ON INTERVAL CONTROL OF PARALLEL KINEMATIC MACHINES

This paper presents a method to design a robust controller for interval parallel kinematic machines. The method involves using a systematic approach to design a robust stabilizing controller for a parallel kinematic machine that can be described by nonlinear second order differential equation with interval parameters. 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 linearized yielding an interval linear model and a controller with interval parameter gains is then found. A numerical study on a dynamic model of Stewart platform based parallel kinematics machine demonstrates the design procedure and shows its effectiveness. In the study, the model is simulated assuming lower and upper limits for some of the parameters.