Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods

Active fault-tolerant control of nonlinear systems with wind turbine application

The thesis concerns the theoretical development of Active Fault-Tolerant Control (AFTC) methods for nonlinear system via T-S multiple-modelling approach. The thesis adopted the estimation and compensation approach to AFTC within a tracking control framework. In this framework, the thesis considers several approaches to robust T-S fuzzy control and T-S fuzzy estimation: T-S fuzzy proportional multiple integral observer (PMIO); T-S fuzzy proportional-proportional integral observer (PPIO); T-S fuzzy virtual sensor (VS) based AFTC; T-S fuzzy Dynamic Output Feedback Control TSDOFC; T-S observer-based feedback control; Sliding Mode Control (SMC). The theoretical concepts have been applied to an offshore wind turbine (OWT) application study. The key developments that present in this thesis are:• The development of three active Fault Tolerant Tracking Control (FTTC) strategies for nonlinear systems described via T-S fuzzy inference modelling. The proposals combine the use of Linear Reference Model Fuzzy Control (LRMFC) with either the estimation and compensation concept or the control reconfiguration concept.• The development of T-S fuzzy observer-based state estimate fuzzy control strategy for nonlinear systems. The developed strategy has the capability to tolerate simultaneous actuator and sensor faults within tracking and regulating control framework. Additionally, a proposal to recover the Separation Principle has also been developed via the use of TSDOFC within the FTTC framework.• The proposals of two FTTC strategies based on the estimation and compensation concept for sustainable OWTs control. The proposals have introduced a significant attribute to the literature of sustainable OWTs control via (1) Obviating the need for Fault Detection and Diagnosis (FDD) unit, (2) Providing useful information to evaluate fault severity via the fault estimation signals.• The development of FTTC architecture for OWTs that combines the use of TSDOFC and a form of cascaded observers (cascaded analytical redundancy). This architecture is proposed in order to ensure the robustness of both the TSDOFC and the EWS estimator against the generator and rotor speed sensor faults.• A sliding mode baseline controller has been proposed within three FTTC strategies for sustainable OWTs control. The proposals utilise the inherent robustness of the SMC to tolerate some matched faults without the need for analytical redundancy. Following this, the combination of SMC and estimation and compensation framework proposed to ensure the close-loop system robustness to various faults.• Within the framework of the developed T-S fuzzy based FTTC strategies, a new perspective to reduce the T-S fuzzy control design conservatism problem has been proposed via the use of different control techniques that demand less design constraints. Moreover, within the SMC based FTTC, an investigation is given to demonstrate the SMC robustness against a wider than usual set of faults is enhanced via designing the sliding surface with minimum dimension of the feedback signals

On-line estimation approaches to fault-tolerant control of uncertain systems

This thesis is concerned with fault estimation in Fault-Tolerant Control (FTC) and as such involves the joint problem of on-line estimation within an adaptive control system. The faults that are considered are significant uncertainties affecting the control variables of the process and their estimates are used in an adaptive control compensation mechanism. The approach taken involves the active FTC, as the faults can be considered as uncertainties affecting the control system. The engineering (application domain) challenges that are addressed are: (1) On-line model-based fault estimation and compensation as an FTC problem, for systems with large but bounded fault magnitudes and for which the faults can be considered as a special form of dynamic uncertainty. (2) Fault-tolerance in the distributed control of uncertain inter-connected systems The thesis also describes how challenge (1) can be used in the distributed control problem of challenge (2). The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control action and the second acting as an adaptive compensation for significant uncertainties and fault effects. The fault effects are a form of uncertainty which is considered too large for the application of passive FTC methods. The thesis considers several approaches to robust control and estimation: augmented state observer (ASO); sliding mode control (SMC); sliding mode fault estimation via Sliding Mode Observer (SMO); linear parameter-varying (LPV) control; two-level distributed control with learning coordination

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

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

Intelligent model-based control of complex three-link mechanisms

The aim of this study is to understand the complexity and control challenges of the locomotion of a three-link mechanism of a robot system. In order to do this a three-link robot gymnast (Robogymnast) has been built in Cardiff University. The Robogymnast is composed of three links (one arm, one torso, one leg) and is powered by two geared DC motors. Currently the robot has three potentiometers to measure the relative angles between adjacent links and only one tachometer to measure the relative angular position of the first link. A mathematical model for the robot is derived using Lagrange equations. Since the model is inherently nonlinear and multivariate, it presents more challenges when modelling the Robogymnast and dealing with control motion problems. The proposed approach for dealing with the design of the control system is based on a discrete-time linear model around the upright position of the Robogymnast. To study the swinging motion of the Robogymnast, a new technique is proposed to manipulate the frequency and the amplitude of the sinusoidal signals as a means of controlling the motors. Due to the many combinations of the frequency and amplitude, an optimisation method is required to find the optimal set. The Bees Algorithm (BA), a novel swarm-based optimisation technique, is used to enhance the performance of the swinging motion through optimisation of the manipulated parameters of the control actions. The time taken to reach the upright position at its best is 128 seconds. Two different control methods are adopted to study the balancing/stablising of the Robogymnast in both the downward and upright configurations. The first is the optimal control algorithm using the Linear Quadratic Regulator (LQR) technique with integrators to help achieve and maintain the set of reference trajectories. The second is a combination of Local Control (LC) and LQR. Each controller is implemented via reduced order state observer to estimate the unmeasured states in terms of their relative angular velocities. From the identified data in the relative angular positions of the upright balancing control, it is reported that the maximum amplitude of the deviation in the relative angles on average are approximately 7.5° for the first link and 18° for the second link. It is noted that the third link deviated approximately by 2.5° using only the LQR controller, and no significant deviation when using the LQR with LC. To explore the combination between swinging and balancing motions, a switching mechanism between swinging and balancing algorithm is proposed. This is achieved by dividing the controller into three stages. The first stage is the swinging control, the next stage is the transition control which is accomplished using the Independent Joint Control (IJC) technique and finally balancing control is achieved by the LQR. The duration time of the transition controller to track the reference trajectory of the Robogymnast at its best is found to be within 0.4 seconds. An external disturbance is applied to each link of the Robogymnast separately in order to study the controller's ability to overcome the disturbance and to study the controller response. The simulation of the Robogymnast and experimental realization of the controllers are implemented using MATLAB® software and the C++ program environment respectively

Model-based Friction Compensation

Friction is present in all mechanical systems and causes a wide range of problems for control. The development of model-based strategies accounting for Friction in the designed control has been a vast area of Research since these last decades. A promising Friction model which received a lot of attention these last years is the so-called LuGre model, which originates in the collaboration between the two control Research groups of Lund (Sweden) and Grenoble (France). This model is quite simple and is capable of capturing a wide range of well known friction phenomena, such as the Stribeck effect or the frictionnal lag. In particular this model is used in [Robertsson et al., 2004], where a general method for friction compensation for nonlinear systems is presented. The compensation strategy is simple: it just consists in adding to the control signal a friction estimate, computed using a LuGre model based observer. This thesis deals with the application of the theory of this article on a real experiment: the stabilization of the Furuta pendulum in the upright position. First, attention is paid so that the initial hypothesis of this article be satisfied. These hypotheses consist in finding a stabilizing control for the system when Friction is neglected, and an associated Lyapunov function verifying some properties. Then, Friction is included by following the procedure presented in the article. The friction estimate is computed according to the discretized LuGre form, presented in fFreidovich et al., 2006g, and the main result of the article is verified both in Simulation and on the real process, the simulations being carried out with Matlab-Simulink and the real experiments by using a dSPACE device. From a practical point of view, the implemented compensation scheme works perfectly in Simulation: the limit cycles originating from an uncompensated friction are totally annihilated, while for real experiments this oscillating behaviour is still remaining, but happens to be significantly reduced. From a theoretical point of view, the results of [Robertsson et al., 2004] are fully verified in Simulation, while for real experiments the presence of remaining limit cycles prevents a perfect verification of the theory