A nonlinear H_∞control design in robotic systems under parameter perturbation and external disturbance

Abstract

A state feedback H∞optimal disturbance attenuation for the model reference control of rigid robotic systems is studied. The disturbances affecting the system dynamics come from the residue of the applied torques due to perturbations of the system parameters and external noise. The design objective is that the disturbance attentuation level must be less than or equal to a desired positive value γ. By combining the nonlinear minimax control technique with the work of Johansson (1990) we are able to present an explicit global solution to this nonlinear time-varying H∞ -control problem. In particular, it turns out that if y, the desired attenuation level, is greater than the magnitude of the weighting matrix on control inputs, then a state feedback law achieving the desired performance can be explicitly constructed. Hence, it is advantageous to consider our approach for H∞ tracking control of other physical systems, Finally, extensive simulations are made for tracking control of a two-link robotic manipulator with the proposed H∞ designs.