An approach to improve active disturbance rejection control

ABSTRACT

In order to reduce the error and phase delay of the classical extended state observer (ESO) in estimating the system state and disturbance, in this paper, we combine ESO and tracking differentiator (TD) to construct a tracking differential extended state observer (TDESO). The observation error and observation speed of TDESO are also discussed. Then a nonlinear active disturbance rejection control system improved by TDESO for a linear plant is transformed into a Lurie system. Moreover, the circular criterion is used to analyse the absolute stability of the transformed Lurie system. Finally, TDESO is optimised and an improved linear state error feedback (PLSEF) is proposed to improve the rapidity of the system by using simulation and time domain analysis. And a second-order system is used to illustrate the performance of the proposed scheme. The simulation results show that our algorithm is effective.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

H ∞ Control for uncertain system with time-delay and nonlinear external disturbance via adaptive control method

This paper considers the H _∞ control problem for the uncertain time delay system with nonlinear external disturbance. Given a system containing nonlinear external disturbance, our purpose is to design a robust controller such that the uncertain system is asymptotically stable with a generalized H _∞ disturbance attenuation level ρ. In this paper we propose a new approach to design the controller for the uncertain system which is composed of a linear controller and an adaptive controller. The problem is solved by introducing a switching function and using the idea of formulation. Based on Lyapunov stability theory, new sufficient conditions are obtained in terms of linear matrix inequalities. The effectiveness and advantages of the proposed controller design are shown via a numerical example.     

Stochastic Stability and H∞ Disturbance Attenuation of A Class of Nonlinear Stochastic Delayed Systems

In this paper, we consider stochastic stability analysis and H_∞ disturbance attenuation for a class of discrete-time nonlinear stochastic retarded systems whose nonlinearities are described by statistical means. First a sufficient condition on mean square stability, which is independent of delay, is proposed using the stochastic Lyapunov functional approach. Then, H_∞ disturbance attenuation property of the system is analyzed. It is shown that the H_∞ disturbance attenuation of such nonlinear systems can be reduced to a linear matrix inequality problem.     

L2‐Gain Analysis for Synchronization of Stochastic Complex Network with Switched Topology and Time‐Varying Delay

We investigate the exponential stability and L₂‐gain analysis for the synchronization of stochastic complex networks under average dwell time switched topology with consideration of external disturbance, internal noise and fast time‐varying delay in the synchronized process. Based on the proposed stochastic network, a new L₂‐gain synchronization is proposed to solve the mean‐square exponential stable under switched topology with an H_∞ performance from the extrinsic disturbances to the synchronization error. The obtained results are applicable for the fast time‐varying case with larger‐than‐1 delay derivative. Finally, numerical simulations are performed to demonstrate the effectiveness of our strategies.     

Stability analysis of nonlinear multi-agent relay tracking systems over a finite time interval

ABSTRACT

This paper explores the stability of a class of multi-agent systems with proposed relay tracking strategy over a finite time interval. In this paper, agents are deployed in an area to monitor and track the intruded targets. According to proposed relay tracking strategy, the tracking agents and their communication topologies switch during the whole tracking process. This results in impulsive effects on the overall tracking errors. The relationship of finite time interval against desired overall tracking errors and control parameter is derived quantitatively for the multi-agent relay tracking system. Moreover, stability conditions for the system with disturbances and impulsive effects are obtained. Performance of proposed relay tracking strategy and correctness of derived results on stability over finite time intervals are demonstrated by a set of simulations.     

Delay Management in Mesh-Based P2P Live Streaming Using a Three-Stage Peer Selection Strategy

Peer-to-peer (P2P) live streaming systems have gained popularity due to the self-scalability property of the P2P overlay networks. In P2P live streaming, peers retrieve stream content from other peers in the system. Therefore, peer selection strategy is a fundamental element to build an overlay which manages the playback delay and startup delay experienced by the peers. In this paper, we propose a peer selection strategy which manages to build a minimum delay overlay using three different stages of overlay construction. In the first stage, the tracker suggests some peers as prospective partners to a new peer. In the second stage, the peer selects its partners out of these peers such that delay is minimized. The third stage is the topology adaptation phase of peers, where peers reposition themselves in the overlay to maintain minimum delay during peer churn. In the proposed peer selection strategy, peers are selected in all the stages based on parameters such as propagation delay, upload capacity, buffering duration and buffering level. The proposed strategy is compared with two existing strategies in the literature: Fast-Mesh (Ren et al. in IEEE Trans Multimed 11: 1446, 2009) and Hybrid live p2p streaming protocol (Hammami et al., 2014) using simulations. Our results show that playback delay and startup delay are reduced significantly with the help of proposed strategy. We demonstrate that the stability of the system also improves during peer churn.     

H∞ output tracking fuzzy control for nonlinear systems with time-varying delay

This paper proposes an observer-based output tracking control via virtual desired reference model for a class of nonlinear systems with time-varying delay and disturbance. First, the Takagi–Sugeno fuzzy model represents the nonlinear system with time-varying delay and disturbance. Then we design an observer to estimate immeasurable states and controller to drive the error between estimated state and virtual desired variables (VDVs) to zero such that the overall control output tracking system has H_∞ control performance. Using Lyapunov–Krasovskii functional, we derive sufficient conditions for stability. The advantages of the proposed output control system are (i) systematic approach to derive VDVs for controller design; (ii) relaxes need for real reference model; (iii) drops need for information of equilibrium; (iv) relaxed condition is provided via three-step procedure to find observer and controller gain. We carry out simulation using a continuous stirred tank reactor system where the effectiveness of the proposed controller is demonstrated by satisfactory numerical results.     

Robust Optimal Disturbance Observer Design for the Non‐Minimum Phase System

In this paper, a design strategy of robust disturbance observer is proposed systematically for stable non‐minimum phase systems. This strategy synthesizes the internal and robust stability, relative order and mixed sensitivity design requirements together to establish the optimization function. The optimal solution is obtained by standard H_∞ control theory under the condition of guarantying the presented requirements. Simulation results of a rotary mechanical system show the effectiveness of the proposed strategy.     

Active disturbance rejection control to MIMO nonlinear systems with stochastic uncertainties: approximate decoupling and output-feedback stabilisation

ABSTRACT

In this paper, we apply the active disturbance rejection control, an emerging control technology, to output-feedback stabilisation for a class of uncertain multi-input multi-output nonlinear systems with vast stochastic uncertainties. Two types of extended state observers (ESO) are designed to estimate both unmeasured states and stochastic total disturbance which includes unknown system dynamics, unknown stochastic inverse dynamics, external stochastic disturbance without requiring the statistical characteristics, uncertain nonlinear interactions between subsystems, and uncertainties caused by the deviation of control parameters from their nominal values. The estimations decouple approximately the system after cancelling stochastic total disturbance in the feedback loop. As a result, we are able to design an ESO-based stabilising output-feedback and prove the practical mean square stability for the closed-loop system with constant gain ESO and the asymptotic mean square stability with time-varying gain ESO, respectively. Some numerical simulations are presented to demonstrate the effectiveness of the proposed output-feedback control scheme.     

Further results on H∞ control for discrete-time Markovian jump time-delay systems

This paper studies the problem of H_∞ control for a class of discrete-time Markovian jump systems with time delay. The purpose is to improve the existing results on H_∞ controller design for Markovian jump systems. A novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality, which is proved to be less conservative than most results in the literature. Then the state feedback controller is designed, which guarantees the stochastic stability of the closed-loop system with a given disturbance attenuation. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques.     

ROBUSTLY STABLE MODEL-FOLLOWING CONTROL OF UNCERTAIN CONTINUOUS TIME PLANTS WITH THE USE OF A CORRECTING CONTROLLER

ABSTRACT

This paper deals with the robust stability of model-following control schemes for linear plants under parametric uncertainties and/or unmodeled dynamics and external disturbances. Apart from the nominal controller, a correcting one is incorporated to improve the disturbance rejection in certain ranges of frequencies. A Bode-type design is proposed to improve the reliability of the proposed method.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Disturbance decoupling for time delay systems

In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input and the disturbance of the corresponding time delay systems. A stability study using some results due to Pontryagin is presented for the resultant closed-loop system when the delay system is linear. Also, an approximate causal solution is proposed for the nonlinear time delay system based on its linearization around an equilibrium point. © 1997 by John Wiley & Sons, Ltd.     

随机时滞马尔可夫跳跃系统的比例-积分跟踪控制

针对具有时变时滞和未知非线性的随机马尔可夫跳变系统,基于传统的PI控制策略和线性矩阵不等式算法,提出一种具有随机稳定性能、跟踪性能和鲁棒性能的多目标控制器设计方案.运用Lyapunov稳定性理论并引入L<,1>性能指标,构造出具有PI结构的跟踪控制器,保证了随机马尔可大跳跃系统的稳定性和跟踪性能,实现了系统跟踪性能的优...     

典型二阶积分对象的新型控制策略

针对工业控制中常见的一类具有时滞的二阶积分对象,根据内模控制原理,提出一种新型控制策略。在该结构中,由参考模型来实现系统期望的设定值跟随响应特性,利用内模控制鲁棒性强的特点来抑制参数变化和干扰对系统的影响,从而使系统获得良好的干扰抑制特性和鲁棒性。调节参考模型参数和内模控制器参数,可使系统同时具有良好的设定值跟随特性和干扰抑制特性。仿真结果表明了方法的优越性。     

IS A MIXED DESIGN OF OBSERVER‐CONTROLLERS FOR TIME‐DELAY SYSTEMS INTERESTING?

This paper deals with H∞ observer‐based feedback control for linear time‐delay systems, in the framework of delay independent stability. We will propose a new LMI solution to observer‐controller design that ensures a disturbance attenuation level for the controlled output as well as for the state estimation error, which is an open problem. This will be compared with a well‐known solution and with a usual strategy in control which consists in designing the observer and the controller separately. Our aim is to try to bring a positive answer to the following question: is there an interest to solve the problem in a single (unique) formulation or should we design separately the observer and the controller? An application to a wind tunnel model is provided to emphasize the interest of the given results, particularly in comparison with existing results on H∞ observer‐based control.     

基于扩张状态观测器的分散模型预测控制

针对复杂关联系统中分散控制方法无法有效解决子系统间的耦合和干扰问题, 提出一种基于扩张状态观测器的分散模型预测控制算法. 首先将复杂关联系统分解为多个状态维数较低、控制变量较少的子系统, 并为每个子系统设计本地预测控制器; 然后, 采用扩张状态观测器对子系统的耦合项以及干扰项进行估计, 进而利用估计值对子系统进行前馈补偿, 从而降低复杂关联系统的计算复杂度, 提高系统的稳定性和抗干扰能力; 最后, 利用液位控制系统验证了所提出算法的有效性.

     

Stability and control of uncertain ICPT system considering time‐varying delay and stochastic disturbance

This paper studies the problem of robust exponential stability for uncertain inductively coupled power transfer (ICPT) system considering time‐varying delay and stochastic disturbance. Firstly, the model of the system is set up via a time domain method. Secondly, based on the Newton‐Leibnitz formula and stability theory, a new stability analysis of the ICPT system with uncertain parameter and time‐varying delay or stochastic disturbance is presented respectively. The proposed approach can be applied for analyzing other similar systems, and the obtained results can be also used for estimating convergence rate and region of stability. Thirdly, based on the Lyapunov‐Krasovskii functional (LKF) approach and the stochastic stability theory, robust exponential stability criteria in the mean square are derived and the relevant controller is designed. The proposed method can further reduce conservatism. Finally, the correctness and effectiveness of the obtained results are verified by an example and simulations indicate that the larger time delay, the slower attenuation. Simultaneously, the uncertain parameter and the stochastic disturbance have a significant influence on the region of stability. In addition, in respect of reducing conservatism, the effectiveness of the proposed method is demonstrated by comparing with other papers. In addition, the designed controller shows better performance for the ICPT system with the parameter uncertainty, the time‐varying delay, and the stochastic disturbance.     

Stability analysis of systems via a new double free-matrix-based integral inequality with interval time-varying delay

ABSTRACT

This paper investigates the problem of delay-dependent stability analysis for systems with interval time-varying delay. By means of a new double free-matrix-based integral inequality and augmented Lyapunov–Krasovskii functionals containing as much information of time-varying delay as possible, a new stability criterion for systems is established. Firstly, by a double integral term two-step estimation approach and combined with single free-matrix-based integral inequalities, a stability criteria is presented. Then, compared with the double integral term two-step estimation approach, the proposed new double free-matrix-based integral inequality with more related time delays has potential to lead to a criterion with less conservatism. Finally, the validity of the presented method is demonstrated by two numerical examples.