Modelling of signal uncertainty and control objectives in robust controller design

摘要

This work develops a new paradigm for optimal robust controller synthesis in the frequency domain. A detailed examination is made of the engineering motivation and engineering efficacy underlying the various strands of robust control theory. The modelling of (a) signal uncertainty and (b) control system objectives in both Tioo and C control theories is considered in particular detail. Based on this examination, a theory which can fa irly be described as ‘a m odified 7ioo control theory’ or ‘a frequency domain C control theory’ is proposed. New signal sets for the modelling of uncertain signals are introduced. It is argued that these models more faithfully capture the way in which uncertain signals act on real physical systems. It is shown that by adopting these new models for uncertain signals, control theory can be used toudnon-conservatively minimise maximum tracking errors in the time domain, in the SISO case. In the MIMO case, the problem of optimally synthesising a controller to non-conservatively minimise tracking errors in the time domain leads to a modest variation on existing control theory, requiring the usual norm to be modifiedudslightly. It is argued th a t the proposed paradigm in general achieves a better quality of control and more fa ith fu lly expresses the true objectives of feedback control systems. The proposed development is seen to also extend naturally to Ti.2 control theory, and indeed provides a new deterministic justification for the 7^2 control problem in the MIMO case.ududThe question of design transparency in the synthesis of optimal robust controllers for multivariable systems is considered in detail. The implications of the proposed paradigm for transparency of design and weighting function selection are detailed. A decoupling design procedure for robust controller synthesis is proposed which, under certain restrictive conditions, allows the calculation of super-optimal robust controllers on a loop by loop basis. The usefulness of a classical decoupling approach to MIMO control system design in the context of multivariable robust control theory is demonstrated.ududA number of design examples are presented which show how the ideas and methods developed in this work can be applied to realistic control problems.