Time-varying Parameter Perturbations Research Articles

Iterative Design Algorithm for Robust Disturbance-Rejection Control

An iterative design algorithm is developed for robust disturbance–rejection control of uncertain systems with time-varying parameter perturbations in this paper. For more design degrees of freedom, a generalized equivalent-input-disturbance estimator is adopted to approximate the effect of both disturbances and uncertainties. By the bound real lemma, the H∞ norm is used to evaluate the robust disturbance–rejection performance of the closed-loop uncertain system. To avoid the constraints introduced by the widely used commutative condition, the control gains are divided into two groups and calculated by steps. Further, two robust quadratic stability conditions are derived, and an iterative design algorithm is developed to optimize the robust H∞ disturbance–rejection performance. Finally, the effectiveness and advantages of the developed method are demonstrated by a case study of a suspension system of modern vehicles.

Intermittent Exponential Synchronization for Memristor-Based Neural Networks With Inertial Items and Mixed Time-Varying Delays

This article investigates the exponential synchronization problem for a class of memristor-based neural networks with mixed time-varying delays and parameter perturbations, and inertial items are considered (MINNs). A periodically intermittent control protocol is designed to guarantee the exponential synchronization between two MINNs. Then, by adopting nonsmooth analysis, Halanay inequality, and Lyapunov theory, the exponential synchronization criteria for MINNs under the proposed controller are obtained. Furthermore, instead of the reduced-order method, the synchronization of MINNs is considered under the framework of the second-order system directly, which is different from existing literature. Some numerical simulations are presented to show the validity of the proposed criteria in the end.

New delay-range-dependent exponential stability criterion and $ H_\infty $ performance for neutral-type nonlinear system with mixed time-varying delays

<abstract><p>For a neutral system with mixed discrete, neutral and distributed interval time-varying delays and nonlinear uncertainties, the problem of exponential stability is investigated in this paper based on the $ H_\infty $ performance condition. The uncertainties are nonlinear time-varying parameter perturbations. By introducing a decomposition matrix technique, using Jensen's integral inequality, Peng-Park's integral inequality, Leibniz-Newton formula and Wirtinger-based integral inequality, utilization of a zero equation and the appropriate Lyapunov-Krasovskii functional, new delay-range-dependent sufficient conditions for the $ H_\infty $ performance with exponential stability of the system are presented in terms of linear matrix inequalities. Moreover, we present numerical examples that demonstrate exponential stability of the neutral system with mixed time-varying delays, and nonlinear uncertainties to show the advantages of our method.</p></abstract>

Delay-Dependent Robust H∞ Performance for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper deals with the problems of delay-dependent stability and H∞ performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved H∞ performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.

Control Design of Sampled-data Uncertain Systems with Time-varying Input Delay and Parameter Perturbations

Control Design of Sampled-data Uncertain Systems with Time-varying Input Delay and Parameter Perturbations

Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.

Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper considers the problem of robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations. Two type uncertainties such as nonlinear time-varying parameter perturbations and norm-bounded uncertainties have been discussed. Based on the new Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a new delay-dependent stability criterion for the system is established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations

This paper studies delay-dependent robust stability problem for neutral system with mixed time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Based on Lyapunov functional approach and linear matrix inequality technology, some improved delay-dependent stability conditions are derived by introducing free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Delay-dependent Robust Stability of Neutral Systems with Mixed Delays and Nonlinear Perturbations

Abstract This paper concerns the delay-dependent robust stability problem of uncertain neutral systems with mixed neutral and discrete delays. Nonlinear time-varying parameter perturbations are considered. Based on the newly established integral inequalities, the neutral-delay-dependent and discrete-delay-dependent stability criterion is derived without using a fixed model transformation. The condition is presented in terms of linear matrix inequality and can be easily solved by existing convex optimization techniques. A numerical example is given to demonstrate the less conservatism of the proposed results.

Robust speed tracking of permanent magnet synchronous motor servo systems by equivalent disturbance attenuation

A new robust controller consisting of a nominal controller and a robust compensator is proposed. The controller is applied to a permanent magnet synchronous motors servo system to eliminate speed-tracking error due to time-varying load torque uncertainty and parameter perturbations. It is proved that the speed-tracking error can be made as small as desired if the initial conditions are zeros. For cases where the initial conditions are non-zero but bounded, after a finite transient period, the same speed-tracking error reduction can be achieved. Simulation results are presented to confirm the efficiency of the proposed method.

Delay-dependent guaranteed cost control for uncertain neutral systems with nonlinear parameter perturbations

The delay-dependent guaranteed cost control problem for uncertain neutral systems with nonlinear time-varying parameter perturbations is studied. By using a newly established integral inequality, the delay-dependent conditions for the existence of memoryless and memory state feedback guaranteed cost controllers are derived in terms of nonlinear matrix inequalities without involving model transformation and bounding technique for cross terms. An iterative algorithm involving convex optimisation is presented to solve these nonlinear matrix inequalities. A numerical example is given to demonstrate the effectiveness and superiority of the proposed results.

A Mixed Robust/Optimal Active Vibration Control for Uncertain Flexible Structural Systems with Nonlinear Actuators Using Genetic Algorithm

In this article, a mixed robust/optimal control approach is proposed to treat the active vibration control (or active vibration suppression) problems of flexible structural systems under the effects of mode truncation, linear time-varying parameter perturbations and nonlinear actuators. A new robust stability condition is derived for the flexible structural system which is controlled by an observer-based controller and is subject to mode truncation, nonlinear actuators and linear structured time-varying parameter perturbations simultaneously. Based on the robust stability constraint and the minimization of a defined H 2 performance, a hybrid Taguchi-genetic algorithm (HTGA) is employed to find the optimal state feedback gain matrix and observer gain matrix for uncertain flexible structural systems. A design example of the optimal observer-based controller for a simply supported beam is given to demonstrate the combined application of the presented sufficient condition and the HTGA.

Stability robustness of optimal active uncertain suspensions incorporating human sensitivity to vibration

In this article, the human sensitivity to vibration acceleration at various frequencies is incorporated in the design of active suspension by using the frequency-shaped linear-quadratic-Gaussian (LQG) method. And three new sufficient conditions of stability robustness for the frequency-shaped LQG active suspension systems subject to both disturbance/noise uncertainties and linear time-varying parameter perturbations are also presented in this article. The proposed new sufficient conditions provide a quantitative measure for automotive designers to design the frequency-shaped LQG active suspension systems with robustness properties. An illustrated example is given to demonstrate the applicability of the proposed new sufficient criteria.

Robust stability of linear neutral systems with nonlinear parameter perturbations

The robust stability of uncertain linear neutral systems with time-varying discrete and neutral delays is investigated. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Both delay-dependent and delay-derivative-dependent stability criteria are proposed and are formulated in the form of linear matrix inequalities (LMIs). The results in this paper contain some existing results as their special cases. A numerical example is also given to indicate significant improvements over some existing results.

Stability robustness of optimal active uncertain suspensions incorporating human sensitivity to vibration

In this article, the human sensitivity to vibration acceleration at various frequencies is incorporated in the design of active suspension by using the frequency-shaped linear-quadratic-Gaussian (LQG) method. And three new sufficient conditions of stability robustness for the frequency-shaped LQG active suspension systems subject to both disturbance/noise uncertainties and linear time-varying parameter perturbations are also presented in this article. The proposed new sufficient conditions provide a quantitative measure for automotive designers to design the frequency-shaped LQG active suspension systems with robustness properties. An illustrated example is given to demonstrate the applicability of the proposed new sufficient criteria.

Robust Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems with Persistent Excitation

ABSTRACTBased on the frequency-shaping optimal control method, this paper proposes a time-domain robust disturbance rejection design approach for a class of uncertain flexible mechanical systems subject to persistent disturbances and time-varying parameter perturbations. In the approach, a frequency-shaping output filter is first employed to combine with the mechanical system and a Kalman filter to form an augmented system. Some eigenvalues of the frequency-shaping output filter coincide with the unstable poles of the disturbance dynamics to perform disturbance rejection. Then, for the designed closed-loop system to have asymptotic stability, a new robust stability condition is proposed. It is shown that, using the proposed stability condition, the resulting controller can suppress the persistent disturbance and keep the flexible mechanical system from the possibility of instability caused by spillover and time-varying parameter perturbations. Finally, two examples are given to demonstrate the use of the design approach.

Robust observer-based frequency-shaping optimal vibration control of uncertain flexible linkage mechanisms

Based on the state-space model of the flexible linkage mechanism equipped with piezoelectric materials, a robust observer-based frequency-shaping optimal feedback (OBFSOF) control methodology is presented for actively suppressing the elastodynamic responses of the high-speed flexible linkage mechanism with linear structured time-varying parameter perturbations. The advantage of the proposed OBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, this paper also presents two robust stability criteria to guarantee that the designed OBFSOF controller can make the controlled flexible linkage mechanism system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Numerical simulation of a slider–crank mechanism example is performed to evaluate the improvement of the elastodynamic responses.

Robust Kalman-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems

ABSTRACTThis paper presents a time-domain control methodology, which is named as the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method, to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high frequencies unmodelled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise),and noise uncertainties. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rotor system.

ROBUST Hinfinity CONTROL FOR SYSTEMS WITH TIME-VARYING PARAMETER UNCERTAINTY AND VARIANCE CONSTRAINTS

In this paper, the problem of designing robust Hinfinity controllers for linear continuous-time systems subjected to time-varying parameter uncertainty and steady-state variance constraints is considered. The goal of this problem is to design the state feedback controller, such that for all admissible time-varying parameter perturbations, the steady-state variance of each state is not more than the individual prespecified upper bound and the Hinfinity norm of the transfer function from disturbance inputs to system outputs meets the prespecified upper bound constraint, simultaneously. The parameter uncertainties are allowed to be time-varying and norm-bounded. A purely algebraic matrix equation approach is effectively utilized to solve the problem addressed. The existence conditions as well as the explicit expression of desired controllers are presented, and two illustrative examples are used to demonstrate the applicability of the proposed design procedure.