Static H∞ loop shaping real-time control of a double inverted pendulum system

This paper introduces a simple technique for designing a static H∞ loop shaping controller. Sufficient conditions are established in Linear matrix inequality (LMI) form for the existence. The order of controller is equal to sum of the orders of the weighing functions. The genetic algorithms (GA) which guarantee the stability, performance in terms of H∞ specifications, are adopted to optimize the loop-shaping weighing functions. It is avoided to select the weighing functions by a trial-error method based on the designer's experience. So the paper introduces a systemic technique for designing a low order H∞ loop shaping controller. Real-time experimental results on a double inverted pendulum (DIP) system demonstrate the validity and applicability of the proposed approach.