Stabilization of Rotary Inverted Pendulum by Gain-scheduling of Weight and H∞ Loop Shaping Controller

Gain-scheduling control is one of effective methods for plants whose dynamics changes significantly according to its operating point. A frozen parameter method is known to be a practical gain-scheduling controller synthesis, which interpolates the controllers designed at the prespecified (frozen) operating points according to the current operation point. Hyde et al. proposed a gain-scheduling control that H_∞ loop shaping procedure is adopted as a controller synthesis at each operating point. H_∞ loop shaping procedure is based on loop shaping of an open loop characteristic by frequency weights and is known to be effective for plants with bad condition number. However, weight selection satisfying control specifications is a hard job for a designer. This paper describes the design of a suboptimal weight and a controller by means of algorithm that maximizes the robust stability margin and shapes the open loop characteristic into the desired shape at each operating point. Moreover, we formulate a weight optimization problem as a generalized eigenvalue minimization problem, which reduces the designer´s burden of weight selection. Finally, we realize robust and high performance control system by scheduling both weights and controllers. The effectiveness of the proposed control system is verified in terms of the achieved robust stability margin and experimental time responses of a rotary inverted pendulum which involves strong nonlinear dynamics