In this thesis we propose to improve the performance of the standard single degree-of-freedom under-damped mass-spring-damper (MSD) system using variable structure control. Two controllers are proposed: both of them switch the parameters of the system between their nominal values and their negative values. This approach results in a hybrid system comprised of the nominal system, which is asymptotically stable, and an unstable system. The first controller is based on switched stiffness whereas the second controllers is based on switched stiffness and damping. For both controllers, the parameters are switched based on the location of the system in its configuration space. A phase portrait analysis indicates that the resulting hybrid systems are asymptotically stable although they switch between an asymptotically stable and an unstable system. A comparison of the step response of the hybrid systems with that of the original under-damped system indicates that the switched systems have better performance in terms of rise time, settling time, and reduced or no overshoot. Different designs of the switching logic have been investigated and they provide clues on how the switching logic can be designed to achieve the maximum improvement in performance.
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