Analysis and identification of robust linear models for multivariable control

Abstract

<p>This study considers control problems associated with robust stability and performance of linear, time-invariant multivariable controllers. The robust stability and performance problems considered here are determined exclusively by the steady-state properties of closed-loop systems, and therefore they are independent of controller design and tuning methods. New approaches, one based on geometric interpretations and the other on singular value decomposition, are proposed to analyze the effects of steady-state model mismatches. The new analysis approaches are able to distinguish the critical differences between a process and its model that cause the control problems, and to identify the crucial process characteristics that must be preserved in the model if the closed-loop system is to be robust. This study shows that these properties are related to specific geometric differences and to particular elements in the singular value decomposition matrices, and that it is the structure rather than the magnitude of multivariate model mismatch that dominates the robustness properties. These results explain the fact that many nonlinear processes can be controlled by linear controllers with robustness over a wide range of operating conditions, in spite of the large mismatch magnitudes arising from process nonlinearities. Physical examples of these processes are given in this thesis. The analysis results are also used to specify new criteria for experimental designs to identify linear models that lead to robust multivariable controllers. The new experimental designs are based on minimizing model uncertainities in the multivariate model structure rather than simply the mismatch magnitude. The significance of the new experimental design approach is that it can identify robust models that yields high-performance control even for ill-conditioned processes. These robust identification designs usually require input perturbations that are drastically different from traditional designs.</p>