Quarter Car Active Suspension System: Minimum Time Controller Design Using Singular Perturbation Method

Quarter Car Active Suspension System: Minimum Time Controller Design Using Singular Perturbation Method

Suspension systems have been widely applied to vehicles. Every vehicle moving on the randomly profiledroad is exposed to vibration and shocks which is harmful both for the passengers in terms of comfort andfor the durability of the vehicle itself. From this point of view, it is important to reset to zero displacement, velocityand acceleration of car in minimum time. So, this paper proposes a new minimum time controller basedon bang-bang control for the quarter car active suspension systems. First by using singular perturbation methodthe original suspension system is decomposed into two fast and slow singular subsystems in theory, and then byPontryagain’s Minimum Principle (PMP) and switching functions, the controller is designed for each subsystemand finally the optimal final time is obtained as maximum optimal time concluded of two subsystems. By using adegree of stability technique with two parameters (instead of four parameters), the optimal time is more reducedand leads to great simplifications in practical implementation. The performance of the controller is compared withthe 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 andsimpler in eliminating fluctuations in suspension systems that finally provide the passengers comfort.

Suspension systems have been widely applied to vehicles. Every vehicle moving on the randomly profiledroad is exposed to vibration and shocks which is harmful both for the passengers in terms of comfort andfor the durability of the vehicle itself. From this point of view, it is important to reset to zero displacement, velocityand acceleration of car in minimum time. So, this paper proposes a new minimum time controller basedon bang-bang control for the quarter car active suspension systems. First by using singular perturbation methodthe original suspension system is decomposed into two fast and slow singular subsystems in theory, and then byPontryagain’s Minimum Principle (PMP) and switching functions, the controller is designed for each subsystemand finally the optimal final time is obtained as maximum optimal time concluded of two subsystems. By using adegree of stability technique with two parameters (instead of four parameters), the optimal time is more reducedand leads to great simplifications in practical implementation. The performance of the controller is compared withthe 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 andsimpler in eliminating fluctuations in suspension systems that finally provide the passengers comfort.