Designing Robust Control for Mechanical Systems: Constraint Following and Multivariable Optimization

Abstract

This article proposes a novel robust control design for mechanical systems based on constraint following and multivariable optimization. The state of the concerned system is affected by (possibly fast) time-varying and bounded uncertainty. The objective is to drive the system to obey a set of prescribed constraints. A $\beta$ -measure is defined to gauge the constraint-following error; based on which, a feedback robust control scheme, which invokes design parameters, is proposed. For the seeking of optimal design parameters, a multivariable constrained optimization problem is formulated. The problem is successfully solved: with the existence, uniqueness , and analytical expression (i.e., closed form) of the optimal design parameters demonstrated. With the optimal parameters, the proposed robust control can render dual performance: guaranteed and optimal. As the guaranteed performance, the $\beta$ -measure is assured to be uniform boundedness and uniform ultimate boundedness. As the optimal performance, the performance index is globally minimized. This article is the first ever endeavour to cast both the constraint following and multivariable optimization into the control framework for uncertain mechanical systems.