μ-Synthesis Robust Control: What's wrong and how to fix it?

Abstract

The theory of /spl mu/-synthesis introduced in [1, 2] provides, in principle, a broadly applicable theory for the optimal synthesis of multiloop feedback control laws that robustly meet performance and disturbance attenuation specifications despite unknown-but-bounded nonlinearities and parameter variations. Commercial MATLAB-based software packages implementing a crude approximation to the theory are available [3, 4], but these computer packages address the complex /spl mu/-synthesis problem via a somewhat flawed implementation of the original D-K iteration algorithm which involves the repetition of the following three operations on a suitable augmented closed-loop system transfer function: 1. Optimize a diagonal scaling frequency response matrix D(jw) for a fixed control law K(s). 2. Perform an ad hoc state space curve-fit to D(jw). 3. Use H/sup /spl infin// control to compute a control law K(s) with the diagonal scaling D(s) fixed. The curve-fitting of Step 2 has, until now, been a major obstacle to the realization of the original vision of a completely automated /spl mu/-synthesis procedure for robust control design. This paper describes new theoretical results and how they enable one to bypas the difficult and awkward curve-fitting of Step 2. The result is the first reliable computational algorithm for /spl mu/-synthesis controller design. The technique has been implemented on MATLAB. An example involving real /spl mu/-synthesis for the ACC Benchmark problem is included.