A robust <i>H</i> ^∞ model reference tracking design for non-holonomic mechanical control systems

Abstract

We propose a robust model reference tracking control design for non-holonomic mechanical systems under parametric perturbation and external disturbance. A design procedure with three-stage control is developed to solve the robust tracking problem for perturbative non-holonomic mechanical control systems. In the first stage, by a proper choice of transformation matrix, the perturbative non-holonomic mechanical system is transformed into a reduced form of non-holonomic mechanical system for the convenience of control design. In the second stage, based on the concept of ‘input/output decoupling’ in nonlinear control theory, a decoupled system with parameter perturbation and external disturbance is established via a nonlinear dynamic state feedback control. In the third stage, H ∞ criteria to specify desired model reference tracking performance in the face of parametric perturbation and external disturbance are proposed for the decoupled system. H ∞ controllers that achieve these H ∞ tracking performance are also explicitly constructed. Finally, two typical non-holonomic examples—a knife edge and a vertical wheel moving on a given plane—are given with computer simulation to illustrate the significant advantages of the proposed method.