Identification and control of non-linear distributed parameter systems

Automatic control has become an important aspect of engineering and science ever since James Watt invented the centrifugal governor to control the speed of a steam engine in the 18th century.; Many chemical processes like heat exchangers, tubular reactors, chromatographic columns continuous pulp digesters etc., are distributed parameter systems (DPS) described by partial differential equations (PDEs) and exhibit some degree of nonlinearity. To deal with the nonlinear dynamics and the distributed nature in a simpler setting, the PDEs are discretized to obtain ordinary differential equations and the nonlinearities are linearized. The resulting equations are usually easy to analyze and use in controller design. However, stringent environmental regulations and intense economic competition call for a higher degree of optimization of complex chemical processes. Linear and discretized models cannot achieve the higher level of expectations as they present an oversimplified model of the actual operation. Therefore, it is necessary to study nonlinear DPS processes with minimum approximations on the process dynamics.; The controller design methods for nonlinear DPS can be divided into two categories based on the method of obtaining a model for the process. (1) Fundamental model approach: The methods use fundamental models either by reducing or transforming the differential equations into a suitable form for controller design. (2) Input-output data approach: Input-output data is used to derive nonlinear models. Identification of such models is often a “black-box” approach where the parameters of the model do not have any physical representation.; The work in this dissertation makes contributions towards finding a control law for nonlinear DPS using both approaches. The fundamental approach is based on the connection between the geometric nature of the system of equations and algebraic group theory and is applicable to any nonlinear distributed process equations without any approximations on the equations itself.; The input-output data approach designs controllers based on nonlinear Wiener models. A structure for multi-input multi-output (MIMO) Wiener models is suggested and a recursive algorithm developed to identifying the parameters. The model developed is used to describe the dynamics of a continuous pulp digester. Model Predictive Control (MPC) using the MIMO Wiener model controls the reaction profile in the digester. Control strategies used for chip level control in the digester were also studied.