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A method of determining regions of attraction for a system with multiple nonlinearities is considered in this thesis. Application of the method involves finding the global minimum of a nonconvex Lyapunov function. This is done by finding a graphical solution using Lagrange multipliers and then applying the projected gradient method to determine the exact solution. A three machine power system example is included to illustrate the application. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Vita. / Digitized by Kansas Correctional Industries

In maintaining power system stability; especially that of large interconnected systems, in the face of large disturbances it is desirable to have a non-linear control technique that is simple and inexpensive to implement. This thesis presents a non-linear control technique which relies on angle measurements taken at strategic points in the power system with the aid of the G.P.S. ( Global Positioning System ) timing signal. A method for estimating these bus angles which is faster than previous methods is developed as well as a technique for choosing the locations of these transducers. This transducer placement algorithm aims to place transducers at locations whose bus voltage response to the less well damped inter-area modes is maximised and whose response to the better damped local modes is minimised. Since the control techniques are based on aggregated classical models of coherent generators it is important to be able to estimate the internal voltages of these aggregate machines. The placement algorithm ensures maximally precise angle estimates in the presence of noise by minimising the condition number of the observation matrix relating transducer bus voltages to internal aggregated machine voltages. The non-linear control techniques presented rely on an energy function developed in this thesis which is based on the physical circuit energy of the system. One technique; the Direct Energy technique looks at maximising the negativity of the time rate of change of the energy function, assuming that the energy function is positive during the time frame of interest. It is shown that should the number of controllers be less than the number of modes, excluding the centre of area mode, then sustained oscillations appear which will only be damped by the natural damping of the system. This may be overcome by using techniques which rely on reducing the entire system energy over the time frame of interest. These so-called Lookahead techniques can rely on higher order time derivatives of the energy function or on co-states, the latter being the principal focus of this thesis. The Lookahead control technique developed is based on co-states which are estimated by the using the solution to the time independent Ricatti equation for a LQ model of the system. It is shown to produce good damping in a number of case studies. Furthermore it is shown to perform well in the presence of both static and dynamic load models. Also it is shown that the path dependent terms introduce some ambiguity as to whether or not the system will converge to a stable equilibrium point. It is shown that it is possible to put a bound on the region to which the power system can be assured to converge. Furthermore the addition of the above-mentioned control strategies has the effect of overcoming the effect of the path dependent terms and, should the control action be strong enough, completely swamping them and ensuring system convergence to a stable operating point. In any case the energy function could be directly monitored since all the data needed is being collected anyway for control purposes. / PhD Doctorate

An improved robot manipulator decentralized non-linear adaptive controller that performs well in the presence of disturbances with unknown parameters and non-linearities is presented in this work. The proposed decentralized adaptive structure is a modification of the controller developed by Seraji [13-17] and is characterized by an auxiliary signal that compensates for the unmodeled dynamics and improves the tracking performance, by a feedforward component based on the inverse system to ensure high performance over a wide range and by a PD feedback component of constant gain to improve the speed of response of the system. As a result, a very accurate and fast path tracking is achieved despite the non-linearities. The scheme requires only the measurement of angular speed and displacement of each joint, and it does not require any knowledge about the mathematical model of the manipulator. Due to its decentralized structure, it can be implemented on parallel processors to speed up the operation. The main advantages of the proposed control scheme over similar controllers are that the control activity is smoother, it is less sensitive to sampling size and to the time period elapsed when the whole trajectory is traversed, as verified by simulations of several test conditions of-two of the joints of the PUMA 560 robot arm. / Graduation date: 1991

The objective of this investigation is the development of improved techniques for the estimation of robustness for dynamic systems with structured uncertainties, a problem which was approached by application of the Lyapunov direct method. This thesis considers the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the traditional method of the sign properties of the derivative itself. This proposed approach relaxes the sufficient conditions of stability, and is used to generate techniques for the robust design of control systems with structured perturbations. The need for such techniques has been demonstrated by recent research interest in the area of robust control design. The system considered is assumed to be nominally linear, with time-variant, nonlinear bounded perturbations. Application of the proposed technique warrants that estimates of robustness will either match or constitute an improvement upon those obtained by application of the traditional Lyapunov approach. The application of numerical procedures are used to demonstrate improvements in estimations of robustness for two-, three- and four-dimensional dynamic systems with one or more structured perturbations. The proposed numerical approaches obtain improved bounds, which are considered in the sense of their engineering aspects. To increase the accuracy of the numerical procedures, symbolic algebraic calculations are utilized. / Graduation date: 1991

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