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On robust control of a class of nonlinear mechanical systems with parametric uncertainty

This article presents a method to design a robust controller for a class of nonlinear mechanical systems. The parameters of the system are assumed uncertain in the sense that they are known only within intervals of known lower and upper limits. The method involves using Kharitonov stability theory of interval polynomials to design a robust stabilising controller for the considered class of systems. To formulate the interval parameter problem in joint space, the dynamic equation, which is derived in Cartesian space for parallel kinematic machines, is transformed to joint space using the Jacobian matrix and its time derivative. The nonlinear joint space model is linearised yielding an interval linear model and a robust controller with interval parameter gains is then found. A simulation study on a dynamic model of Stewart platform based parallel kinematics machine demonstrates the design procedure and shows its effectiveness.