On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Experimental Validation Of An Integrated Guidance And Control System For Marine Surface Vessels

Autonomous operation of marine surface vessels is vital for minimizing human errors and providing efficient operations of ships under varying sea states and environmental conditions which is complicated by the highly nonlinear dynamics of marine surface vessels. To deal with modelling imprecision and unpredictable disturbances, the sliding mode methodology has been employed to devise a heading and a surge displacement controller. The implementation of such a controller necessitates the availability of all state variables of the vessel. However, the measured signals in the current study are limited to the global X and Y positioning coordinates of the boat that are generated by a GPS system. Thus, a nonlinear observer, based on the sliding mode methodology, has been implemented to yield accurate estimates of the state variables in the presence of both structured and unstructured uncertainties. Successful autonomous operation of a marine surface vessel requires a holistic approach encompassing a navigation system, robust nonlinear controllers and observers. Since the overwhelming majority of the experimental work on autonomous marine surface vessels was not conducted in truly uncontrolled real-world environments. The first goal of this work was to experimentally validate a fully-integrated LOS guidance system with a sliding mode controller and observer using a 16’ Tracker Pro Guide V-16 aluminium boat with a 60 hp. Mercury outboard motor operating in the uncontrolled open-water environment of Lake St. Clair, Michigan. The fully integrated guidance and controller-observer system was tested in a model-less configuration, whereby all information provided from the vessel’s nominal model have been ignored. The experimental data serves to demonstrate the robustness and good tracking characteristics of the fully-integrated guidance and controller/observer system by overcoming the large errors induced at the beginning of each segment and converging the boat to the desired trajectory in spite of the presence of environmental disturbances. The second focus of this work was to combine a collision avoidance method with the guidance system that accounted for “International Regulations for Prevention of Collisions at Sea” abbreviated as COLREGS. This new system then needed to be added into the existing architecture. The velocity obstacles method was selected as the base to build upon and additional restrictions were incorporated to account for these additional rules. This completed system was then validated with a software in the loop simulation

Non-Linear Robust Observers For Systems With Non-Collocated Sensors And Actuators

Challenges in controlling highly nonlinear systems are not limited to the development of sophisticated control algorithms that are tolerant to significant modeling imprecision and external disturbances. Additional challenges stem from the implementation of the control algorithm such as the availability of the state variables needed for the computation of the control signals, and the adverse effects induced by non-collocated sensors and actuators. The present work investigates the adverse effects of non-collocated sensors and actuators on the phase characteristics of flexible structures and the ensuing implications on the performance of structural controllers. Two closed-loop systems are considered and their phase angle contours have been generated as functions of the normalized sensor location and the excitation frequency. These contours were instrumental in the development of remedial actions for rendering structural controllers immune to the detrimental effects of non-collocated sensors and actuators. Moreover, the current work has focused on providing experimental validation for the robust performances of a self-tuning observer and a sliding mode observer. The observers are designed based on the variable structure systems theory and the self-tuning fuzzy logic scheme. Their robustness and self-tuning characteristics allow one to use an imprecise model of the system and eliminate the need for the extensive tuning associated with a fixed rule-based expert fuzzy inference system. The first phase of the experimental work was conducted in a controlled environment on a flexible spherical robotic manipulator whose natural frequencies are configuration-dependent. Both controllers have yielded accurate estimates of the required state variables in spite of significant modeling imprecision. The observers were also tested under a completely uncontrolled environment, which involves a 16-ft boat operating in open-water under different sea states. Such an experimental work necessitates the development of a supervisory control algorithm to perform PTP tasks, prescribed throttle arm and steering tasks, surge speed and heading tracking tasks, or recovery maneuvers. This system has been implemented herein to perform prescribed throttle arm and steering control tasks based on estimated rather than measured state variables. These experiments served to validate the observers in a completely uncontrolled environment and proved their viability as reliable techniques for providing accurate estimates for the required state variables

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

RBF-based supervisor path following control for ASV with time-varying ocean disturbance

1028-1036A robust model-free path following controller is developed for autonomous surface vehicle (ASV) with time-varying ocean disturbance. First, the geometrical relationship between ASV and virtual tracking point on the reference path is investigated. The differentiations of tracking errors are described with the relative motion method, which greatly simplified the direct differential of tracking errors. Furthermore, the control law for the desired angular velocity of the vehicle and virtual tracking point are built based on the Lyapunov theory. Second, the traditional proportional-integral-derivative (PID) controller is developed based on the desired velocities and state feedback. The radial basic function (RBF) neural network taking as inputs the desired surge velocity and yaw angular velocity is developed as the supervisor to PID controller. Besides, RBF controller tunes weights according to the output errors between the PID controller and supervisor controller, based on the gradient descent method. Hence, PID controller and RBF supervisor controller act as feedback and feed forward control of the system, respectively. Finally, comparative path following simulation for straight path and sine path illustrate the performance of the proposed supervisor control system. The PID controller term reports loss of control even in the unknown disturbance

Observer-Based Adaptive Control

The work present in this master thesis relates to output feedback adaptive control and observer design of nonlinear systems, and in particular of robot manipulators. A continuous-time velocity observer and a discrete-time adaptive velocity observer for robots are shown, and an observer backstepping controller is also proposed, which can be used together with both the observers. The resulting closed-loop system is proven to be semiglobally asymptotically stable with respect to both the velocity observation error and the tracking error, and stable with respect to the parameter estimation error. Furthermore an on-line parameter estimation method for a class of nonlinear system is presented, which can be easily extended for the robot equation. Unfortunately the way to use it in combination with the previous observer-controller has not been found and it has not been used in the experiments. In the Appendix A some technical details about the al-gorithm implementation are included, and in the Appendix B a paper already submitted to the 2002 Conference in Decision and Control is included, in which the adaptive output-feedback control scheme is extended for ship control. All the work has been conducted in the Department of Automatic Control, Lund Institute of Technology, Lund University

Synchronization controller for a 3-RRR parallel manipulator

A 3-RRR parallel manipulator has been well-known as a closed-loop kinematic chain mechanism in which the end-effector generally a moving platform is connected to the base by several independent actuators. Performance of the robot is decided by performances of the component actuators which are independently driven by tracking controllers without acknowledging information from each other. The platform performance is degraded if any actuator could not be driven well. Therefore, this paper aims to develop an advanced synchronization (SYNC) controller for position tracking of a 3-RRR parallel robot using three DC motor-driven actuators. The proposed control scheme consists of three sliding mode controllers (SMC) to drive the actuators and a supervisory controller named PID-neural network controller (PIDNNC) to compensate the synchronization errors due to system nonlinearities, uncertainties and external disturbances. A Lyapunov stability condition is added to the PIDNNC training mechanism to ensure the robust tracking performance of the manipulator. Numerical simulations have been performed under different working conditions to demonstrate the effectiveness of the suggested control approach