Disturbance Attenuation Problem Research Articles

Output Feedback $H_\infty$ Control of Continuous-Time Infinite Markovian Jump Linear Systems via LMI Methods

The output feedback $H_\infty$ control is addressed for a class of continuous-time Markov jump linear systems with the Markov process taking values in an infinite countable set $\mathcal{S}$. We consider that only an output and the jump parameters are available to the controller. Via a certain bounded real lemma, together with some extensions of Schur complements and of the projection lemma, a theorem which characterizes whether there exists a full-order solution to the disturbance attenuation problem is devised in terms of two different linear matrix inequality (LMI) feasibility problems. This result connects a certain projection approach to an LMI problem which is more amenable to computer solution, and hence for design. We conclude the paper with some design algorithms for the construction of such controllers and an illustrative example.

Nonlinear control design of an airfoil with active flutter suppression in the presence of disturbance

The nonlinear flutter suppression of a typical wing section is investigated. A structural nonlinearity is considered in the pitch direction. Integral-input-to-state stability (iISS) concept is utilised for the construction of a feedback controller. One of the advantages of this design is its simplicity and straightforwardness. A backstepping method is used to compare the results for the typical section, which is a multi-input system. The iISS controller has an outstanding performance in comparison to the backstepping method, especially with regards to the disturbance attenuation problem. A Lyapunov-based controller was also introduced for the system.

On dissipativity, passivity and dynamic operability of nonlinear processes

Passivity and dissipativity have long being important tools in nonlinear systems analysis and control design. In this article, connections between dissipativity and the dynamic operability of nonlinear processes are explored. In particular, we study nonlinear processes that are dissipative with respect to a supply rate quadratic in the inputs and outputs. These type of dissipative systems include processes that can be unstable and can have unstable zero dynamics. Two methods to quantify operability are proposed. The first method analyses the speed of response of the closed-loop with no exogenous signals. The second method studies the output disturbance attenuation problem. The proposed framework reveals important insights into those nonlinear process characteristics that can limit dynamic operability.

Output‐feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states

AbstractIn this paper, the problems of stochastic disturbance attenuation and asymptotic stabilization via output feedback are investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. For the first problem, under the condition that the stochastic inverse dynamics are generalized stochastic input‐to‐state stable, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system noise‐to‐state stable. For the second problem, under the conditions that the stochastic inverse dynamics are stochastic input‐to‐state stable and the intensity of noise is known to be a unit matrix, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system globally asymptotically stable in probability. Using a feedback domination design method, we construct these two controllers in a unified way. Copyright © 2007 John Wiley & Sons, Ltd.

Dynamic surface control for stabilization of the oscillating eccentric rotor

The present paper presents a new solution for the stabilization and disturbance attenuation problems of the oscillating eccentric rotor (OER), an extensively studied non-linear under-actuated mechanical system. Designing control law for such systems is a challenging task owing to the under-actuation property, which poses problems in exact feedback linearization. Presented non-linear controller design exploits the recently introduced dynamic surface control technique in a novel manner. The task of the controller is not only to de-spin the rotor but also to stop the translational oscillations. The design procedure is simpler and more intuitive than currently available integrator backstepping or energy-shaping-based designs. Stability is analysed by decomposing the system into a cascade of several subsystems. Advantages over existing controller designs are analysed theoretically and verified using numerical simulations. The design is found to attenuate oscillation amplitude effectively in the presence of an external sinusoidal translational disturbance besides aggressive stabilization.

Passivity-Based Dynamic Visual Feedback Control for Three-Dimensional Target Tracking: Stability and $L_{2}$-Gain Performance Analysis

This paper investigates vision-based robot control based on passivity for three-dimensional (3-D) target tracking. First, using standard body-attached coordinate frames (the world frame, camera frame, and object frame), we represent the relative position and orientation between a moving target and a camera as an element of SE(3). Using this representation we derive a nonlinear observer to estimate the relative rigid body motion from the measured camera data. We then establish the relationship between the estimation error in a 3-D workspace and in the image plane. We show passivity of the dynamic visual feedback system by combining the passivity of both the visual feedback system and the manipulator dynamics which allows us to prove stability in the sense of Lyapunov for the full 3-D dynamic visual feedback system. The L2 -gain performance analysis, which deals with the disturbance attenuation problem, is then considered via dissipative systems theory. Finally, experimental results are presented to verify the stability and L2-gain performance of the dynamic visual feedback system

計測不可能な入力の推定機能をもつオブザーバを用いた外乱抑制制御系

A disturbance observer is well known as a control system which can reduce the adverse effect of disturbances. In order to synthesize the disturbance observer, the exact dynamical model of disturbance is required. However, in general, it is difficult to obtain the exact disturbance model. On the other hand, an observer with a function of estimating unmeasurable inputs has been already proposed. By using this observer, unmeasurable disturbances can be estimated without the exact disturbance model. However, disturbance attenuation problem based on the observer still remains as an open issue. In this paper, a synthesis method of the control system for disturbance attenuation based on an observer with a function of estimating unmeasurable inputs is proposed and the class of compensators which guarantee the internal stability of the closed loop system is clarified.

Adaptive H-infinity control of a class of uncertain nonlinear systems

It is concerned with the problem of disturbance attenuation with stability for uncertain nonlinear systems by adaptive output feedback. By a partial-state observer and Backstepping technique, an adaptive output feedback controller was constructed, which can solve the standard gain disturbance attenuation problem with internal stability.

Delay-dependent robust H∞ control of uncertain neutral systems with state and input delays: LMI optimization approach

Abstract The H ∞ robust control problem for a class of uncertain neutral system with both state and input delays is considered. By choosing a Lyapunov–Krasovskii functional, some delay-dependent criteria are proposed to guarantee stabilization and disturbance attenuation of the systems. Linear matrix inequality (LMI) optimization approach is used to solve the H ∞ control disturbance attenuation problem. Significant improvement for the delay-dependent results has been reached. Computer software Matlab can be applied to obtain all the proposed results. Finally, some numerical examples are given to illustrate the improvement archived in this paper.

H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions

This paper presents the issue of robust disturbance attenuation and robust asymptotic stability problem for finite-dimensional linear parameter-dependent state-delayed systems. The use of polynomial parameter-dependent quadratic Lyapunov functions and linear matrix inequalities (LMIs) formulations for robust H ∞ control are considered. It is shown that the state feedback control can be determined to guarantee the stability of the closed-loop system independently of the time-delay. We present an illustrative example to demonstrate the applicability of the proposed design approach.

H∞ disturbance attenuation for uncertain mechanical systems with input delay

The paper deals with the robust H disturbance attenuation problem for uncertain mechanical systems with input delay. The parameter uncertainties for the mass, damping and stiffness matrices take an additive a priori norm-bounded form. The time delay for the input is time-invariant but has a known constant bound. A robust static H state-feedback controller is designed to attenuate the disturbance on the controlled output to a prescribed level for all admissible parameter uncertainties and input delay. The design approach is formulated in terms of the feasibility of certain delay-dependent linear matrix inequalities. A numerical example is employed to illustrate the effectiveness of the approach.

TRACKING WITH BOUNDED ACTUATORS: SCHEDULED CONTROLLERS

We extend a class of scheduled controllers, that were originally developed to address actuator saturation in the disturbance attenuation problem, to the problem of tracking of generally unknown signals. The main assumption is that some (possibly conservative) bounds be known for peak magnitude and rate of the tracking signal. Both state feedback for and static output feedback controllers are presented, though the choice of the approach to obtain the latter is left to the user. The solvability conditions and effectiveness are shown through an example.

Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach

In this paper the disturbance attenuation and rejection problem is investigated for a class of MIMO nonlinear systems in the disturbance-observer-based control (DOBC) framework. The unknown external disturbances are supposed to be generated by an exogenous system, where some classic assumptions on disturbances can be removed. Two kinds of nonlinear dynamics in the plants are considered, respectively, which correspond to the known and unknown functions. Design schemes are presented for both the full-order and reduced-order disturbance observers via LMI-based algorithms. For the plants with known nonlinearity, it is shown that the full-order observer can be constructed by augmenting the estimation of disturbances into the full-state estimation, and the reduced-order ones can be designed by using of the separation principle. For the uncertain nonlinearity, the problem can be reduced to a robust observer design problem. By integrating the disturbance observers with conventional control laws, the disturbances can be rejected and the desired dynamic performances can be guaranteed. If the disturbance also has perturbations, it is shown that the proposed approaches are infeasible and further research is required in the future. Finally, simulations for a flight control system is given to demonstrate the effectiveness of the results. Copyright © 2005 John Wiley & Sons, Ltd.

ROBUST REGULATION OF A CLASS OF NONLINEAR SINGULARLY PERTURBED SYSTEMS

In this paper, robust regulation of a class of nonlinear singularly perturbed systems, via nonlinear H∞ approach is considered. Under appropriate assumptions, it is shown through two new theorems that the existence of a positive definite solution for the Hamilton-Jacobi-Isaacs inequality related to the problem of disturbance attenuation for the main singularly perturbed system, can be related to the existence of a solution of a (simpler) Hamilton-Jacobi-Isaacs inequality arising in the problem of disturbance attenuation for the reduced-order system.

An Adaptive Type-2 Fuzzy Neural Controller for Nonlinear Uncertain Systems

This article proposes a new control scheme using type-2 fuzzy neural network (type-2 FNN) and adaptive filter for controlling nonlinear uncertain systems. This type-2 FNN model combines the advantages of type-2 fuzzy logic systems and neural networks. The type-2 FNN system has the ability of universal approximation, that is, identification of nonlinear dynamic systems. We herein adopt it to develop a novel control scheme for nonlinear uncertain systems. The proposed control scheme consists of a PD-type adaptive FNN controller and a pre-filter. The adaptive filter is used to provide better performance under transient response and to treat the problem of disturbance attenuation. The tuning parameters for the filter and the type-2 FNN controller will change according to the learning algorithm. By the Lyapunov stability theorem, the convergence of parameters is given in order to guarantee the stability of nonlinear uncertain systems. The effectiveness of the proposed controller is demonstrated by simulated results.

1114 未知入力システムに対する線形関数オブザーバの構成法と外乱抑制問題への応用(GS8 微細加工・生産システム,一般セッション)

1114 未知入力システムに対する線形関数オブザーバの構成法と外乱抑制問題への応用(GS8 微細加工・生産システム,一般セッション)

ON THE DISTURBANCE ATTENUATION FOR INPUT DELAY SYSTEMS

This paper addresses the disturbance attenuation problem for multivariable linear systems with a delayed input. To solve this problem, we use a static feedback based on a state prediction, which allows us to analyze an equivalent linear system without delay. Then, geometric conditions are given on this new equivalent system, and a numerical example illustrates our results.

MIMO Disturbance and Plant Uncertainty Attenuation by Feedback

This paper investigates the ability of feedback to reduce plant and disturbance uncertainties in the multiple-input-multiple-output (MIMO) case, by solving two fundamental problems posed by Zames in the late seventies. The first problem is termed the MIMO extension of the optimal robust disturbance attenuation problem, the second is a filtering of plant uncertainty two-degree of freedom feedback problem. The optimal solutions of these problems are characterized using Banach space duality theory and shown to satisfy an allpass condition and an extremal identity. Moreover, the duality description leads to a dual pair of optimizations and the introduction of two nonstandard matrix norms. In particular, the primal-dual optimization reduces naturally to approximate finite dimensional convex optimizations within desired tolerance. Whereas the computation of the nonstandard matrix norms are shown to be equivalent to specific semi-definite programming problems, and a numerical solution based on convex programming is provided. It is also shown using Douglas' range inclusion theorem that performance is a monotonic function of uncertainty, and some qualitative implications for feedback are derived.

Application of Constrained H∞ Control to Active Suspension Systems on Half-Car Models

This paper formulates the active suspension control problem as disturbance attenuation problem with output and control constraints. The H∞ performance is used to measure ride comfort such that more general road disturbances can be considered, while time-domain hard constraints are captured using the concept of reachable sets and state-space ellipsoids. Hence, conflicting requirements are specified separately and handled in a nature way. In the framework of Linear Matrix Inequality (LMI) optimization, constrained H∞ active suspensions are designed on half-car models with and without considering actuator dynamics. Analysis and simulation results show a promising improvement on ride comfort, while keeping suspension strokes and control inputs within bounds and ensuring a firm contact of wheels to road.

Nonlinear generalization of scaled ℋ︁∞ control: global robustification against nonlinearly bounded uncertainties

AbstractThis paper proposes a novel approach to the problem of ℒ︁2 disturbance attenuation with global stability for nonlinear uncertain systems by placing great emphasis on seamless integration of linear and nonlinear controllers. This paper develops a new concept of state‐dependent scaling adapted to dynamic uncertainties and nonlinear‐gain bounded uncertainties that do not necessarily have finite linear‐gain, which is a key advance from previous scaling techniques. The proposed formulation of designing global nonlinear controllers is not only a natural extension of linear robust control, but also the approach renders the nonlinear controller identical with the linear control at the equilibrium. This paper particularly focuses on scaled ℋ︁∞ control which is widely accepted as a powerful methodology in linear robust control, and extends it nonlinearly. If the nonlinear system belongs to a generalized class of triangular systems allowing for unmodelled dynamics, the effect of the disturbance can be attenuated to an arbitrarily small level with global asymptotic stability by partial‐state feedback control. A procedure of designing such controllers is described in the form of recursive selection of state‐dependent scaling factors. Copyright © 2004 John Wiley & Sons, Ltd.