Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces

Cooperativity and its use in robust control and state estimation for uncertain dynamic systems with engineering applications

This work shows a general applicable approach to robustly control uncertain dynamic systems, where the uncertainty is given by bounded intervals. The presented robust control methods rely on a verified enclosure of the state intervals. Since state-of-the-art-methods to calculate this fail, the property of cooperativity is used. However, since not all systems are naturally cooperative, a transformation routine is established to widen the possible application of this method. Different application scenarios chosen from a variety of engineering fields are used to validate the theoretical findings.Diese Arbeit zeigt einen generell verwendbaren Ansatz, um ein unsicheres dynamisches System robust zu regeln. Der gezeigte Ansatz verwendet dabei verifizierte Intervalleinschlüsse, die sich aus der intervallbasierten Unsicherheit ergeben. Da moderne Rechenmethoden hierbei versagen, wird die Eigenschaft der Kooperativität ausgenutzt, um dies dennoch zu ermöglichen. Da nicht alle Systeme diese Eigenschaft direkt aufweisen, wird eine Transformationsroutine entwickelt, um den gezeigten Ansatz auf andere Einsatzszenarien zu erweitern. Dies wird durch verschiedene Anwendungen in der Arbeit bewiesen

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Hierarchical Adaptive Control of Modular and Reconfigurable Robot Manipulator Platforms

Within the rapidly growing interest in today's robotics industry, modular and reconfigurable robots (MRRs) are among the most auspicious systems to expand the adaptability of robotic applications. They are adaptable to multiple industrial field applications but they also have additional advantages such as versatile hardware, easier maintenance, and transportability. However, such features render the controller design that manages a variety of robot configurations with reliable performance more complex since their system dynamics involve not only nonlinearities and uncertainties but also changing dynamics parameters after the reconfiguration. In this thesis, the motion control problem of MRR manipulators is addressed and hierarchical adaptive control architecture is developed for MRRs. This hierarchical structure allows the adjustment of the nominal parameters of an MRR system for system parameter identification and control design purposes after the robot is reconfigured. This architecture simplifies the design of adaptive control for MRRs which is effective in the presence of dynamic parameter uncertainty, unmodeled dynamics, and disturbance. The proposed architecture provides flexibility in choosing adaptive algorithms applicable to MRRs. The developed architecture consists of high-level and low-level modules. The high-level module handles the dynamic parameters changes and reconstructs the parametric model used for on-line parameter identification after the modules are reassembled. The low-level structure consists of an adaptive algorithm updated by an on-line parameter estimation to handle the dynamic parameter uncertainties. Furthermore, a robust adaptive term is added into this low-level controller to compensate for the unmodeled dynamics and disturbances. The proposed adaptive control algorithms guarantee uniformly ultimate boundedness (UUB) of the MRR trajectories in terms of robust stability despite the dynamic parameter uncertainty, unmodeled dynamics, changes in the system dynamics, and disturbance

Affine Arithmetic Based Methods for Power Systems Analysis Considering Intermittent Sources of Power

Intermittent power sources such as wind and solar are increasingly penetrating electrical grids, mainly motivated by global warming concerns and government policies. These intermittent and non-dispatchable sources of power affect the operation and control of the power system because of the uncertainties associated with their output power. Depending on the penetration level of intermittent sources of power, the electric grid may experience considerable changes in power flows and synchronizing torques associated with system stability, because of the variability of the power injections, among several other factors. Thus, adequate and efficient techniques are required to properly analyze the system stability under such uncertainties. A variety of methods are available in the literature to perform power flow, transient, and voltage stability analyses considering uncertainties associated with electrical parameters. Some of these methods are computationally inefficient and require assumptions regarding the probability density functions (pdfs) of the uncertain variables that may be unrealistic in some cases. Thus, this thesis proposes computationally efficient Affine Arithmetic (AA)-based approaches for voltage and transient stability assessment of power systems, considering uncertainties associated with power injections due to intermittent sources of power. In the proposed AA-based methods, the estimation of the output power of the intermittent sources and their associated uncertainty are modeled as intervals, without any need for assumptions regarding pdfs. This is a more desirable characteristic when dealing with intermittent sources of power, since the pdfs of the output power depends on the planning horizon and prediction method, among several other factors. The proposed AA-based approaches take into account the correlations among variables, thus avoiding error explosions attributed to other self-validated techniques such as Interval Arithmetic (IA).4 month

Design of Adaptive Sliding Mode Fuzzy Control for Robot Manipulator Based on Extended Kalman Filter

In this work, a new adaptive motion control scheme for robust performance control of robot manipulators is presented. The proposed scheme is designed by combining the fuzzy logic control with the sliding mode control based on extended Kalman filter. Fuzzy logic controllers have been used successfully in many applications and were shown to be superior to the classical controllers for some nonlinear systems. Sliding mode control is a powerful approach for controlling nonlinear and uncertain systems. It is a robust control method and can be applied in the presence of model uncertainties and parameter disturbances, provided that the bounds of these uncertainties and disturbances are known. We have designed a new adaptive Sliding Mode Fuzzy Control (SMFC) method that requires only position measurements. These measurements and the input torques are used in an extended Kalman filter (EKF) to estimate the inertial parameters of the full nonlinear robot model as well as the joint positions and velocities. These estimates are used by the SMFC to generate the input torques. The combination of the EKF and the SMFC is shown to result in a stable adaptive control scheme called trajectory-tracking adaptive robot with extended Kalman (TAREK) method. The theory behind TAREK method provides clear guidelines on the selection of the design parameters for the controller. The proposed controller is applied to a two-link robot manipulator. Computer simulations show the robust performance of the proposed scheme

Optimization techniques for error bounds of ODEs

Fehlerschranken von Anfangswertproblemen mit unbestimmten Anfangsbedingungen werden herkömmlicherweise mit Hilfe von Intervallanalysis berechnet, allerdings mit mäßigem Erfolg. Die traditionelle Herangehensweise führt zu asymptotischen Fehlerabschätzungen, die nur gültig sind, wenn die maximale Schrittweite gegen Null geht. Jedoch benötigt eine effiziente Approximation größtmögliche Schrittweiten, ohne die Genauigkeit zu mindern. Neue Entwicklungen in der globalen Optimierung ermöglichen es, das Finden von Fehlerschranken als globales Optimierungsproblem aufzufassen. Das ist insbesondere wichtig im Fall, dass die Differentialgleichungen oder die Anfangsbedingungen bedeutende Unschärfen enthalten. Es wurde ein neuer Solver - DIVIS (Differential Inequality based Validated IVP Solver) - entwickelt, um die Fehlerschranken für Anfangswertprobleme mit Hilfe von Fehlerabschätzungen und Optimierungstechniken zu berechnen. Die Idee dabei ist, die Fehlerabschätzung von Anfangswertproblemen durch elliptische Approximation zu berechnen. Die validierten Zustandseinschliessungen werden mit Hilfe von Differentialungleichungen berechnet. Die Konvergenz dieser Methode hängt von der Wahl geeigneter Vorkonditionierer ab. Das beschriebene Schema wurde in MATLAB und AMPL implementiert. Die Ergebnisse wurden mit VALENCIA-IVP, VNODE-LP und VSPODE verglichen.Error bounds of initial value problems with uncertain initial conditions are traditionally computed by using interval analysis but with limited success. Traditional analysis only leads to asymptotic error estimates valid when the maximal step size tends to zero, while efficiency in the approximation requires that step sizes are as large as possible without compromising accuracy. Recent progress in global optimization makes it feasible to treat the error bounding problem as a global optimization problem. This is particularly important in the case where the differential equations or the initial conditions contain significant uncertainties. A new solver DIVIS (Differential Inequality based Validated IVP Solver) has been developed to compute the error bounds of initial value problems by using defect estimates and optimization techniques. The basic idea is to compute the defect estimates of initial value problems by using outer ellipsoidal approximation. The validated state enclosures are computed by applying differential inequalities. Convergence of the method depends upon a suitable choice of preconditioner. The scheme is implemented in MATLAB and AMPL and the resulting enclosures are compared with VALENCIA-IVP, VNODE-LP and VSPODE