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Predictive control has attracted much attention from both industry and academia alike due to its intuitive time domain formulation and since it easily affords adaption. The time domain formulation enables the user to build in prior knowledge of the operating constraints and thus the process can be controlled more efficiently, and the adaptive mechanism provides tighter control for systems whose behaviour changes with time. This thesis presents a fusion of technologies for dealing with the more practical aspects of obtaining suitable models for predictive control, especially in the adaptive sense. An accurate model of the process to be controlled is vital to the success of a predictive control scheme, and most the of work to date has assumed that this model is of fixed order, a restriction which can lead to poor controller performance associated with under/overparameterisation of the estimated model. To overcome this restriction a strategy which estimates both the parameters and the order of a linear model of the time-varying plant online is suggested. This Multiple Model Least-Squares technique is based on the recent work of Niu and co-workers who have ingeniously extended Bierman's method of UD updating so that, with only a small change to the existing UD update code, a wealth of additional information can be obtained directly from the U and D matrices including estimates of all the lower order models and their loss functions. The algorithm is derived using Clarke's Lagrange multiplier approach leading to a neater derivation and possibly a more direct understanding of Niu's Augmented UD Identification algorithm. An efficient and robust forgetting mechanism is then developed by analysing the properties of the continuous-time differential equations corresponding to existing parameter tracking methods. The resulting Multiple Model Recursive Least-Squares estimator is also ported to the δ-domain in order to obtain models for predictive controllers that employ fast sampling. The MMRLS estimator is then used in an adaptive multiple model based predictive controller for a coupled tanks system to compare performance with the fixed model order case.

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Process control has been playing an increasingly important role in many industrial applications as an effective way to improve product quality, process costeffectiveness and safety. Simple linear dynamic models are used extensively in process control practice, but they are limited to the type of process behavior they can approximate. It is well-documented that simple nonlinear models can often provide much better approximations to process dynamics than linear models. It is evident that there is a potential of significant improvement of control quality through the implementation of the model-based control procedures. However, such control applications are still not widely implemented because mathematical process models in model-based control could be very difficult and expensive to obtain due to the complexity of those systems and poor understanding of the underlying physics. The main objective of this thesis is to develop new approaches to modeling and control of nonlinear processes. In this thesis, the multivariable nonlinear processes are approximated using a model with a static nonlinearity and a linear dynamics. In particular, the Hammerstein model structure, where the nonlinearity is on the input, is used. Cardinal spline functions are used to identify the multivariable input nonlinearity. Highlycoupled nonlinearity can also be identified due to flexibility and versatility of cardinal spline functions. An approach that can be used to identify both the nonlinearity and linear dynamics in a single step has been developed. The condition of persistent excitation has also been derived. Nonlinear control design approaches for the above models are then developed in this thesis based on: (1) a nonlinear compensator; (2) the extended internal model control (IMC); and (3) the model predictive control (MPC) framework. The concept of passivity is used to guarantee the stability of the closed-loop system of each of the approaches. In the nonlinear compensator approach, the passivity of the process is recovered using an appropriate static nonlinearity. The non-passive linear system is passified using a feedforward system, so that the passified overall system can be stabilized by a passive linear controller with the nonlinear compensator. In the extended IMC approach, dynamic inverses are used for both the input nonlinearity and linear dynamics. The concept of passive systems and the passivity-based stability conditions are used to obtain the invertible approximations of the subsystems and guarantee the stability of the nonlinear closed-loop system. In the MPC approach, a numerical inverse is implemented. The condition for which the numerical inversion is guaranteed to converge is derived. Based on these conditions, the input space in which the numerical inverse can be obtained is identified. This constitutes new constraints on the input space, in addition to the physical input constraints. The total input constraints are transformed into linear input constraints using polytopic descriptions and incorporated in the MPC design.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references and index.

Thesis (MScIng)--University of Stellenbosch, 2006. / Bibliography. Also available via the Internet.

Thesis (Ph.D.)--McMaster University, 2004. / Supervisors: John F. MacGregor, Theodora Kourti. Includes bibliographical references (leaves 221-227). Also available via World Wide Web.