Showing papers on "Robust control published in 2009"

Hybrid dynamical systems

Abstract: Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.

Robust Power System Frequency Control

Abstract: Frequency control as a major function of automatic generation control is one of the important control problems in electric power system design and operation, and is becoming more significant today due to the increasing size, changing structure, emerging new uncertainties, environmental constraints, and the complexity of power systems. Robust Power System Frequency Control uses the recent development of linear robust control theory to provide practical, systematic, fast, and flexible algorithms for the tuning of power system load-frequency controllers. The physical constraints and important challenges related to the frequency regulation issue in a deregulated environment are emphasized, and most results are supplemented by real-time simulations. The developed control strategies attempt to bridge the existing gap between the advantages of robust/optimal control and traditional power system frequency control design. The material summarizes the long term research outcomes and contributions of the author’s experience with power system frequency regulation. It provides a thorough understanding of the basic principles of power system frequency behavior over a wide range of operating conditions. It uses simple frequency response models, control structures and mathematical algorithms to adapt modern robust control theorems with frequency control issues as well as conceptual explanations. The engineering aspects of frequency regulation have been considered, and practical methods for computer analysis and design are also discussed. Robust Power System Frequency Control provides a comprehensive coverage of frequency control understanding, simulation and design. The material develops an appropriate intuition relative to the robust load frequency regulation problem in real-world power systems, rather than to describe sophisticated mathematical analytical methods.

Robust Finite-Time Consensus Tracking Algorithm for Multirobot Systems

Abstract: This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.

Self-Triggered Feedback Control Systems With Finite-Gain ${\cal L}_{2}$ Stability

Abstract: This paper examines a class of real-time control systems in which each control task triggers its next release based on the value of the last sampled state. Prior work used simulations to demonstrate that self-triggered control systems can be remarkably robust to task delay. This paper derives bounds on a task's sampling period and deadline to quantify how robust the control system's performance will be to variations in these parameters. In particular we establish inequality constraints on a control task's period and deadline whose satisfaction ensures that the closed-loop system's induced L 2 gain lies below a specified performance threshold. The results apply to linear time-invariant systems driven by external disturbances whose magnitude is bounded by a linear function of the system state's norm. The plant is regulated by a full-information H infin controller. These results can serve as the basis for the design of soft real-time systems that guarantee closed-loop control system performance at levels traditionally seen in hard real-time systems.

Decentralized Robust Adaptive Control for the Multiagent System Consensus Problem Using Neural Networks

Abstract: A robust adaptive control approach is proposed to solve the consensus problem of multiagent systems. Compared with the previous work, the agent's dynamics includes the uncertainties and external disturbances, which is more practical in real-world applications. Due to the approximation capability of neural networks, the uncertain dynamics is compensated by the adaptive neural network scheme. The effects of the approximation error and external disturbances are counteracted by employing the robustness signal. The proposed algorithm is decentralized because the controller for each agent only utilizes the information of its neighbor agents. By the theoretical analysis, it is proved that the consensus error can be reduced as small as desired. The proposed method is then extended to two cases: agents form a prescribed formation, and agents have the higher order dynamics. Finally, simulation examples are given to demonstrate the satisfactory performance of the proposed method.

Nonlinear Robust Adaptive Control of Flexible Air-Breathing Hypersonic Vehicles

Abstract: This paper describes the design of a nonlinear robust adaptive controller for a flexible air-breathing hypersonic vehicle model. Because of the complexity of a first-principle model of the vehicle dynamics, a control-oriented model is adopted for design and stability analysis. This simplified model retains the dominant features of the higher-fidelity model, including the nonminimum phase behavior of the flight-path angle dynamics, the flexibility effects, and the strong coupling between the engine and flight dynamics. A combination of nonlinear sequential loop closure and adaptive dynamic inversion is adopted for the design of a dynamic state-feedback controller that provides stable tracking of the velocity and altitude reference trajectories and imposes a desired set point for the angle of attack. A complete characterization of the internal dynamics of the model is derived for a Lyapunov-based stability analysis of the closed-loop system, which includes the structural dynamics. The proposed methodology addresses the issue of stability robustness with respect to both parametric model uncertainty, which naturally arises when adopting reduced-complexity models for control design, and dynamic perturbations due to the flexible dynamics. Simulation results from the full nonlinear model show the effectiveness of the controller.

Neural-Network-Based Terminal Sliding-Mode Control of Robotic Manipulators Including Actuator Dynamics

Abstract: A neural-network-based terminal sliding-mode control (SMC) scheme is proposed for robotic manipulators including actuator dynamics. The proposed terminal SMC (TSMC) alleviates some main drawbacks (such as contradiction between control efforts in the transient and tracking errors in the steady state) in the linear SMC while maintains its robustness to the uncertainties. Moreover, an indirect method is developed to avoid the singularity problem in the initial TSMC. In the proposed control scheme, a radial basis function neural network (NN) is adopted to approximate the nonlinear dynamics of the robotic manipulator. Meanwhile, a robust control term is added to suppress the modeling error and estimate the error of the NN. Finite time convergence and stability of the closed loop system can be guaranteed by Lyapunov theory. Finally, the proposed control scheme is applied to a robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.

A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control

Abstract: In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.

Dynamic inversion with zero-dynamics stabilisation for quadrotor control

Abstract: For a quadrotor, one can identify the two well-known inherent rotorcraft characteristics: underactuation and strong coupling in pitch-yaw-roll. To confront these problems and design a station-keeping and tracking controller, dynamic inversion is used. Typical applications of dynamic inversion require the selection of the output control variables to render the internal dynamics stable. This means that in many cases, perfect tracking cannot be guaranteed for the actual desired outputs. Instead, the internal dynamics of the feedback linearised system is stabilised using a robust control term. Unlike standard dynamic inversion, the linear controller gains are chosen uniquely to satisfy the tracking performance. Stability and tracking performance are guaranteed using a Lyapunov-type proof. Simulation with a typical nonlinear quadrotor dynamic model is performed to show the effectiveness of the designed control law in the presence of input disturbances.

Design and Implementation of a Robust Current Controller for VSI Connected to the Grid Through an LCL Filter

Abstract: This paper describes the design and implementation of a discrete controller for grid-connected voltage-source inverters with an LCL filter usually found in wind power generation systems. First, a theorem that relates the controllability of the discrete dynamic equation of the inverter with LCL filter and the sampling frequency is derived. Then, a condition to obtain a partial state feedback controller robust to grid impedance uncertainties and based on linear matrix inequalities is proposed. This controller guarantees the stability and damping of the LCL filter resonance for a large set of grid conditions without requiring self-tuning procedures. Finally, an internal model controller is added to ensure asymptotic reference tracking and disturbance rejection, significantly reducing the impact of grid background voltage distortion on the output currents. Experimental results are presented to support the theoretical analysis and to demonstrate the system performance.

High-Order Sliding-Mode Control of Variable-Speed Wind Turbines

Abstract: This paper deals with the power generation control in variable-speed wind turbines. These systems have two operation regions which depend on wind turbine tip speed ratio. A high-order sliding-mode control strategy is then proposed to ensure stability in both operation regions and to impose the ideal feedback control solution in spite of model uncertainties. This control strategy presents attractive features such as robustness to parametric uncertainties of the turbine. The proposed sliding-mode control approach has been validated on a 1.5-MW three-blade wind turbine using the national renewable energy laboratory wind turbine simulator FAST (Fatigue, Aerodynamics, Structures, and Turbulence) code. Validation results show that the proposed control strategy is effective in terms of power regulation. Moreover, the sliding-mode approach is arranged so as to produce no chattering in the generated torque that could lead to increased mechanical stress because of strong torque variations.

Practical Nonsingular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control

Abstract: This paper presents a practical nonsingular terminal sliding-mode (TSM) tracking control design for robot manipulators using time-delay estimation (TDE). The proposed control assures fast convergence due to the nonlinear TSM, and requires no prior knowledge about the robot dynamics due to the TDE. Despite its model-free nature, the proposed control provides high-accuracy control and robustness against parameters variations. The simplicity, robustness, and fast convergence of the proposed control are verified through both 2-DOF planar robot simulations and 3-DOF PUMA-type robot experiments.

A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay

Abstract: This paper investigates the problem of delay-dependent robust H infin filtering design for a class of uncertain discrete-time state-delayed Takagi-Sugeno (T-S) fuzzy systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel fuzzy-basis-dependent Lyapunov-Krasovskii functional combined with Finsler's lemma and an improved free-weighting matrix technique for delay-dependent criteria, a new sufficient condition for robust H infin performance analysis is first derived, and then, the filter synthesis is developed. It is shown that by using a simple linearization technique incorporating a bounding inequality, a unified framework can be developed such that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, simulation examples are provided to illustrate the advantages and less conservatism of the proposed approach.

Active Disturbance Rejection Control for MEMS Gyroscopes

Abstract: A new control method is presented to drive the drive axis of a Micro-Electro-Mechanical Systems (MEMS) gyroscope to resonance and to regulate the output amplitude of the axis to a fixed level. It is based on a unique active disturbance rejection control (ADRC) strategy, which actively estimates and compensates for internal dynamic changes of the drive axis and external disturbances in real time. The stability analysis shows that both the estimation error and the tracking error of the drive axis output are bounded and that the upper bounds of the errors monotonously decrease with the increase of the controller bandwidth. The control system is simulated and tested using a field-programmable-gate-array-based digital implementation on a piezoelectric vibrational gyroscope. Both simulation and experimental results demonstrate that the proposed controller not only drives the drive axis to vibrate along the desired trajectory but also compensates for manufacture imperfections in a robust fashion that makes the performance of the gyroscope insensitive to parameter variations and noises. Such robustness, the fact that the control design does not require an accurate plant model, and the ease of implementation make the proposed solution practical and economic for industrial applications.

Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters

Abstract: This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.

Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach

Abstract: This technical note presents necessary and sufficient conditions for the stability and stabilization of fractional-order interval systems. The results are obtained in terms of linear matrix inequalities. Two illustrative examples are given to show that our results are effective and less conservative for checking the robust stability and designing the stabilizing controller for fractional-order interval systems.

Attitude Tracking and Disturbance Rejection of Rigid Spacecraft by Adaptive Control

Abstract: In this technical note, we deal with the attitude tracking and disturbance rejection problem of spacecraft for a class of persistent disturbances with unbounded energy which include the sinusoidal disturbance as a special case. The approach involves the integration of techniques from robust control, adaptive control, and robust output regulation theory.

Robust LQR Control for PWM Converters: An LMI Approach

Abstract: A consistent framework for robust linear quadratic regulators (LQRs) control of power converters is presented. Systems with conventional LQR controllers present good stability properties and are optimal with respect to a certain performance index. However, LQR control does not assure robust stability when the system is highly uncertain. In this paper, a convex model of converter dynamics is obtained taking into account uncertainty of parameters. In addition, the LQR control for switching converters is reviewed. In order to apply the LQR control in the uncertain converter case, we propose to optimize the performance index by using linear matrix inequalities (LMIs). As a consequence, a new robust control method for dc-dc converters is derived. This LMI-LQR control is compared with classical LQR control when designing a boost regulator. Performance of both cases is discussed for load and line perturbations, working at nominal and non nominal conditions. Finally, the correctness of the proposed approach is verified with experimental prototypes.

A Control Approach for Thrust-Propelled Underactuated Vehicles and its Application to VTOL Drones

Abstract: A control approach is proposed for a class of underactuated vehicles in order to stabilize reference trajectories either in thrust direction, velocity, or position. The basic modeling assumption is that the vehicle is pro-pulsed via a thrust force along a single body-fixed direction and that it has full torque actuation for attitude control (i.e., a typical actuation structure for aircrafts, vertical take-off and landing (VTOL) vehicles, submarines, etc.). Additional assumptions on the external forces applied to the vehicle are also introduced for the sake of control design and stability analyses. They are best satisfied for vehicles which are subjected to an external force field (e.g., gravity) and whose shape induces lift forces with limited amplitude, unlike airplanes but as in the case of many VTOL drones. The interactions of the vehicle with the surrounding fluid are often difficult to model precisely whereas they may significantly influence and perturb its motion. By using a standard Lyapunov-based approach, novel nonlinear feedback control laws are proposed to compensate for modeling errors and perform robustly against such perturbations. Simulation results illustrating these properties on a realistic model of a VTOL drone subjected to wind gusts are reported.

Robust Fault Detection for Switched Linear Systems With State Delays

Abstract: This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H infin-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Adaptive Neural Sliding Mode Control of Nonholonomic Wheeled Mobile Robots With Model Uncertainty

Abstract: This brief proposes an adaptive neural sliding mode control method for trajectory tracking of nonholonomic wheeled mobile robots with model uncertainties and external disturbances. The dynamic model with model uncertainties and the kinematic model represented by polar coordinates are considered to design a robust control system. Self recurrent wavelet neural networks (SRWNNs) are used for approximating arbitrary model uncertainties and external disturbances in dynamics of the mobile robot. From the Lyapunov stability theory, we derive online tuning algorithms for all weights of SRWNNs and prove that all signals of a closed-loop system are uniformly ultimately bounded. Finally, we perform computer simulations to demonstrate the robustness and performance of the proposed control system.

Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control

Abstract: This paper deals with the robustness of Model Predictive Controllers for constrained uncertain nonlinear systems. The uncertainty is assumed to be modeled by a state and input dependent signal and a disturbance signal. The framework used for the analysis of the robust stability of the systems controlled by MPC is the wellknown Input-to-State Stability. It is shown how this notion is suitable in spite of the presence of constraints on the system and of the possible discontinuity of the control law.

A Discrete-Time Approach to Stability Analysis of Systems With Aperiodic Sample-and-Hold Devices

Abstract: Motivated by the widespread use of networked and embedded control systems, an algorithm for stability analysis is proposed for sampled-data feedback control systems with uncertainly time-varying sampling intervals. The algorithm is based on the robustness of related discrete-time systems against perturbation caused by the variation of sampling intervals. The validity of the algorithm is demonstrated by numerical examples.

Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems

Abstract: Positive Forms.- Positivity Gap.- Robustness with Time-varying Uncertainty.- Robustness with Time-invariant Uncertainty.- Robustness with Bounded-rate Time-varying Uncertainty.- Distance Problems with Applications to Robust Control.

Adaptive Fuzzy Output-Feedback Controller Design for Nonlinear Time-Delay Systems With Unknown Control Direction

Abstract: In this paper, the robust-control problem is investigated for a class of uncertain nonlinear time-delay systems via dynamic output-feedback approach. The considered system is in the strict-feedback form with unknown control direction. A full-order observer is constructed with the gains computed via linear matrix inequality at first. Then, with the bounds of uncertain functions known, we design the dynamic output-feedback controller such that the closed-loop system is asymptotically stable. Furthermore, when the bound functions of uncertainties are not available, the adaptive fuzzy-logic system is employed to approximate the uncertain function, and the corresponding output-feedback controller is designed. It is shown that the resulting closed-loop system is stable in the sense of semiglobal uniform ultimate boundedness. Finally, simulations are done to verify the feasibility and effectiveness of the obtained theoretical results.