Thesis (Ph. D.)--University of Missouri--Rolla, 2007. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed December 6, 2007) Includes bibliographical references.

The main focus of this work is on the problem of existence of nonlinear optimal controllers realizable by artificial neural networks. Theoretical justification, currently available for control applications of neural networks, is rather limited. For example, it is unclear which neural architectures are capable of performing which control tasks. This work addresses applicability of neural networks to the synthesis of approximately optimal state feedback. Discrete-time setting is considered, which brings extra regularity into the problem and simplifies mathematical analysis. Two classes of optimal control problems are studied: time-optimal control and optimal control with summable quality index. After appropriate relaxation of the optimization problem, the existence of a suboptimal feedback mapping is demonstrated in both cases. It is shown that such a feedback may be realized by a multilayered network with discontinuous neuron activation functions. For continuous networks, similar results are obtained, with the existence of suboptimal feedback demonstrated, except for a set of initial states of an arbitrarily small measure. The theory developed here provides basis for an attractive approach of the synthesis of near-optimal feedback using neural networks trained on optimal trajectories generated in open loop. Potential advantages of control based on neural networks are illustrated on application to stabilization of interconnected power systems. A nearly time-optimal controller is designed for a single-machine system using neural networks. The obtained controller is then utilized as an element of a hierarchical control architecture used for stabilization of a multimachine power transmission system. This example demonstrates applicability of neural control to complicated, nonlinear dynamic systems. / Graduation date: 1995

When large disturbances occur in interconnected power systems, there exists the danger that the power system states may leave an associated region of stability, if timely corrective action is not taken. Open-loop remedial control actions such as field-forcing, line-tripping, switching of series-capacitors, energizing braking resistors, etc., are helpful in reducing the effects of the disturbance, but do not guarantee that the post-fault power system will be stabilized. Linear controllers are widely used in the power industry, and provide excellent damping when the power system state is close to the equilibrium. In general, they provide conservative regions of stability. This study focuses on the development of nonlinear controllers to enhance the stability of interconnected power systems following large disturbances, and allow stable operation at high power levels. There is currently interest in the power industry in using thyristor-controlled series-capacitors for the dual purpose of exercising tighter control on steady-state power flows and enhancing system stability. This device is used to implement the nonlinear controller in this dissertation. A mathematical model of the power system controlled by the thyristor-controlled series-capacitor is developed for the purpose of controller design. Discrete-time, nonlinear predictive controllers are derived by minimizing criterion functions that are quadratic in the output variables over a finite-horizon of interest, with respect to the control variables. The control policies developed in this manner are centralized in nature. The stabilizing effect of such controllers is discussed. A potential drawback is the need to have large prediction horizons to assure stability. In this context, a coordinated-control policy is proposed, in which the nonlinear predictive controller is designed with a small prediction horizon. For a class of disturbances, such nonlinear predictive controllers return the power system state to a small neighborhood of the post-fault equilibrium, where linear controllers provide asymptotic stabilization and rapid damping. Methods of coordinating the controllers are discussed. Simulation results are provided on a sample four-machine power system model. There exists considerable uncertainty in power system models due to constantly shifting loads and generations, line-switching following disturbances, etc. The performance of fixed-parameter controllers may not be good when the plant description changes considerably from the reference. In this context, a bilinear model-based self-tuning controller is proposed for the stabilization of power systems for a class of faults. A class of generic predictive controllers are presented for use with the self-tuning controller. Simulation results on single-machine and multimachine power systems are provided. / Graduation date: 1995

Packet switched networks offer a particularly challenging research subject to the control community: the dynamics of a network buffer, their simplest component, are nonlinear and exhibit a saturation effect that cannot be neglected. In many practical cases, networks are made up of the interconnection of a large number of such basic elements. This gives rise to high dimensional nonlinear systems for which few general results exist today in the literature. Furthermore, these physical interconnections that may sometimes span a very long distance induce a transmission delay and the queues in intermediary nodes induce a buffering delay. Finding a model able to both take into account as much of this complexity as possible while being simple enough to be analysed mathematically and used for control purposes is the first objective of this thesis. To accomplish this goal, a so-called "fluid-flow model" based on fluid exchange between buffers is presented. Neglecting the transmission and propagation delays, this model concentrates on the dynamics of the buffer loads and is particularly well suited for a mathematical analysis. Throughout the work, a systematic system point of view is adopted in an effort to perform a rigorous analysis using tools from automatic control and dynamical systems theory. This model is then used to study a feedback control law where each node receives state information from its directly connected neighbours, hence referred to as hop-by-hop control. The properties of the closed-loop system are analysed and a global stability analysis is performed using existing results from the compartmental and cooperative system literature. The global mass conservation typically ensured by end-to-end control protocols is studied in the last chapter using, once again, a compartmental framework. Finally, a numerical study of a strategy combining the end-to-end and the hop-by-hop approaches is presented. It is shown that problems encountered with hop-by-hop control may then be successfully alleviated.

A custom-made Peltier-based thermal device is designed to perform miniaturized bio-molecular reactions in a microfluidic platform for medical diagnostic tests, especially the polymerase chain reaction for DNA amplification. The cascaded two-stage device is first approximated by multiple local linear models whose parameters are obtained by system identification. A decentralized switching controller is proposed, where two internal model-based PI controllers are used in local stabilizations and PD and PI controllers are applied during transitions respectively. Couplings and drift are further reflected into the controllers. Desired temperature tracking performance on the transition speed and overshoot is achieved, and the feasibility of the Peltier device in a microfluidic platform is further validated by the successful applications of viral detection. To achieve fast and smooth transition while avoiding tuning by trial-and-errors, a nonlinear model is developed based on the first principles, whose parameters are partially calculated from empirical rules and partially determined by open-loop and closed-loop experimental data. Two novel nonlinear controllers are designed based on the nonlinear model. The first controller extends the input-to-state feedback linearization technique to a class of nonlinear systems that is affine on both the control inputs and the square of control inputs (including the Peltier system). Additional local high gain controllers are introduced to reduce the steady-state errors due to parameter uncertainty. The second controller is a time-based switching controller which switches between nonlinear pseudo-PID/ state feedback controllers and local PI controllers. Calculation burden is reduced and steady-state error is minimized using a PI controller locally, while fast and smooth transition is achieved by the nonlinear counterpart. The robustness of the controller is verified in simulation under worse case scenarios. Both simulation and experimental results validated the effectiveness of the two nonlinear controllers. The proposed linear/ nonlinear, switching/ non-switching controllers provide different options for the Peltier-based thermal applications. The scalability and the parameter updating capability of the nonlinear controllers facilitate the extension of the Peltier device to other microfluidic applications. / Controls

A new decentralized nonlinear controller for Robot Manipulators is presented in this thesis. Based on concepts of Lyapunov stability theory and some control ideas proposed in [3]-[7], we obtain continuous nonlinear decentralized control laws which guarantee position and velocity tracking to within an arbitrarily small error. Assumptions based on physical constraints of manipulators are made to guarantee the existence of the controller and asymptotic stability of the closed loop system. Simulations show how well this rather simple control scheme works on two of the links of the Puma 560 Manipulator. The main contribution of this thesis is that it extends the results of a class of complex centralized control algorithms to the decentralized robust control of interconnected nonlinear subsystems like robot manipulators. / Graduation date: 1992

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate.

In this thesis we study the stabilization of closed sets for passive nonlinear control systems, developing necessary and sufficient conditions under which a passivity-based feedback stabilizes a given goal set. The development of this result takes us to a journey through the so-called reduction problem: given two nested invariant sets G1 subset of G2, and assuming that G1 enjoys certain stability properties relative to G2, under what conditions does G1 enjoy the same stability properties with respect to the whole state space? We develop reduction principles for stability, asymptotic stability, and attractivity which are applicable to arbitrary closed sets. When applied to the passivity-based set stabilization problem, the reduction theory suggests a new definition of detectability which is geometrically appealing and captures precisely the property that the control system must possess in order for the stabilization problem to be solvable. The reduction theory and set stabilization results developed in this thesis are used to solve a distributed coordination problem for a group of unicycles, whereby the vehicles are required to converge to a circular formation of desired radius, with a specific ordering and spacing on the circle.

In this thesis we study the stabilization of closed sets for passive nonlinear control systems, developing necessary and sufficient conditions under which a passivity-based feedback stabilizes a given goal set. The development of this result takes us to a journey through the so-called reduction problem: given two nested invariant sets G1 subset of G2, and assuming that G1 enjoys certain stability properties relative to G2, under what conditions does G1 enjoy the same stability properties with respect to the whole state space? We develop reduction principles for stability, asymptotic stability, and attractivity which are applicable to arbitrary closed sets. When applied to the passivity-based set stabilization problem, the reduction theory suggests a new definition of detectability which is geometrically appealing and captures precisely the property that the control system must possess in order for the stabilization problem to be solvable. The reduction theory and set stabilization results developed in this thesis are used to solve a distributed coordination problem for a group of unicycles, whereby the vehicles are required to converge to a circular formation of desired radius, with a specific ordering and spacing on the circle.

This thesis presents the design, analysis, and numerical and experimental evaluation of nonlinear controllers for co-operation among several hydraulic robots operating in the presence of significant system uncertainties, non-linearities and friction. The designed controllers allow hydraulically driven manipulators to (i) co-operatively handle a rigid object (payload) following a given trajectory, (ii) share the payload and (iii) maintain an acceptable internal force on the object. A general description of the kinematic and dynamic relations for a hydraulically actuated multi-manipulator system is presented first. The entire mathematical model incorporates object dynamics, robot dynamics, hydraulic actuator functions and friction dynamics. For the purpose of simulations, a detailed numerical simulation program of such a system is also developed, in which two three-link planar robot manipulators resembling the Magnum hydraulic manipulators manufactured by ISE, interact with each other through manipulating a common object. The regulating control problem is studied next, in which the desired position of the object and the corresponding desired link displacement change step-wise. Initially, a controller is designed based on a backstepping technique, assuming that full knowledge of the dynamics and kinematics of the system is available. The assumption is then relaxed and the control system is analyzed. Based on the analysis, the controller is then modified to account for the uncertainty of the payload, robot dynamic parameters and hydraulic functions. Next, the regulating controller is extended to a tracking controller, which allows the object to follow a given trajectory and is robust against parameter uncertainties. Additionally, an observer is added to the controller to avoid the need of acceleration feedback. To investigate the effect of friction force, the above controllers are examined by introducing the most recent and complete LuGre friction model into the system dynamics. The tracking controller is then redesigned to compensate the effect of friction. Observers are designed to observe the immeasurable friction states. Based on the observed friction states and estimated friction parameters, an appropriate friction compensation scheme is designed which does not directly use velocity in order to avoid the need of acceleration feedback by the controller. Finally, the problem of “explosion of terms” coming from the backstepping method is solved by using the concept of dynamic surface control in which a low pass filter is integrated to avoid model differentiation. Simulations are carried out for analysis of the control system and verification of the developed controllers. Experimental examinations are performed on an available hydraulic system consisting of two single-axis hydraulic actuators. / February 2008