Showing papers on "Robust control published in 2004"

Adaptive Sliding Mode Control Design for a Hypersonic Flight Vehicle

Abstract: A multi-input/multi-output adaptive sliding controller is designed and analyzed for the longitudinal dynamics of a generic hypersonic air vehicle. This vehicle model is nonlinear, multivariable, and unstable and includes uncertain parameters. Simulation studies are conducted for trimmed cruise conditions of 110,000 ft and Mach 15 where the responses of the vehicle to a step change in altitude and airspeed are evaluated. The commands are 100-ft/s step velocity and 2000-ft step altitude. The controller is evaluated for robustness with respect to parameter uncertainties using simulations. Simulation studies demonstrate that the proposed controller is robust with respect to parametric uncertainty and meets the performance requirements with relatively low-amplitude control inputs.

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

Abstract: In this note, we present a new continuous control mechanism that compensates for uncertainty in a class of high-order, multiple-input-multiple-output nonlinear systems. The control strategy is based on limited assumptions on the structure of the system nonlinearities. A new Lyapunov-based stability argument is employed to prove semiglobal asymptotic tracking.

Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems

Abstract: Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q < 0, these systems are shown to approach the equilibrium point in finite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2,...,2)T. The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.

Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis

Abstract: In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the "disturbance-like" term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.

A general framework for tackling the output regulation problem

Abstract: Output regulation aims to achieve, in addition to closed-loop stability, asymptotic tracking and disturbance rejection for a class of reference inputs and disturbances. Thus, it poses a more challenging problem than stabilization. For over a decade, the nonlinear output regulation problem has been one of the focuses in nonlinear control research, and active research on this problem has generated many fruitful results. Nevertheless, there are two hurdles that impede the further progress of the research on the output regulation problem. The first one is the assumption that the solution or the partial solution of the regulator equations is polynomial. The second one is the lack of a systematic mechanism to handle the global robust output regulation problem. We establish a general framework that systematically converts the robust output regulation problem for a general nonlinear system into a robust stabilization problem for an appropriately augmented system. This general framework, on one hand, relaxes the polynomial assumption, and on the other hand, offers a greater flexibility to incorporate recent new stabilization techniques, thus setting a stage for systematically tackling the robust output regulation with global stability.

Robust and adaptive backstepping control for nonlinear systems using RBF neural networks

Abstract: In this paper, two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By a special design scheme, the controller singularity problem is avoided perfectly in both approaches. Furthermore, the closed loop signals are guaranteed to be semiglobally uniformly ultimately bounded and the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The control performances of the closed-loop systems can be shaped as desired by suitably choosing the design parameters. Simulation results obtained demonstrate the effectiveness of the approaches proposed. The differences observed between the inputs of the two controllers are analyzed briefly.

Randomized Algorithms for Analysis and Control of Uncertain Systems

Abstract: Overview.- Elements of Probability Theory.- Uncertain Linear Systems and Robustness.- Linear Robust Control Design.- Some Limits of the Robustness Paradigm.- Probabilistic Methods for Robustness.- Monte Carlo Methods.- Randomized Algorithms in Systems and Control.- Probability Inequalities.- Statistical Learning Theory and Control Design.- Sequential Algorithms for Probabilistic Robust Design.- Sequential Algorithms for LPV Systems.- Scenario Approach for Probabilistic Robust Design.- Random Number and Variate Generation.- Statistical Theory of Radial Random Vectors.- Vector Randomization Methods.- Statistical Theory of Radial Random Matrices.- Matrix Randomization Methods.- Applications of Randomized Algorithms.- Appendix.

Force tracking impedance control of robot manipulators under unknown environment

Abstract: In this paper, a new simple stable force tracking impedance control scheme that has the capability to track a specified desired force and to compensate for uncertainties in environment location and stiffness as well as in robot dynamic model is proposed. The uncertainties in robot dynamics are compensated by the robust position control algorithm. After contact, in force controllable direction the new impedance function is realized based on a desired force, environment stiffness and a position error. The new impedance function is simple and stable. The force error is minimized by using an adaptive technique. Stability and convergence of the adaptive technique are analyzed for a stable force tracking execution. Simulation studies with a three link rotary robot manipulator are shown to demonstrate the robustness of the proposed scheme under uncertainties in robot dynamics, and little knowledges of environment position and environment stiffness. Experimental results are carried out to confirm the proposed controller's performance.

A delay-dependent approach to robust H/sub /spl infin// filtering for uncertain discrete-time state-delayed systems

Abstract: A delay-dependent approach to robust H/sub /spl infin// filtering is proposed for linear discrete-time uncertain systems with multiple delays in the state. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed H/sub /spl infin// noise attenuation level. The proposed filter design methodology incorporates some recently appeared results, such as Moon's new version of the upper bound for the inner product of two vectors and de Oliveira's idea of parameter-dependent stability, which greatly reduce the overdesign introduced in the derivation process. In addition to the full-order filtering problem, the challenging reduced-order case is also addressed by using different linearization procedures. Both full- and reduced-order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies.

New delay-dependent stability criteria and stabilizing method for neutral systems

Abstract: This note concerns delay-dependent robust stability criteria and a design method for stabilizing neutral systems with time-varying structured uncertainties. A new way of deriving such criteria is presented that combines the parameterized model transformation method with a method that takes the relationships between the terms in the Leibniz-Newton formula into account. The relationships are expressed as free weighting matrices obtained by solving linear matrix inequalities. Moreover, the stability criteria are also used to design a stabilizing state-feedback controller. Numerical examples illustrate the effectiveness of the method and the improvement over some existing methods.

Evaluation of time delay effects to wide-area power system stabilizer design

Abstract: Centralized control using system-wide data has been suggested to enhance the dynamic performance of large interconnected power systems. Because of the distance involved in wide-area interconnections, communication delay cannot be ignored. Long time delay may be detrimental to system stability and may degrade system performance. The time delay tolerance of a centralized controller and the associated performance tradeoff is analyzed using a small gain criterion. Special attention is paid to the choice of weighting functions in a robust control design. As expected, it is found that time delay tolerance decreases when the system bandwidth increases, while the nominal system time-domain performance is concomitantly improved. Several approaches which can maintain a good system performance while increasing the time delay tolerance are suggested and compared. A modern controller design technique, like gain scheduling via linear matrix inequalities, is evaluated for the design of the supervisory power system stabilizer accounting for various time delays.

A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

Abstract: In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.

Control of Uncertain LTI Systems Based on an Uncertainty and Disturbance Estimator

Abstract: This paper proposes a robust control strategy for uncertain LTI systems. The strategy is based on an uncertainty and disturbance estimator (UDE). It brings similar performance as the time-delay control (TDC). The advantages over TDC are: (i) no delay is introduced into the system; (ii) there are no oscillations in the control signal; and (iii) there is no need of measuring the derivatives of the state vector. The robust stability of LTI-SISO systems is analyzed, and simulations are given to show the effectiveness of the UDE-based control with a comparison made with TDC.

Robust stability and stabilization of discrete singular systems: an equivalent characterization

Abstract: This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.

Application of linear matrix inequalities for load frequency control with communication delays

Abstract: Load frequency control has been used for decades in power systems. Traditionally, this has been a centralized control by area with communication over a dedicated and closed network. New regulatory guidelines allow for competitive markets to supply this load frequency control. In order to allow an effective market operation, an open communication infrastructure is needed to support an increasing complex system of controls. While such a system has great advantage in terms of cost and reliability, the possibility of communication signal delays and other problems must be carefully analyzed. This paper presents a load frequency control method based on linear matrix inequalities. The primary aim is to find a robust controller that can ensure good performance despite indeterminate delays and other problems in the communication network.

Control of distributed generation systems-Part I: Voltages and currents control

Abstract: This paper discusses a digital control strategy for three-phase pulse-width modulation voltage inverters used in a single stand-alone ac distributed generation system. The proposed control strategy utilizes the perfect robust servomechanism problem control theory to allow elimination of specified unwanted voltage harmonics from the output voltages under severe nonlinear load and to achieve fast recovery performance on load transient. This technique is combined with a discrete sliding mode current controller that provides fast current limiting capability necessary under overload or short circuit conditions. The proposed control strategy has been implemented on a digital signal processor system and experimentally tested on an 80-kVA prototype unit. The results showed the effectiveness of the proposed control algorithm.

Direct torque control of sensorless induction motor drives: a sliding-mode approach

Abstract: Direct torque control (DTC) is known to produce fast response and robust control in ac adjustable-speed drives. However, in the steady-state operation, notable torque, flux, and current pulsations occur. A new, direct torque and flux control strategy based on variable-structure control and space-vector pulsewidth modulation is proposed for induction motor sensorless drives. The DTC transient merits and robustness are preserved and the steady-state behavior is improved by reducing the torque and flux pulsations. A sliding-mode observer using a dual reference frame motor model is introduced and tested. Simulations and comparative experimental results with the proposed control scheme, versus classic DTC, are presented. Very-low-speed sensorless operation (3 r/min) is demonstrated.

Robust damping of multiple swing modes employing global stabilizing signals with a TCSC

Abstract: This paper demonstrates a robust damping control design for multiple swing mode damping in a typical power system model using global stabilizing signals. A multiple-input, single-output (MISO) controller is designed for a thyristor-controlled series capacitor (TCSC) to improve the damping of the critical interarea modes. The stabilizing signals are obtained from remote locations based on observability of the critical modes. A H/sub /spl infin// damping control design based on the mixed-sensitivity formulation in a linear matrix inequality (LMI) framework is carried out. It is shown that, with local signal, supplementary damping control through three flexible AC transmission systems (FACTS) devices is necessary to provide damping to the three dominant interarea modes. On the other hand, the use of global signals has been shown to improve the damping of all the critical interarea modes with a single controller for the TCSC only. The damping performance of the centralized controller was examined in the frequency and the time domain for various operating scenarios. The controller was found to be robust against varying power-flow patterns, load characteristics, tie-line strengths, and system nonlinearities, including saturation.

Robust Tracking Control Design for Spacecraft Under Control Input Saturation

Abstract: A continuous globally stable tracking control algorithm is presented for spacecraft in the presence of control input saturation, parametric uncertainty, and external disturbances. The proposed control algorithm has the following properties: 1) fast and accurate response in the presence of bounded disturbances and parametric uncertainty; 2) explicit accounting for control input saturation; and 3) computational simplicity and straightforward tuning. A detailed stability analysis of the resulting closed-loop system is included. It is shown that global stability of the overall system is guaranteed with continuous control even in the presence of bounded disturbances and parametric uncertainty. In the proposed controller a single parameter is adjusted dynamically in such a fashion that it is possible to prove that both attitude and angular velocity errors will tend to zero asymptotically. The stability proof is based on a Lyapunov analysis and the properties of the quaternion representation of spacecraft dynamics. One of the main features of the proposed design is that it establishes a straightforward relationship between the magnitudes of the available control inputs and those of the desired trajectories and disturbances even with continuous control. Numerical simulations are included to illustrate the spacecraft performance obtained using the proposed controller.

Feedback min‐max model predictive control using a single linear program: robust stability and the explicit solution

Abstract: In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min–max model predictive control problem that can be solved using a single linear program. Furthermore, this is a multi-parametric linear program, which implies that the optimal control law is piecewise affine and can be explicitly pre-computed so that the linear program does not have to be solved on-line. We assume that the plant model is known, is discrete-time and linear time-invariant, is subject to unknown but bounded state disturbances and that the states of the system are measured. Two numerical examples are presented; one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible. Copyright © 2004 John Wiley & Sons, Ltd.

Robust observer-based control of systems with state perturbations via LMI approach

Abstract: In this note, the observer-based control for a class of uncertain, linear systems is considered. Exponential stabilizability for the systems is studied and the convergence rate of the system is estimated. A linear matrix inequality (LMI) approach is used to design the observer-based control. The control and observer gains are given from LMI feasible solution. A numerical example is given to illustrate our results.

A unifying passivity framework for network flow control

Abstract: Network flow control regulates the traffic between sources and links based on congestion, and plays a critical role in ensuring satisfactory performance. In recent studies, global stability has been shown for several flow control schemes. By using a passivity approach, this paper presents a unifying framework which encompasses these stability results as special cases. In addition, the new approach significantly expands the current classes of stable flow controllers by augmenting the source and link update laws with passive dynamic systems. This generality offers the possibility of optimizing the controllers, for example, to improve robustness in stability and performance with respect to time delays, unmodeled flows, and capacity variation.