Application of Genetic Algorithm for Synthesis of H_∞ Controllers for Active Magnetic Bearing Systems

Abstract

This paper discusses designing of weights for both mixed-sensitivity and signal-based H_∞ controller synthesis for active magnetic bearing (AMB) systems using genetic algorithm (GA) optimization. In mixed-sensitivity problem formulation, the weights represent desired upper bounds to closed loop transfer functions and in signal-based problem formulation, the weights represent desired system response under sinusoidal exogenous inputs. In order to cast weight design process as an optimization problem, appropriate cost functions are chosen to guarantee that desired performance objectives are satisfied with a stable controller. First, the validity of the method is demonstrated in simulation by comparing performances achieved using weights designed through the optimization to the weights selected as performance objectives. Then, the weight design via GA for H_∞ controller synthesis is tested experimentally on a small AMB test rig in a disturbance rejection scheme. The designed H_∞ controllers are implemented on the AMB system and tested up to the maximum design speed of 6000 rpm, where the rotor safely passed the first critical speed. Achieved performances are compared to a benchmark PID controller. Results demonstrate validity of using GA for weights design and show the superiority of H_∞ controllers over PID controller for disturbance rejection in AMB systems.