Control of Mechanical Systems Subject to Unilateral Constraints
نویسندگان
چکیده
In this work we consider the problem of control of mechanical systems subject to unilateral constraints. Impulsive forces arise whenever the constraints become active and these forces give rise to nonsmooth dynamics. The dynamics of the system is de ned by a set of di erential equations with discontinuous righthand side using Hamilton's equations of motion. A nonlinear transformation is applied and the dynamics of the system is written in two sets of di erential equations in the transformed coordinates. The rst set of equations has the constraint force terms and the second set has only the free motion variables. Three di erent phases (inactive, transition and active) for the system are formulated depending on the activation/deactivation of the constraints. A discontinuous controller is designed for the three phases. Stability analysis is conducted for all the phases using tools like Filippov's di erential inclusions, nonsmooth Lyapunov analysis and generalized gradients. We give an illustrative example for the theory developed.
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