Abstract
A robust nonlinear H2/H∞ control method is presented for a parallel inverted pendulum system with uncertain parameters and dry friction. The dry friction is quasi-linearized into a describing function model by the random input describing function technique, and the uncertain system under consideration is described by state equations that depend on time invariant, unknown-but-bounded, uncertain parameters. Then, the robust nonlinear H2/H∞ control system that establishes the stability of the closed loop system in face of the nonlinear dry friction and uncertain parameters was constructed. However, it is difficult to solve coupled Riccati equations due to the nonlinear correction term contained in the Riccati equations. Thus, it is shown that the Riccati equations can be solved by some algebraic transformations of the coupled Riccati equations. This result enables robust nonlinear controllers to be designed easily. Hence, if the parameters of the parallel inverted pendulum vary as certain bounds, the proposed control has the robustness to both the system parameter variations and the nonlinear dry friction.
