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A stability robustness test is developed for internally stable, nominal, linear time‐invariant (LTI) feedback systems subject to structured, linear time‐varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ν‐gap metric framework. The scaled LTI ν‐gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ν‐gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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H∞‐norm is widely used in the analysis and synthesis of robust control, a field which continues to flourish and develop. However, H∞‐norm can only be used to measure the distance between two stable systems, not unstable systems. Sometimes, it is not appropriate to measure the gap between two systems. In this paper, a new metric, angular metric, defined in linear spaces of real rational matrices, is used to measure the distance of two systems with different dimensions. It is also used to measure the uncertainties and describe the performance specifications of the robust control system. In the framework of this metric, the robust stability margin is proposed to characterize the stability robustness of the closed‐loop system. When both the plant and the controller have uncertainties simultaneously, we introduce structural robust stability and prove the necessary and sufficient conditions of the robust stability of the feedback control system. 相似文献
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广义不确定周期时变系统的鲁棒稳定性分析 总被引:4,自引:0,他引:4
研究广义不确定周期时变系统的鲁棒稳定性问题.基于广义周期时变系统Lyapunov不等式,提出了广义不确定周期时变系统鲁棒稳定的概念,采用矩阵不等式(LMI)方法,得到了该类系统鲁棒稳定的充分必要条件;然后,进一步研究了在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法;最后,引入了广义周期时变系统二次稳定的概念,并讨论了二次稳定性与鲁棒稳定性之间的关系. 相似文献
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Yuki Hashimoto 《International journal of control》2013,86(5):411-417
The problem of robust output tracking for a class of uncertain nonlinear systems which do not satisfy the conventional matching condition is considered. The main assumption on the uncertainty is that the triangularity condition is satisfied. Based on backstepping method and input/output linearization approach, we propose a class of non-adaptive state feedback controllers which can guarantee exponential stability of the tracking error for the uncertain nonlinear systems first. Next, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we design a class of adaptive robust controllers. It is shown that under the proposed adaptive robust control the tracking error of the controlled system converges to zero as time approaches infinity. 相似文献
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Shinq-Jen Wu Chin-Teng Lin 《Fuzzy Systems, IEEE Transactions on》2002,10(2):128-143
In this paper, we propose a global optimal fuzzy tracking controller, implemented by fuzzily blending the individual local fuzzy tracking laws, for continuous and discrete-time fuzzy systems with the aim of solving, respectively, the continuous and discrete-time quadratic tracking problems with moving or model-following targets under finite or infinite horizon (time). The differential or recursive Riccati equations, and more, the differential or difference equations in tracing the variation of the target, are derived. Moreover, in the case of time-invariant fuzzy tracking systems, we show that the optimal tracking controller can be obtained by just solving algebraic Riccati equations and algebraic matrix equations. Grounding on this, several fascinating characteristics of the resultant closed-loop continuous or discrete time-invariant fuzzy tracking systems can be elicited easily. The stability of both closed-loop fuzzy tracking systems can be ensured by the designed optimal fuzzy tracking controllers. The optimal closed-loop fuzzy tracking systems cannot only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Moreover, the resulting closed-loop fuzzy tracking systems possess infinite gain margin; that is, their stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the performance of the proposed optimal fuzzy tracker design schemes and to demonstrate the proved stability properties 相似文献
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This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results. 相似文献
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In this note, we study the envelope of the Nyquist plots generated by an interval plant family and show that this boundary is not always contained in the Nyquist plots of the Kharitonov plants. With this motivation in mind, we give a sufficient condition for an envelope point to be contained in the Nyquist plot of a Kharitonov plant and use it to generate large and critical portions of the Nyquist envelope; e.g., we show that the outer Nyquist envelope of a stable interval plant is generated by the Nyquist plots of the Kharitonov plants. Another by-product of this sufficient condition is a framework for developing new extreme point results for interval feedback systems. This framework is useful in computing the phase margin and the maximal peaking in the sensitivity and complementary sensitivity functions and in stating a robust version of the circle criterion. We also use this framework to easily explain existing extreme point results for the gain margin, the H ∞ norm and the positive realness of interval plants. One conclusion which emerges is this: Seemingly, all important properties of an interval feedback system are deducible from the Kharitonov plants 相似文献
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A Saturating Extension of an Output Feedback Controller for Internally Damped Euler‐Lagrange Systems
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In this research, a novel extension of the passivity‐based output feedback trajectory tracking controller is developed for internally damped Euler‐Lagrange systems with input saturation. Compared with the previous output feedback controllers, this new design of a combined adaptive controller‐observer system will reduce the risk of actuator saturation effectively via generalized saturation functions. Semi‐global uniform ultimate boundedness stability of the tracking errors and state estimation errors is guaranteed by Lyapunov stability analysis. An application of the proposed saturated output feedback controller is the stabilization of a nonholonomic wheeled mobile robot with saturated actuators towards desired trajectories. Simulation results are provided to illustrate the efficiency of the proposed controller in dealing with the actuator saturation. 相似文献
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Hamid Khaloozadeh Mohammad Ali Nekoui Farid Shahni 《International Journal of Control, Automation and Systems》2010,8(3):527-533
The goal of this paper is global disturbance rejection in nonlinear systems. An output feedback controller with disturbance
rejection is developed for a class of nonlinear multi input-multi output (MIMO) systems. The availability of state variables
and the bound of disturbances are not required to be known in advance and reference tracking will is guaranteed. By the aid
of designing an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed.
For tracking problem, an adaptive pre-compensator is used. The control methodology is robust against both constant and time
varying bounded disturbances, maintaining effective performance. The adaptive laws are derived based on the Lyapunov synthesis
method, therefore closed-loop asymptotic stability is also guaranteed. Moreover, for chattering reduction we use a low-pass
filter. Consequently, small gain theorem is adopted to prove the stability of the closed-loop system. Simulation results are
employed to illustrate the effectiveness of the proposed controller. 相似文献
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In the spirit of Kharitonov, the robust stability of feedback systems under both structured and unstructured perturbations is discussed. Extreme point results are obtained. The stability margin of an interval system family is achieved at pre-specified twelve vertex systems 相似文献
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Hakk? Ula? Ünal 《Automatica》2008,44(11):2950-2953
Small gain theorems are used to verify the stability of a feedback interconnection of causal stable systems. In this work, we extend the small gain condition to test the stability of a feedback interconnection of two stable systems at least one of which is non-causal. This result may find application in the robust controller design for time-delay systems. 相似文献
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Chang-Woo Park 《Journal of Intelligent and Robotic Systems》2004,39(2):131-147
In this paper, a robust stable fuzzy control design based on feedback linearization is presented. Takagi–Sugeno fuzzy model is used as representing the nonlinear plant model and uncertainty is assumed to be included in the model structure with known bounds. For this structured uncertainty, the closed system can be analyzed by applying the perturbation system stability analysis to the fuzzy feedback linearization systems and a sufficient condition is derived to guarantee the stability of the closed-loop system with bounded parameter uncertainties. Based on the developed analysis method, we can design a robust fuzzy controller by choosing the control parameters satisfying the robust stability condition. 相似文献
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This work proposes a robust near-optimal non-linear output feedback controller design for a broad class of non-linear systems with time-varying bounded uncertain variables. Both vanishing and non-vanishing uncertainties are considered. Under the assumptions of input-to-state stable (ISS) inverse dynamics and vanishing uncertainty, a robust dynamic output feedback controller is constructed through combination of a high-gain observer with a robust optimal state feedback controller synthesized via Lyapunov's direct method and the inverse optimal approach. The controller enforces exponential stability and robust asymptotic output tracking with arbitrary degree of attenuation of the effect of the uncertain variables on the output of the closed-loop system, for initial conditions and uncertainty in arbitrarily large compact sets, provided that the observer gain is sufficiently large. Utilizing the inverse optimal control approach and singular perturbation techniques, the controller is shown to be near-optimal in the sense that its performance can be made arbitrarily close to the optimal performance of the robust optimal state feedback controller on the infinite time-interval by selecting the observer gain to be sufficiently large. For systems with non-vanishing uncertainties, the same controller is shown to ensure boundedness of the states, uncertainty attenuation and near-optimality on a finite time-interval. The developed controller is successfully applied to a chemical reactor example. 相似文献
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In our early work, we show that one way to solve a robust control problem of an uncertain system is to translate the robust control problem into an optimal control problem. If the system is linear, then the optimal control problem becomes a linear quadratic regulator (LQR) problem, which can be solved by solving an algebraic Riccati equation. In this article, we extend the optimal control approach to robust tracking of linear systems. We assume that the control objective is not simply to drive the state to zero but rather to track a non-zero reference signal. We assume that the reference signal to be tracked is a polynomial function of time. We first investigated the tracking problem under the conditions that all state variables are available for feedback and show that the robust tracking problem can be solved by solving an algebraic Riccati equation. Because the state feedback is not always available in practice, we also investigated the output feedback. We show that if we place the poles of the observer sufficiently left of the imaginary axis, the robust tracking problem can be solved. As in the case of the state feedback, the observer and feedback can be obtained by solving two algebraic Riccati equations. 相似文献
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The authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty. The basic system considered is that of the classical Lur'e problem of nonlinear control theory. A robust version of the Lur'e problem consisting of a family of linear time-invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector-bounded nonlinear gains is presently treated. By using the Kharitonov theorem to develop some extremal results on positive realness of interval transfer functions (i.e. a family of rational transfer functions with bounded independent coefficient perturbations), the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed. These calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations 相似文献