocks which is harmful both for the passengers in terms of comfort and for the durability of the vehicle itself. From this point of view, it is important to reset to zero displacement, velocity and acceleration of car in minimum time. So, this paper proposes a new minimum time controller based on bang-bang control for the quarter car active suspension systems. First by using singular perturbation method the original suspension system is decomposed into two fast and slow singular subsystems in theory, and then by Pontryagain’s Minimum Principle (PMP) and switching functions, the controller is designed for each subsystem and finally the optimal final time is obtained as maximum optimal time concluded of two subsystems. By using a degree of stability technique with two parameters (instead of four parameters), the optimal time is more reduced and leads to great simplifications in practical implementation. The performance of the controller is compared with the Sub optimal Linear Quadratic Regulator (SLQR) controller using two types of road profiles (step and bump) implemented in MATLAB/Simulink. Test results demonstrate the proposed controller is very more effective and simpler in eliminating fluctuations in suspension systems that finally provide the passengers comfort.