Robust Nonlinear State Feedback Under Structured Uncertainty

Introduction For all but the simplest control schemes to be effective, some description of the process to be controlled must be available. Usually this description is a mathematical model. However a series of difficulties may be encountered while developing a meaningful and realistic mathematical description of the chemical process. Thus for most processes, a “reasonable model” with some “good” values for the model parameters is employed for control purposes. The mismatch between the mathematical model and the true process can lead to serious stability problems for the process, especially when the process is nonlinear. Thus the design of robust control strategies that take care of model uncertainty is of paramount importance for the design of good and efficient control systems for a chemical process. One of the most important contributions in control theory in the past decade has been the development of robust linear controller design methodologies for linear plants in the presence of unstructured uncertainty (Doyle and Stein, 1981). This approach can be applied to the control of nonlinear plants as well, with the understanding that the uncertainty will contain the error introduced by the linear approximation. The key issue is whether the linear approximation error will be small or not. In the case of mild nonlinearities, the uncertainty introduced by the linearization approximation is small enough so that it can successfully be rejected by a robust linear controller without too much sacrifice in performance. In the case of a highly nonlinear process, the frequency domain bounds corresponding to the linear approximation error will be very loose; they will contain not only the nonlinear uncertainties but also a very large class of unstructured uncertainties that fall within these bounds. This will lead to conservativism and therefore poor performance. Thus robust linear control theory is insufficient for highly non-