Gain‐scheduling control of a rotary inverted pendulum by weight optimization and H ∞ loop shaping procedure

Gain‐scheduling control is an effective method for use with plants whose dynamics change significantly according to the operating point. The frozen parameter method, a practical gain‐scheduling controller synthesis method, interpolates the controllers designed at prespecified (frozen) operating points according to the current operation point. Hyde and Glover proposed a gain‐scheduling control method in which the H∞ loop shaping procedure is adopted as a controller synthesis method at each operating point. The 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 numbers. However, weight selection satisfying the control specifications is a difficult job for a designer. This paper describes the design of suboptimal weights and a controller by means of an algorithm that maximizes the robust stability margin and shapes the open‐loop characteristic into the desired shape at each operating point. In addition, we formulate the weight optimization problem as a generalized eigenvalue minimization problem, which reduces the burden on the designer in weight selection. Finally, we realize a robust, 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 the experimental time responses of a rotary inverted pendulum, which involves strong nonlinear dynamics. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(2): 30–40, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20647