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

Under-actuated systems are mechanical control systems withfewer controls than the number of configuration variables.Based on recent surveys, control of general under-actuatedsystems is a major open problem. One of the controlmethods that is recommended for controlling these types ofsystems is Controlled Lagrangians (CL) method. Thismethod is a control design approach based on energy. In thispaper, The CL method is investigated for tracking control ofa 2 DOF half-car model with only one actuation. First thesystem is linearized at its equilibrium, then the CL method isused for the linearized system to design its trackingcontroller. The matching conditions satisfied for thecontroller are demonstrated. Solving the matchingconditions, associate controllers are obtained. Thesimulation results verify effectiveness of the proposedmethod.