Dynamic modeling and optimal robust approximate constraint-following control of constrained mechanical systems under uncertainty: A fuzzy approach

Abstract

A novel and systematic approach for dynamic modeling and approximate constraint-following servo control of con- strained mechanical systems under uncertainty is proposed. Fundamental equation of constrained mechanical systems is first obtained based on Udwadia-Kalaba approach which is applicable to holonomic and nonholonomic constrained systems no matter whether they satisfy the D'Alember's principle. The uncertainty (possibly fast time-varying) in mechanical systems is bounded and the bound is unknown. Fuzzy set theory is used to describe the unknown bound. The performance requirement is modeled as servo constraints in second-order form. A model-based robust control is presented to approximately follow the servo constraints. The proposed control is deterministic and is not IF-THEN rules-based. The uniform boundedness and uniform ultimate bounded- ness of the tracking error are guaranteed, regardless of the uncertainty. A performance index (the combined cost, which includes average fuzzy system performance and control effort) is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved (explicitely or numerically) by minimizing the performance index. The resulting control design is systematic and is able to guarantee the deterministic performance as well as minimizing the cost.