Robust Nonlinear $\small{H_2}$/$\small{H_{\infty}}$Control for a Parallel Inverted Pendulum

Title & Authors
Robust Nonlinear $\small{H_2}$/$\small{H_{\infty}}$Control for a Parallel Inverted Pendulum
Han, Seong-Ik; Kim, Jong-Sik;

Abstract
A robust nonlinear $\small{H_2}$/$\small{H_{\infty}}$ control method for a parallel inverted pendulum with structured perturbation and dry friction is proposed. By the random input describing function techniques, the nonlinear dry friction is approximated into the quasi-linear system. Introducing the quadratic robustness theorem, the robust $\small{H_2}$/$\small{H_{\infty}}$ control system is constructed for the quasi-linear perturbed system. But it is difficult to design a controller due to the nonlinear correction term in Riccati equation. With some transformations on the Riccati equation containing nonlinear correction term, the design of the robust nonlinear controller can be done easily. Hence when the stiffness and mass of the parallel inverted pendulum vary in certain ranges, the proposed control scheme has the robustness for both the structured perturbation and dry friction. The results of computer simulation show the effectiveness of our proposed control method.
Keywords
Parallel Inverted Pendulum;Describing Function;$\small{H_2}$/$\small{H_{\infty}}$ Control;Dry Friction;
Language
Korean
Cited by
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