Robust control of multivariable nonlinear systems

The chemical industry has traditionally relied on linear control laws (PI and PID control algorithms) for process control. However, these controllers do not perform satisfactorily in the presence of severe nonlinearities and parametric uncertainty. Nonlinearities appears very often in chemical process models derived either from first principles (e.g. Arhenius relation, radiation heat transfer) or empirically (e.g. power law models, Michaelis-Menten models). Furthermore, the process parameters (e.g. reaction rates, heat transfer coefficients) in the model are not exactly known; this introduces uncertainty in the model. Hence advanced model based process control algorithms are needed to design robust controllers which guarantee not only nominal stability and performance, but also robustness in the face of these uncertainties. This dissertation focuses on the development of systematic procedures for the design of such robust controllers for input-output linearizable nonlinear processes.; Robust control of nonsquare nonlinear systems are developed in three stages. First, a methodology for Input/Output linearization of nonsquare systems is developed. It is shown that by using all available manipulated inputs for each control variable one can reduce the control effort significantly. Linearization is achieved by use of a pseudo-inverse which incorporates the optimal cost of the inputs. In the second stage a controller design strategy for robust control of SISO systems is developed. In the presence of uncertainties, I/O methodology leads to inexact linearization and results in loss of performance and stability. A controller design methodology is developed based on Input/Output linearization and multi-objective $H2/H\infty$ synthesis that ensures robust stability and performance. Finally, these two methodologies are combined to design robust controller for nonsquare nonlinear systems. The performance of the three controllers is illustrated via simulation of regulation problems in a Continuous Stirred Tank Reactor.