ANALYSIS OF LINEAR CONTROL FOR NONLINEAR SYSTEM: CONTINUOUS STIRRED TANK REACTOR (CSTR)

Linear control may be favorable over nonlinear control because linear design techniques greatly facilitate the controller design process and because linear controllers impose lower requirements on the implementation and operation as compared to nonlinear controllers. It is therefore a tempting idea to use linear models and linear controller design methods also for nonlinear systems. It is for instance common practice in control engineering to use models obtained from linearization instead of complete nonlinear models. However, in order to guarantee the suitability of a linear model or the proper functioning of a linear controller in presence of the model due to linearization, a rigorous justification is required. This dissertation presents a general framework to design linear controller for nonlinear system based on linear model that guarantees stability for the nonlinear closed loop. Prior to controller design, a nominal linear model has to be derived. While the linearization is a common choice as a linear model for a nonlinear system, it does not need to be the best choice for a given region of operation. This dissertation has two main areas of contribution. The first area is the derivation and assessment of linear model for nonlinear system and the second area is the utilization of this information for controller design. The main contribution of the first part of this dissertation is to identify a novel unifying framework for nonlinearity assessment. In the second part of this dissertation, stability conditions and controller design procedures for linear control of nonlinear systems are presented. The results of this dissertation build a bridge between nonlinearity assessment and control theory. The key feature of the proposed methods is thereby to bring together nonlinearity measures, the development and assessment of linear models for nonlinear systems and the design of linear controllers for nonlinear systems under a unifying framework

ANALYSIS OF LINEAR CONTROL FOR NONLINEAR SYSTEM: CONTINUOUS STIRRED TANK REACTOR (CSTR)

Linear control may be favorable over nonlinear control because linear design techniques greatly facilitate the controller design process and because linear controllers impose lower requirements on the implementation and operation as compared to nonlinear controllers. It is therefore a tempting idea to use linear models and linear controller design methods also for nonlinear systems. It is for instance common practice in control engineering to use models obtained from linearization instead of complete nonlinear models. However, in order to guarantee the suitability of a linear model or the proper functioning of a linear controller in presence of the model due to linearization, a rigorous justification is required. This dissertation presents a general framework to design linear controller for nonlinear system based on linear model that guarantees stability for the nonlinear closed loop. Prior to controller design, a nominal linear model has to be derived. While the linearization is a common choice as a linear model for a nonlinear system, it does not need to be the best choice for a given region of operation. This dissertation has two main areas of contribution. The first area is the derivation and assessment of linear model for nonlinear system and the second area is the utilization of this information for controller design. The main contribution of the first part of this dissertation is to identify a novel unifying framework for nonlinearity assessment. In the second part of this dissertation, stability conditions and controller design procedures for linear control of nonlinear systems are presented. The results of this dissertation build a bridge between nonlinearity assessment and control theory. The key feature of the proposed methods is thereby to bring together nonlinearity measures, the development and assessment of linear models for nonlinear systems and the design of linear controllers for nonlinear systems under a unifying framework

A unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback

We study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties. Our approach relies on well-known H-infinity linear control tools and allows one to recover and improve, in the unifying framework of a semiglobal separation result, existing results on the semiglobal stabilization via output feedback. In particular, we discuss the case of uncorrupted outputs, input and output nonlinearities, or model uncertainties, which may include, for example, practical situations such as backlash, hysteresis, and saturations. The key feature of our design procedure is given by the choice of two continuous functions: the first one is instrumental in constructing a stabilizing controller; the second one arises in the candidate Lyapunov function for the closed-loop system. Relying on our main theorem, we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems