In this work we address the problem of friction compensation in a pneumatic control valve. It is proposed a nonlinear control law that uses algebraic estimators in its structure, in order to adapt the controller to the aging of the valve. For that purpose we estimate parameters related to the valve\'s Karnopp model, necessary to friction compensation, online. The estimators and the controller are validated through simulations. / Nessa pesquisa, estudamos o problema de compensação de atrito em válvulas pneumáticas. É proposta uma lei de controle não linear que tem estimadores algébricos em sua estrutura, para adaptar o controlador ao envelhecimento da válvula. Para isso, estimam-se os valores de parâmetros relacionados ao modelo de Karnopp da válvula, necessários à compensação do atrito, de maneira online. Os estimadores e o controlador são validados através de simulações.

Faults and failures in system components are the two main reasons for the instability and the degradation in control performance. In recent decades, fault-tolerant control (FTC) approaches were introduced to improve the resiliency of the control system against faults and failures. In general, FTC techniques are classified into two major groups: passive and active. Passive FTC systems do not rely on the fault information to control the system and are closely related to the robust control techniques while an active FTC system performs based on the information received from the fault detection and isolation (FDI) system, and the fault problem will be tackled more intelligently without affecting other parts of the system. This dissertation technically reviews fault and failure causes in control systems and finds solutions to compensate for their effects. Recent achievements in FDI approaches, and active and passive FTC designs are investigated. Thorough comparisons of several different aspects are conducted to understand the advantages and disadvantages of different FTC techniques to motivate researchers to further developing FTC, and FDI approaches. Then, a novel active FTC system framework based on online FDI is presented which has significant advantages in comparison with other state of the art FTC strategies. To design the proposed active FTC, a new FDI approach is introduced which uses the artificial neural network (ANN) and a model based observer to detect and isolate faults and failures in sensors and actuators. In addition, the extended Kalman filter (EKF) is introduced to tune ANN weights and improve the ANN performance. Then, the FDI signal combined with a nonlinear dynamic inversion (NDI) technique is used to compensate for the faults in the actuators and sensors of a nonlinear system. The proposed scheme detects and accommodates faults in the actuators and sensors of the system in real-time without the need of controller reconfiguration. The proposed active FTC approach is used to design a control system for three different applications: Unmanned aerial vehicle (UAV), load frequency control system, and proton exchange membrane fuel cell (PEMFC) system. The performance of the designed controllers are investigated through numerical simulations by comparison with conventional control approaches, and their advantages are demonstrated.

Differential geometric nonlinear control of a multiple stage evaporator system of the liquor burning facility associated with the Bayer process for alumina production at Alcoa Wagerup alumina refinery, Western Australia was investigated.Mathematical models for differential geometric analysis and nonlinear controller synthesis for the evaporator system were developed. Two models, that were structurally different from each other, were used in the thesis for simulation studies. Geometric nonlinear control structure, consisting of nonlinear state feedback control laws and multi-loop single-input single-output proportional-integral controllers, were designed for the industrial evaporator system. The superiority of the geometric nonlinear control structure for regulatory control of the evaporator system was successfully demonstrated through computer simulations and real-time simulator implementation. The implementation trial has verified the practicality and feasibility of these type of controllers. It also re-solved some practical issues of the geometric nonlinear control structure for industrial control applications. In addition, the implementation trial also established a closer link between the academic nonlinear control theory and the industrial control practices.Geometric nonlinear output feedback controller, consisting of the geometric nonlinear control structure and reduce-order observer was proposed for actual plant implementation on the evaporator system on-site. Its superior performance was verified through computer simulations, but its feasibility on the evaporator system on-site has yet to be investigated either through simulator implementation or actual plant implementation. This investigation was not performed due to the time constraint on the preparation of this thesis and the inavailability of the plant personnel required for this implementation.Robust ++ / nonlinear control structures that are simple and computationally efficient have been proposed for enhancing the performance of geometric nonlinear controllers in the presence of plant/model mismatch and/or external disturbances. The robust nonlinear control structures are based on model error compensation methods. Robustness properties of the proposed robust nonlinear control structures on the evaporator system were investigated through computer simulations and the results indicated improved performance over the implemented geometric nonlinear controller in terms of model uncertainty and disturbance reductions.A software package was developed in MAPLE computing environment for the analysis of nonlinear processes and the design of geometric nonlinear controllers. This developed symbolic package is useful for obtaining fast and exact solutions for the analysis and design of nonlinear control systems. Procedures were also developed to simulate the geometric nonlinear control systems. It was found that MAPLE, while it is superior for the analyses and designs, is not viable for simulations of nonlinear control systems. This was due to limitation of MAPLE on the physical, or virtual, memory management. The use of both symbolic and numeric computation for solutions of nonlinear control system analysis, design and simulation is recommended.To sum up, geometric nonlinear controllers have been designed for an industrial multiple stage evaporator system and their simplicity, practicality, feasibility and superiority for industrial control practices have been demonstrated either through computer simulations or real-time implementation. It is hoped that the insights provided in this thesis will encourage more industry-based projects in nonlinear control, and thereby assist in closing the widening gap between academic nonlinear control theory and industrial control ++ / practice.Keywords: geometric nonlinear control, input-output linearization, multiple stage evaporator, robust geometric nonlinear control, control performance enhancement.

Thesis (M.S.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Sciences, Electrical Engineering Department. / Includes bibliographical references.

<p>The contributions of this thesis are in the area of control of systems with nonlinear dynamics. The thesis is divided into three parts. The two first parts are similar in the sense that they both consider output feedback of rather general classes of nonlinear systems, and both approaches are based on mathematical programming (although in quite different ways). The third part contains a state feedback approach for a specific system class, and is more application oriented.</p><p>The first part treats control of systems described by nonlinear difference equations, possibly with uncertain terms. The system dynamics are represented by piecewise affine difference inclusions, and for this system class, piecewise affine controller structures are suggested. Controller synthesis inequalities for such controller structures are given in the form of Bilinear Matrix Inequalities (BMIs). A solver for the BMIs is developed. The main contribution is to the output feedback case, where an observer-based controller structure is proposed. The theory is exemplified through two examples.</p><p>In the second part the output feedback problem is examined in the setting of Nonlinear Model Predictive Control (NMPC). The state space formulation of NMPC is inherently a state feedback approach, since the state is needed as initial condition for the prediction in the controller. Consequently, for output feedback it is natural to use observers to obtain estimates of the state. A high gain observer is applied for this purpose. It is shown that for several existing NMPC schemes, the state feedback stability properties ``semiglobally'' hold in the output feedback case. The theory is illuminated with a simple example.</p><p>Finally, a state feedback controller for a class of positive systems is proposed. Convergence of the state to a certain subset of the first orthant, corresponding to a constant ``total mass'' (interpreting states as masses) is obtained. Conditions are given under which convergence to this set implies asymptotic stability of an equilibrium. Simple examples illustrate some properties of the controller. Furthermore, the control strategy is applied to the stabilization of a gas-lifted oil well, and simulations on a rigorous multi-phase dynamic simulator of such a well demonstrate the controller performance.</p>

The contributions of this thesis are in the area of control of systems with nonlinear dynamics. The thesis is divided into three parts. The two first parts are similar in the sense that they both consider output feedback of rather general classes of nonlinear systems, and both approaches are based on mathematical programming (although in quite different ways). The third part contains a state feedback approach for a specific system class, and is more application oriented. The first part treats control of systems described by nonlinear difference equations, possibly with uncertain terms. The system dynamics are represented by piecewise affine difference inclusions, and for this system class, piecewise affine controller structures are suggested. Controller synthesis inequalities for such controller structures are given in the form of Bilinear Matrix Inequalities (BMIs). A solver for the BMIs is developed. The main contribution is to the output feedback case, where an observer-based controller structure is proposed. The theory is exemplified through two examples. In the second part the output feedback problem is examined in the setting of Nonlinear Model Predictive Control (NMPC). The state space formulation of NMPC is inherently a state feedback approach, since the state is needed as initial condition for the prediction in the controller. Consequently, for output feedback it is natural to use observers to obtain estimates of the state. A high gain observer is applied for this purpose. It is shown that for several existing NMPC schemes, the state feedback stability properties ``semiglobally'' hold in the output feedback case. The theory is illuminated with a simple example. Finally, a state feedback controller for a class of positive systems is proposed. Convergence of the state to a certain subset of the first orthant, corresponding to a constant ``total mass'' (interpreting states as masses) is obtained. Conditions are given under which convergence to this set implies asymptotic stability of an equilibrium. Simple examples illustrate some properties of the controller. Furthermore, the control strategy is applied to the stabilization of a gas-lifted oil well, and simulations on a rigorous multi-phase dynamic simulator of such a well demonstrate the controller performance.

In this thesis, we consider problems connected to navigation and tracking for autonomousrobots under the assumption of constraints on sensors and kinematics. We study formation controlas well as techniques for filtering and smoothing of noise contaminated input. The scientific contributions of the thesis comprise five papers.In Paper A, we propose three cascaded, stabilizing formation controls for multi-agent systems.We consider platforms with non-holonomic kinematic constraints and directional rangesensors. The resulting formation is a leader-follower system, where each follower agent tracksits leader agent at a specified angle and distance. No inter-agent communication is required toexecute the controls. A switching Kalman filter is introduced for active sensing, and robustnessis demonstrated in experiments and simulations with Khepera II robots.In Paper B, an optimization-based adaptive Kalman filteringmethod is proposed. The methodproduces an estimate of the process noise covariance matrix Q by solving an optimization problemover a short window of data. The algorithm recovers the observations h(x) from a system˙ x = f (x), y = h(x)+v without a priori knowledge of system dynamics. The algorithm is evaluatedin simulations and a tracking example is included, for a target with coupled and nonlinearkinematics. In Paper C, we consider the problem of estimating a closed curve in R2 based on noisecontaminated samples. A recursive control theoretic smoothing spline approach is proposed, thatyields an initial estimate of the curve and subsequently computes refinements of the estimateiteratively. Periodic splines are generated by minimizing a cost function subject to constraintsimposed by a linear control system. The optimal control problem is shown to be proper, andsufficient optimality conditions are derived for a special case of the problem using Hamilton-Jacobi-Bellman theory.Paper D continues the study of recursive control theoretic smoothing splines. A discretizationof the problem is derived, yielding an unconstrained quadratic programming problem. Aproof of convexity for the discretized problem is provided, and the recursive algorithm is evaluatedin simulations and experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics. Finally, in Paper E we explore the issue of optimal smoothing for control theoretic smoothingsplines. The output of the control theoretic smoothing spline problem is essentially a tradeoff between faithfulness to measurement data and smoothness. This tradeoff is regulated by the socalled smoothing parameter. In Paper E, a method is developed for estimating the optimal valueof this smoothing parameter. The procedure is based on general cross validation and requires noa priori information about the underlying curve or level of noise in the measurements. / QC 20100722

This thesis concerns the analysis of dynamical systems suitable to be modelled by piecewise-smooth differential equations. In such systems the continuous-in-time dynamics is interrupted by discrete-in-time jumps in the state or governing equations of motion. Not only can this framework be used to describe existing systems with strong nonlinear behaviour such as impacts and friction, but the non-smooth properties can be exploited to design new mechanical devices. As suggested in this work it opens up the possibility of, for example, fast limit switches and energy transfer mechanisms. Particularly, the dynamics at the onset of low-velocity impacts in systems with recurrent dynamics, so called grazing bifurcations in impact-oscillators, are investigated. As previous work has shown, low-velocity impacts is a strong source of instability to the dynamics, and efforts to control the behaviour is of importance. This problem is approached in two ways in this work. One is to investigate the influence of parameter variations on the dynamic behaviour of the system. The other is to implement low-cost control strategies to regulate the dynamics at the grazing bifurcation. The control inputs are of impulsive nature, and utilizes the natural dynamics of the system to the greatest extent. The scientific contributions of this work is collected in five appended papers. The first paper consists of an experimental verification of a map that captures the correction to the smooth dynamics induced by an impact, known in the literature as the discontinuity map. It is shown that the lowest order expansion of the map accurately captures the transient growth rate of impact velocities. The second paper presents a constructive proof of a control algorithm for a rather large class of impact oscillators. The proof is constructive in the sense that it gives control parameters which stabilizes the dynamics at the onset of low-velocity impacts. In the third paper a piecewise-smooth quarter-car model is derived, and the control strategy is implemented to reduce impact velocities in the suspension system. In the fourth and fifth papers the grazing bifurcation of an impact oscillator with dry friction type damping is investigated. It turns out that the bifurcation is triggered by the disappearance of an interval of stable stick solutions. A condition on the parameters of the system is derived which differentiates between stable and unstable types of bifurcation scenarios. Additionally, a low-cost control strategy is proposed, similar to the one previously mentioned, to regulate the bifurcation scenario. / QC 20100811

This dissertation addresses the control problem for the general class of control non-affine, non-standard singularly perturbed continuous-time systems. The problem of control for nonlinear multiple time scale systems is addressed here for the first time in a systematic manner. Toward this end, this dissertation develops the theory of feedback passivation for non-affine systems. This is done by generalizing the Kalman-Yakubovich-Popov lemma for non-affine systems. This generalization is used to identify conditions under which non-affine systems can be rendered passive. Asymptotic stabilization for non-affine systems is guaranteed by using these conditions along with well-known passivity-based control methods. Unlike previous non-affine control approaches, the constructive static compensation technique derived here does not make any assumptions regarding the control influence on the nonlinear dynamical model. Along with these control laws, this dissertation presents novel hierarchical control design procedures to address the two major difficulties in control of multiple time scale systems: lack of an explicit small parameter that models the time scale separation and the complexity of constructing the slow manifold. These research issues are addressed by using insights from geometric singular perturbation theory and control laws are designed without making any assumptions regarding the construction of the slow manifold. The control schemes synthesized accomplish asymptotic slow state tracking for multiple time scale systems and simultaneous slow and fast state trajectory tracking for two time scale systems. The control laws are independent of the scalar perturbation parameter and an upper bound for it is determined such that closed-loop system stability is guaranteed. Performance of these methods is validated in simulation for several problems from science and engineering including the continuously stirred tank reactor, magnetic levitation, six degrees-of-freedom F-18/A Hornet model, non-minimum phase helicopter and conventional take-off and landing aircraft models. Results show that the proposed technique applies both to standard and non-standard forms of singularly perturbed systems and provides asymptotic tracking irrespective of the reference trajectory. This dissertation also shows that some benchmark non-minimum phase aerospace control problems can be posed as slow state tracking for multiple time scale systems and techniques developed here provide an alternate method for exact output tracking.

In this thesis we study a number of nonlinear control problems motivated by their appearance in flight control. The results are presented in a general framework and can also be applied to other areas. The two main topics are backstepping and control allocation. Backstepping is a nonlinear control design method that provides an alternative to feedback linearization. Here, backstepping is used to derive robust linear control laws for two nonlinear systems, related to angle of attack control and flight path angle control, respectively. The resulting control laws require less modeling information than corresponding designs based on feedback linearization, and achieve global stability in cases where feedback linearization can only be performed locally. Further, a method for backstepping control of a rigid body is developed, based on a vector description of the dynamics. We also discuss how to augment an existing nonlinear controller to suppress constant input disturbances. Two methods, based on adaptive backstepping and nonlinear observer design, are proposed. Control allocation deals with actuator utilization for overactuated systems. In this thesis we pose the control allocation problem as a constrained least squares problem to account for actuator position and rate constraints. Efficient solvers based on active set methods are developed with similar complexity to existing, approximate, pseudoinverse methods. A method for dynamic control allocation is also proposed which enables a frequency dependent control distribution among the actuators to be designed. Further, the relationship between control allocation and linear quadratic control is investigated. It is shown that under certain circumstances, the two techniques give the same freedom in distributing the control effort among the actuators. An advantage of control allocation, however, is that since the actuator constraints are considered, the control capabilities of the actuator suite can be fully exploited.