The problem of robust performance analysis is solved for SISO control systems with uncorrelated model parameter uncertainties. The robust performance problem is formulated in a manner consistent with structured singular value µ-analysis - for SISO systems this means restricting the magnitude of a weighted closed-loop sensitivity function. The solution to the problem is graphical in nature and well suited to a computer-aided controller-design procedure. It utilizes region boundaries on the complex plane that contain specified sets of process models at each frequency. An algorithm is presented for locating the region boundaries corresponding to model transfer-functions with uncertain real coefficients and time-delay. Convergence and containment properties of the algorithm are proven.
The region-based analysis is combined with the Internal Model Control design procedure to form a controller synthesis method for robust performance. Tradeoffs between performance and robustness are transparent to the designer in the proposed synthesis method. Useful tables of controller parameters are presented in tabular form for a wide range of parameter uncertainty levels in a first-order-with-time-delay model. The controller resulting from the IMC design procedure is compared with the µ-optimal controller. Although the new synthesis procedure is generally applicable to SISO systems, it can be used to design decentralized controllers for MIMO systems with uncertain scalar dynamics and symmetric interactions. The particular application of cross-machine-direction basis-weight control in paper manufacturing is discussed in detail. Robust performance and robust failure tolerance of desirable decentralized controllers for this system are proven.
