Structured H∞ synthesis: A systematic design approach for fully and underactuated systems

Abstract

The task of designing a robust control system using structured H∞ algorithm involves several issues: choosing the system topology, the controller structure and tuning parameters to achieve robust stability and performance. Its application can lead to a trial-and-error approach at some stage. In order to minimize that effort, a methodology is proposed. A step-by-step guide is provided and includes modelling an uncertain system and designing roll-off, notch and setpoint filters aided by singular value analysis. The step of choosing a suitable topology for the control system and the controller structure is accomplished by RGA matrix analysis. Using a mixed-sensitivity approach, the design of weighting functions to achieve desired frequency-based performance is carried out considering plant restrictions. Application of the structured H∞ optimization algorithm is commented and results are validated by means of sensitivity function analysis and nonlinear simulation. A successful study case of control system for tight formation flight is presented which includes nonlinear disturbances, uncertainties, measurement noise, input saturation and restrictions due to RHP poles. Results are compared with those obtained with other robust control techniques.