Control of Parameter-Dependent Mechanical Systems

This dissertation considers the application of recent robust control techniques to parameter-dependent mechanical systems. Particular emphasis is placed on the study of exible dynamic systems that possess lightly-damped, parameter-dependent, resonances at frequencies that are within the bandwidth of the controller. A detailed examination of an example system, highlighting the complexities associated with the control of these systems, is motivated. The applicability of robust control techniques that are based on stabilising unstructured neighbourhoods characterised by the gap and -gap metrics is examined. Particular di culties arising when these techniques are applied to the chosen class of systems are highlighted, and it is shown how the frequency-response interpretation permitted by the -gap metric can be used to overcome them. For systems that undergo large parameter variations, it is shown how controllers can be designed for each of the sets in a nite cover of the parameter space. Switching techniques based on real-time parameter measurements are used to switch between the controllers. The issues of bumpless transfer and reference signal injection are addressed through the use of appropriate coprime factorisations of the controllers. An experimental facility is developed to evaluate the applicability of these control techniques on a real system. The importance of the tradeo between robustness and performance is demonstrated, as is the e ectiveness of the switching methodology at achieving bumpless transfer. It is shown that the chosen robust control approach can be used to obtain controllers that achieve a high level of performance while still being robust to time-varying parametric perturbations. New model-reduction techniques are developed, allowing balanced truncation to be extended to bounded-rate, linear, parameter-varying systems. These are based on the solutions of various parameterdependent Lyapunov and Riccati di erential inequalities, the latter allowing both stable and unstable systems to be factorised, enabling the symbol of the system's graph can be approximated. Generalisations of known error bounds for balanced truncation of time-invariant systems are examined. Techniques for solving the di erential inequalities are considered, and procedures for computing the balancing transformation developed. Analytical techniques for synthesising gain-scheduled controllers for parameter-varying systems are extended by allowing explicit rate-bounds to be incorporated into the synthesis, thus reducing conservatism. A speci c four-block synthesis setup is considered in some detail and shown to result in a particularly transparent solution. Direct connections are made between this four-block setup and the model-reduction techniques. An e cient procedure for the synthesis of reduced-order controllers in the four-block setup is developed. The techniques are successfully demonstrated on a missile autopilot design.