The analysis and identification of separable nonlinear single valued systems is carried out from a functional standpoint, by modifying the Volterra series to separate bias and steady state gain from dynamic effects. This analysis is applied to the development of generalised expressions for output bias, variance and correlation functions of nonlinear systems with Gaussian or pseudo-random inputs. An identification procedure is then developed and applied to the testing of both simulated systems, and an electrohydraulic servomotor. An error analysis is carried out showing the limitations of the method, and procedures derived designed at eliminating the effects of random and cyclic noise.

Analytical conditions are derived which enable the root locus shapes of many simple systems to be obtained directly from the relative positions of their open loop poles and zeros. It is also shown that the pole-zero patterns of these systems can often be normalised in order to display all possible forms of their root loci on a single map. Many previously unknown locus shapes are given and these are considered in relation to the corresponding new forms of closed loop response. A computer program is developed which enables root loci to be plotted for systems which include pure time delay or distributed lag. This extension to the method makes it possible to predict the closed loop responses of pure time delay systems directly from their root loci. It also enables these systems to be designed to achieve specified closed loop performance and provides a method of obtaining their open loop dynamics from measurements of closed loop response. The speed of the new computer algorithm makes it feasible to use root locus methods for the design of high order multiloop systems. This improved capability is illustrated for aircraft control systems. A general pole-zero method is developed which enables control laws to be chosen for a desired aircraft response throughout the complete flight envelope. The pure time delay capability of the program is then used to determine human pilot transfer functions from flight records of the pilot-aircraft response. Finally the results of this analysis are used to design improved forms of manual aircraft control systems.

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This thesis considers the optimal control of systems governed by hereditary systems. In particular, the thesis examines the numerical solutions of these optimal control problems, but some theoretical results are obtained. Gradient, conjugate gradient and second order methods for integro-differential systems are presented here together with a proof of the convergence of the ε-method and the minimum principle for these systems. In addition, gradient, conjugate gradient and second order methods for time lag systems are discussed and some results on other hereditary processes are presented, The implementation of the numerical methods for time lag and integro-differential systems is examined at length, and several numerical examples are discussed. Some consideration is given to systems having state variable inequality constraints.

The control of an internal-combustion engine such that it will produce its required output, with a minimum consumption of fuel, even in the presence of random load disturbances, has become a necessary requirement for future prime-mover and vehicular applications. This thesis is concerned with an attempt to produce a practical scheme to meet that requirement from a study of several methods of achieving optimal engine regulation and a method of obtaining optimal start-up. An attempt was made first to identify the response of the engine-transmission-load combination with a mathematical model obtained by the use of computers. The servo-mechanism associated with the throttle was identified also, and then a complete state-variable description of the system was obtained. Next an automatic gear-changing scheme was designed and implemented. With the availability of this practical system an optimal control function was generated then to implement optimal start-up. The optimal function was calculated by solving the associated multi-point boundary value problem by means of technique of quasi-linearisation. To subject the system to random loads an artificial road was simulated, and a scheme was devised to vary the dynamometer loading in response to this 'road' signal. The remainder of the thesis is concerned with a study of several different methods of obtaining optimal or sub-optimal schemes of regulation and with comparisons of experimental results and the results from associated theoretical computer studies. Many suggestions for further investigations are contained in the final chapter.

In the past, Direct Current (dc) machines have been commonly favoured in areas where a precise variable speed operation is highly required. This is due to the feasible linear control of flux and torque, which is accomplished by simply varying the field and armature currents. However, they are bulky, expensive and require periodic maintenance due to the existence of commutators and brushes. Alternating Current (ac) machines particularly the squirrel cage induction type have emerged as an alternative to those of dc machines in the application of speed drive systems. In general, however, they do require more complex control schemes than the dc motors, because of their highly non-linear dynamic structure with strong dynamic interactions. This situation has changed dramatically over the last few years with the advent of fast switching power converters along with high performance micro-controllers, which made a significant contribution to performance enhancement of modem speed drive systems. In addition, various control techniques have made possible the application of induction motors in high performance speed drive operations where traditionally only dc motors were previously available. On the other hand, in many speed drive applications which incorporate either scalar or vector control, the prime objective of the speed controller is the capability of achieving a good speed tracking performance and without sensitivity to parameters and operating condition changes. For these reasons, comprehensive investigation of state-of-the-art modem control schemes, which include fuzzy logic and sliding mode control are discussed. The main principles underlying fuzzy logic and sliding mode control schemes along with their basic theory and general mathematical representation are reviewed. In addition, the application of fuzzy logic concepts to reduce the chattering phenomenon typically inherited in the sliding mode control is successfully presented, which results in a new integrated fuzzy sliding mode control algorithms. Through extensive simulation studies, it is found that the fuzzy logic control scheme attained a good transient performance for the speed drive system in comparison to the conventional sliding mode control and the new integrated fuzzy sliding mode control. Furthermore, the design simplicity of the fuzzy logic control system has made it virtually attractive for the ease of practical implementation of the proposed drive system. Extensive practical testes of the proposed variable speed drive system have been carried out to verify the validity of the simulation analysis of the proposed fuzzy logic control system. Several tests are conducted in order to bring out the effectiveness of the designed control system upon step change in speed command and impact load disturbances. The digital implementation of the proposed fuzzy logic control algorithms is realised on a single chip, Intel 80C196KC 16-bit embedded microcontroller, a low cost derivative of the MCS-96 architecture. The main contribution of this thesis is the novel approach to design a sliding mode control system using concepts from fuzzy logic algorithms to alleviate the chattering problems and improve the dynamics of the induction motor drive.

Many legged robots have been built with a variety of different abilities, from running to hopping to climbing stairs. Despite this however, there has been no consistency of approach to the problem of getting them to walk. Approaches have included breaking down the walking step into discrete parts and then controlling them separately, using springs and linkages to achieve a passive walking cycle, and even working out the necessary movements in simulation and then imposing them on the real robot. All of these have limitations, although most were successful at the task for which they were designed. However, all of them fall into one of two categories: either they alter the dynamics of the robots physically so that the robot, whilst very good at walking, is not as general purpose as it once was (as with the passive robots), or they control the physical mechanism of the robot directly to achieve their goals, and this is a difficult task. In this thesis a novel control model is proposed, inspired by the best walkers and runners around - ourselves - so the controllers produced are based on the vertebrate Central Nervous System. This means that there is a low-level controller which adapts itself to the robot so that, when switched on, it effectively simulates the springs and linkages of the passive robots to produce a walking robot, and this now active mechanism is then controlled by a relatively simple higher level controller. This is the beast of both worlds - we have a robot which is inherently capable of walking, and thus is easy to control like the passive walkers, but also retains the general purpose abilities which makes it so potentially useful.

In Part I, the problem of heating a thin plate or material travelling through a furnace, in which the system is described by first order linear partial differential equations, is introduced as an example of optimal control theory in distributed parameter systems. The variational technique in a fixed domain is used to obtain the necessary conditions for optimality. Many cases of the problem with the state equation described by first order linear partial differential equations are discussed, in which the control function enters into the state equation in different positions. The problems are analysed and solved by making use of characteristic curves. In Part II, we have studied the variation of a functional defined on a variable domain, and we apply it to the problem of finding the optimum shape of the domain in which some performance criterion has an extremum. The problem in which the state equation is Laplace's equation defined on the variable domain of an annular shape with given boundary conditions is discussed and completely solved for the case when the inner boundary of the domain is only a small departure from a circle. We also introduce the method of logarithmic potential of a single layer to solve the boundary value problem of Laplace's equation with mixed boundary conditions and two simple examples are solved by using this method which leads to coupled integral equations.

As many-objective optimisation problems become more prevalent, evolutionary algorithms that are based on Pareto dominance relations are slowly becoming less popular due to severe limitations that such an approach has for this class of problems. At the same time decomposition-based methods, which have been employed traditionally in mathematical programming, are consistently increasing in popularity. These developments have been led by recent research studies that show that decomposition-based algorithms have very good convergence properties compared to Pareto-based algorithms. Decomposition-based methods use a scalarising function to decompose a problem with multiple objectives into several single objective subproblems. The subproblems are defined with the help of weighting vectors. The location on the Pareto front that each subproblem tends to converge, strongly depends on the choice of weighting vectors and the scalarising function. Therefore, the selection of an appropriate set of weighting vectors to decompose the multi-objective problem, determines the distribution of the final Pareto set approximation along the Pareto front. Currently a limiting factor in decomposition-based methods is that the distribution of Pareto optimal points cannot be directly controlled, at least not to a satisfactory degree. Generalised Decomposition is introduced in this thesis as a way to optimally solve this problem and enable the analyst and the decision maker define and obtain the desired distribution of Pareto optimal solutions. Furthermore, many algorithms generate a set of Pareto optimal solutions. An interesting question is whether such a set can be used to generate more solutions in specific locations of the Pareto front. Pareto Estimation - a method introduced in this thesis - answers this question quite positively. The decision maker, using the Pareto Estimation method can request a set of solutions in a particular region on the Pareto front, and although not guaranteed to be generated in the exact location, it is shown that the spatial accuracy of the produced solutions is very high. Also the cost of generating these solutions is several orders of magnitude lower compared with the alternative to restart the optimisation.

Virtual Reality has traditionally taken the form of audio-visual simulations. The desire for more realistic interactions gradually led to pursue the inclusion of touch as an additional feedback modality. Simulation of touch through haptics should ideally integrate both kinaesthetic and tactile feedback. Currently kinaesthetic feedback is applied mainly through force feedback joysticks and to a lesser extent through hand exoskeletons. Hand exoskeletons are desirable for whole- hand interaction but require further development before they can become more widely applicable. Tactile feedback on the other hand is still in its infancy. None of the past efforts has managed to satisfy the stringent performance and design requirements and to present an interoperable and generic tactile display suitable for integration in VR haptic systems. This thesis presents the development of two haptic interfaces designed for tactile- kinaesthetic feedback integration; an interoperable tactile display for the fingertip and an ergonomic exoskeleton for the hand. The tactile display is a compact and lightweight interface for high fidelity tactile feedback. Its operation is based on a 4x4 array of vertically moving tactors for the display of surface shape to an area of the fingertip. The tactors are spring loaded and are actuated remotely by dc motors through a very flexible tendon transmission. This design allows 6DOF tactile exploration in an excellent work envelope. The compact design, high performance, reliability, and straightforward connectivity make this tactile display truly interoperable and suitable for direct integration in any VR haptic system. The exoskeleton is a 7DOF force feedback interface. It is mounted on the dorsal side of the right hand and provides feedback to the thumb, index, middle and ring fingers. It is actuated remotely by DC motors through a tendon transmission. It is adjustable for different hand sizes and has been designed for comfort, easy fitting and removal. The exoskeleton has also been integrated with novel low cost vibrotactile displays for simulation of contact at the fingertips. The developed interfaces have been designed with a scope for performance practicality reliability and interoperability which are reflected in the outcomes of this thesis.