Many control systems of practical importance are multivariable. In such systems, each manipulated variable (input signal) may affect several controlled variables (output signals) causing interaction between the input/output loops. For this reason, control of multivariable systems is typically much more difficult compared to the single-input single-output case. It is therefore of great importance to quantify the degree of interaction so that proper input/output pairings that minimize the impact of the interaction can be formed. For this, dedicated interaction measures can be used. The first part of this thesis treats interaction measures. The commonly used Relative Gain Array (RGA) is compared with the Gramian-based interaction measures the Hankel Interaction Index Array (HIIA) and the Participation Matrix (PM) which consider controllability and observability to quantify the impact each input signal has on each output signal. A similar measure based on the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathcal%20H_2" /> norm is also investigated. Further, bounds on the uncertainty of the HIIA and the PM in case of uncertain models are derived. It is also shown how the link between the PM and the Nyquist diagram can be utilized to numerically calculate such bounds. Input/output pairing strategies based on linear quadratic Gaussian (LQG) control are also suggested. The key idea is to design single-input single-output LQG controllers for each input/output pair and thereafter form closed-loop multivariable systems for each control configuration of interest. The performances of these are compared in terms of output variance. In the second part of the thesis, the activated sludge process, commonly found in the biological wastewater treatment step for nitrogen removal, is considered. Multivariable interactions present in this type of bioreactor are analysed with the tools discussed in the first part of the thesis. Furthermore, cost-efficient operation of the activated sludge process is investigated.

The optimal steady-state control, and suboptimal adaptive control, of disturbed single-input-output systems are introduced, and the class of systems considered is defined. It is noted that the stochastic tracking problem divides into a deterministic tracking problem and a stochastic regulator problem; the solutions to these two problems are shown to be independent but formally similar. The continuous regulator problem is approached via both frequency and time domain methods: the former method is extended to cover unstable systems; the latter method is extended to include systems with input delay. The two regulators are shown to be externally equivalent. The frequency domain method is briefly described for discrete systems, and shown to include the minimum variance regulator of Åström and Peterka as a special case. Some systems which allow measurement noise to be treated as a system disturbance for the purposes of optimal controller design are investigated. A novel class of control laws is described in both continuous and discrete time; in the same way as the minimum variance regulator forms the basis of the self-tuning regulator of Åström and Wittenmark, these minimum variance controllers from the basis of a self-tuning controller. These minimum variance controllers have a number of advantages over the minimum-variance regulator, and are open to a number of interpretations including: a model following control law, and an extension of classical control laws to systems with delay. The optimality of this class of control laws is investigated, and analogies drawn with the previously considered k-step-ahead control laws; some examples are given to illustrate the method. An adaptive control law combining the above minimum variance controllers with a linear least-squares algorithm is proposed and shown to be self-tuning. These self-tuning controllers are only slightly more complex than the self-tuning regulator of Åström and Wittenmark, but have a number of advantages. Intuitive justification is given for the conjecture that some methods of Ljung, developed for the analysis of the self-tuning regulator, are applicable to the self-tuning controller. Simulated examples are given which compare and contrast the performance of the self-tuning controller with that of the self-tuning regulator. The first steps towards a quasi-continuous self-tuning controller are outlined.

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This thesis proposes an intelligent multiple-controller framework for complex systems that incorporates a fuzzy logic based switching and tuning supervisor along with a neural network based generalized learning model (GLM). The framework is designed for adaptive control of both Single-Input Single-Output (SISO) and Multi-Input Multi-Output (MIMO) complex systems. The proposed methodology provides the designer with an automated choice of using either: a conventional Proportional-Integral-Derivative (PID) controller, or a PID structure based (simultaneous) Pole and Zero Placement controller. The switching decisions between the two nonlinear fixed structure controllers is made on the basis of the required performance measure using the fuzzy logic based supervisor operating at the highest level of the system. The fuzzy supervisor is also employed to tune the parameters of the multiple-controller online in order to achieve the desired system performance. The GLM for modelling complex systems assumes that the plant is represented by an equivalent model consisting of a linear time-varying sub-model plus a learning nonlinear sub-model based on Radial Basis Function (RBF) neural network. The proposed control design brings together the dominant advantages of PID controllers (such as simplicity in structure and implementation) and the desirable attributes of Pole and Zero Placement controllers (such as stable set-point tracking and ease of parameters’ tuning). Simulation experiments using real-world nonlinear SISO and MIMO plant models, including realistic nonlinear vehicle models, demonstrate the effectiveness of the intelligent multiple-controller with respect to tracking set-point changes, achieve desired speed of response, prevent system output overshooting and maintain minimum variance input and output signals, whilst penalising excessive control actions.

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