Robust control system design with application to high performance helicopters

This thesis presents one of the first applications of H∞-optimization to the design of controllers for industrial problems. The system considered was an unstable helicopter model, obtained from a large nonlinear simulation (provided by the Royal Aircraft Establishment, Bedford) configured to represent future high performance helicopters. The problem was to design a full authority flight control system, to stabilize the aircraft and decouple the controlled inputs, thus reducing pilot workload. Robustness was a primary issue because of model uncertainty, particularly due to the omission from the design model of higher order rotor dynamics. The optimization problem was based on the minimization of sensitivity (for performance) and control output (for robustness) transfer functions. Simple weighting functions were found to be useful for examining the fundamental performance-versus-robustness trade-off, and to be more effective at shaping the closed loop transfer functions than LQG/LTR techniques. A controller designed for a 4-input, 6-output, 8-state linearized plant model was successfully implemented in a non-linear simulation with rotor dynamics. This stabilized the system and enabled good control for small variations about the design operating point. The 'standard problem', consisting of the plant augmented with weights, had 20 states; the controller had 18, which was much smaller than researchers had been predicting, and it is conjectured that all H∞-optimal controllers will have at most the same number of states as the defining 'standard problem'. An important improvement to the H∞-optimization solution process was the development of a numerically reliable algorithm to perform minimal realization. This algorithm solves for a truncated balanced realization of stable state-space systems that are arbitrarily close to being either uncontrollable and/or unobservable. Depending on the choice of partitioning of the Hankel singular values, it can be used to perform minimal realization, or model reduction, with a guaranteed L∞error bound.