A number of structural problems in linear multivariable control systems are considered in this thesis. The first concerns the detail of the infinite frequency structure of a rational matrix carried in a matrix fraction description (MFD) and the question of how this may be detected in an immediate way. It is shown that any non-prime MFD which is just a column (resp. row) reduced MFD (CRMFD (resp. RRMFD)) readily displays such information. Of particular interest are those CRMFDs (resp. RRMFDs) which display the complete infinite frequency structure, as regards multiplicity and degree of the infinite pole-zero structure.

In the design of process plants safety has assumed an increasingly high profile. One of the techniques used in hazard identification is the fault tree, which involves first the synthesis of the tree and then its analysis. The construction of a fault tree, however, requires special skills and can be a time-consuming process. It is therefore attractive to develop computer aids for the synthesis stage to match those which already exist for the analysis of the tree. A computer based system for fault tree synthesis has been developed at Loughborough University. This thesis is part of a continuing programme of work associated with this facility.

Field oriented control is an established technique for rapid control of torque in induction motors. The controller tracks the orientation of the rotor flux, which rotates at synchronous frequency. The component of stator current in phase with this flux (known as the "flux current"), can be used to maintain a constant flux. Under these conditions, torque is directly proportional to the quadrature component of stator current, or "torque current". It has not proved cost-effective to measure either the rotor flux orientation or the motor torque directly. However both can be estimated from a combination of voltages and/or currents and position (or speed). The standard mathematical model uses the resistances and inductances of the motor equivalent circuit. These parameters may vary with temperature, motor operating speed and load. The underlying cause, range and timescale of these variations is examined, along with techniques for tracking the changes on-line. Detailed off-line characterisation results are presented for the test motor, in order to determine how accurately the parameters can be identified in practice. A number of standard torque and flux estimators have been analysed and implemented. Experimental results are presented for a 5.5kW motor drive system. Parameter errors and delays within the controller, which cause an error in the orientation of the stator currents, are shown to affect the motor performance. The motor is incorrectly fluxed, which may reduce its efficiency and peak torque capability in the steady state. In addition, any change in demanded torque is coupled into the flux current, exciting the natural response of the motor. This is characterised by damped oscillations at slip frequency, decaying at a rate determined by the rotor time constant. The implications for closed loop torque and speed control are discussed.

The problems created by the presence of finite actuators and sensors in the control of linear multivariable systems are well known. These problems, which are particularly evident when high-gain or fast-sampling control is used, are usually the cause of highly oscillatory or even unstable closed-loop time-domain behaviour. Therefore, the presence of finite actuators and sensors is probably one of the major factors responsible for the failure of many of the existing multivariable. control methods to deal with practical control problems, .especially in the case of 'high-performance 1 systems - that require tight non-interacting closed-loop tracking behaviour. In this thesis, the very important field of high-gain and fast-sampling control of linear multivariable systems with explicit actuators and sensors is investigated. In particular, the synthesis of both high-gain analogue and fast-sampling digital error-actuated proportional-plus-integral controllers for linear minimum-phase multivariable plants with explicit actuator and sensor dynamics is presented. More importantly. the tuning of such controllers is systematised to make explicit the choice of the controller tuning parameters based on the gain/sampling frequency, the actuator and/or sensor time-constants, and the required closed-loop time-domain performance of the tracking systems. Furthermore, it is shown that the controller design can be achieved using only data obtained from direct input-output measurements in the time-domain. In this way, the limitations imposed by the requirement for the provision of linearised models in either state-space or transfer function matrix form - a prerequisite of many current design methodologies - for the purposes of controller design are eliminated and, as a result, the scope of practical applicability of the developed design methodology is vastly increased. The various novel facets of this design methodology are illustrated throughout this thesis by considering the multivariable model of a gas turbine with explicit actuator and sensor dynamics. Thus, the performance characteristics of the controllers for this gas turbine designed by the -present methodology are compared with those of controllers designed by previous methodologies.

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2003 / Some important ideas froni classical control theory are introduced with the intention of applying them to chaotic dynamical systems, in particular the coupled logistic equations. The structure of this dissertation is such that a strong foundation in control theory is first established before introducing the coupled logistic map or the methods of control and targetting in chaotic systems. In chapter 1 some aspects of classical control theory are reviewed. Continuous- and discrete-time dynamical systems are introduced and the existence and uniquendss criteria for the continuous case are explored via Lipschitz continuity. The matrix form of an inhomogeneous linear differential equation is presented and several properties of the associated transition matrix are discussed. Several linear algebraic ideas, most notably the Cayley-Hamilton theorem, are employed to explore the important concepts of controllability and observability in linear systems. The stabilisability problem is thoroughly investigated. Finally, the neighbourhood properties of continuous nonlinear dynamical systems with reference to controllability, stability and noise are established. Chapter 2 places emphasis on canonical forms, pole assignments and state observers. The decomposition of a general system into distinct components is facilitated by the general structure theorem, which is proved. The pole placement problem is described and the correspondence between the stabilisability of a system and the placement of poles is noted by the use'of a socalled feedback matrix. Lastly, the notion of a state observer, with reference to some dynamic feedback law, is introduced. The dynamics of the coupled logistic equations are studied in chapter 3. The fixed points of the map are calculated and the subsequent dynamical consequences explored. Using methods introduced in earlier chapters, the stability of the map is investigated. Using the so-called variational equations, the Lyapunov exponents are computed and used to classify, the motion of the system for the parameter values r and a. This chapter concludes with a discussion of the basins of attraction and critical curves associated with the coupled logistic equations. It is in chapter 4 that the models for controlling chaos are instantiated. The famous Ott-Grebogi- Yorke (OGY) method for controlling chaos is explained and related to the pole placement problem, discussed previously. The theory is extended to study the control of periodic orbits with periods greater than one.

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