Tracking Control of an Under-actuated Half-Car Model based on Controlled Lagrangians Method

Under-actuated systems are mechanical control systems with fewer controls than the number of configuration variables. Based on recent surveys, control of general under-actuated systems is a major open problem. One of the control methods that is recommended for controlling these types of systems is Controlled Lagrangians (CL) method. This method is a control design approach based on energy. In this paper, The CL method is investigated for tracking control of a 2 DOF half-car model with only one actuation. First the system is linearized at its equilibrium, then the CL method is used for the linearized system to design its tracking controller. The matching conditions satisfied for the controller are demonstrated. Solving the matching conditions, associate controllers are obtained. The simulation results verify effectiveness of the proposed method.