带阶跃扰动的线性时滞系统最优无静差控制

研究线性时滞系统在阶跃扰动作用下的最优控制问题．首先基于内模原理构造扰动补偿器,以完全消除阶跃扰动对系统的影响。并将原系统的最优无静差扰动抑制问题转化为无扰动最优控制问题;然后利用灵敏度方法,求得由精确的解析项和伴随向量级数形式补偿项组成的最优控制律,通过截取伴随向量级数的有限项和．可得到次优无静差控制律．仿真实例验证了该方法的有效性．     

离散时滞系统的近似最优扰动抑制

研究了状态变量合有时滞的离散系统在外部扰动下的最优控制问题．通过引入一个灵敏度参数,将原系统的最优扰动抑制问题转化为一族不含超前项和时滞项的两点边值问题,并由此导出了最优扰动抑制控制器的这代近似设计方法．得到的最优扰动抑制控制律由解析的前馈一反馈项和伴随向量级数和形式的补偿项组成,截取伴随向量级数的有限和得到原系统的次优扰动抑制控制律．数值仿真表明该近似最优控制器对外部持续扰动具有良好的鲁棒性。     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.     

Active disturbance rejection control for nonlinear fractional‐order systems

This paper investigates active disturbance rejection control involving the fractional‐order tracking differentiator, the fractional‐order PID controller with compensation and the fractional‐order extended state observer for nonlinear fractional‐order systems. Firstly, the fractional‐order optimal‐time control scheme is studied to propose the fractional‐order tracking differentiator by the Hamilton function and fractional‐order optimal conditions. Secondly, the linear fractional‐order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional‐order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional‐order extended state observer. Thirdly, by this observed value, the nonlinear fractional‐order plant is converted into a linear fractional‐order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional‐order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional‐order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

OPTIMAL TRACKING CONTROL FOR DISCRETE TIME‐DELAY SYSTEMS WITH PERSISTENT DISTURBANCES

Optimal tracking control (OTC) for discrete time‐delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time‐advance on time‐delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

具有正弦扰动的时滞系统前馈-反馈次优控制:灵敏度法

研究线性时滞系统在外部正弦扰动作用下的前馈-反馈最优减振问题,提出了一种最优控制律的灵敏度设计方法．通过引入灵敏度参数并围绕它展开幂级数,将系统的最优控制问题简化为不含超前项和时滞项的两点边值问题族．通过截取最优控制级数的有限和获得原系统的前馈-反馈次优控制律．仿真结果表明,与经典状态反馈最优控制相比,本文的算法更加鲁棒,能更加有效地抑制正弦扰动．     

SENSITIVITY APPROACH TO OPTIMAL CONTROL FOR AFFINE NONLINEAR DISCRETE‐TIME SYSTEMS

This paper deals with the optimal control problem for a class of affine nonlinear discrete‐time systems. By introducing a sensitivity parameter and expanding the system variables into a Maclaurin series around it, we transform the original optimal control problem for affine nonlinear discrete‐time systems into the optimal control problem for a sequence of linear discrete‐time systems. The optimal control law consists of an accurate linear term and a nonlinear compensating term, which is an infinite sequence of adjoint vectors. In the present approach, iteration is required only for the nonlinear compensation series. By intercepting a finite sum of the series, we obtain a suboptimal control law that reduces the complexity of the calculations. A numerical simulation shows that the algorithm can be easily implemented and has a fast convergence rate.     

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

This paper investigates the problem of output feedback attitude tracking control of a rigid spacecraft in the presence of external disturbances. Two optimal control laws with a disturbance estimator are developed to deal with this problem. An adapted extended state observer is used to estimate the angular velocity tracking errors and to allow for compensation for the total disturbances. The proposed control can be expressed as the sum of a nonlinear optimal controller and an estimated disturbance. For the optimal controller, the state‐dependent Riccati equation and optimal Lyapunov techniques are employed to solve the infinite‐time nonlinear optimal control problem. The developed controllers can minimize a performance index and ensure the stability of the closed‐loop system and external disturbance attenuation. On the other hand, using the adapted extended state observer, the asymptotic convergence of estimation error dynamics is proven. An example of multiaxial attitude manoeuvres is given and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

Optimal disturbance rejection control for singularly perturbed composite systems with time‐delay

The optimal control problem for a class of singularly perturbed time‐delay composite systems affected by external disturbances is investigated. The system is decomposed into a fast linear subsystem and a slow time‐delay subsystem with disturbances. For the slow subsystem, the feedforward compensation technique is proposed to reject the disturbances, and the successive approximation approach (SAA) is applied to decompose it into decoupled subsystems and solve the two‐point boundary value (TPBV) problem. By combining with the optimal control law of the fast subsystem, the feedforward and feedback composite control (FFCC) law of the original composite system is obtained. The FFCC law consists of analytic state feedback and feedforward terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. Simulation results are employed to test the validity of the proposed design algorithm. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

具有控制时滞系统的最优无静差正弦扰动抑制

研究在外部正弦扰动作用下，控制含时滞的线性系统的最优无静差调节器设计问题．首先利用Artstein变换将控制变量含时滞的系统转化为不舍时滞的系统；然后利用内模原理构造扰动补偿器，将带扰动的系统转化为无扰动的增广系统，从而将无静差扰动抑制问题转化为无扰动增广系统的最优调节器设计问题；最后利用最优控制理论求得最优无静差反馈控制律．仿真结果表明了所提出方法的有效性．     

时滞离散系统正弦扰动的最优抑制

研究状态和控制都含时滞的线性离散系统在正弦扰动下的减振控制问题.首先提出一种变量代换,并利用此代换将原系统转换为不含控制时滞的系统.然后利用逐次逼近法将最优控制问题转化为求解一族无时滞的线性两点边值序列问题.得到的最优控制律由解析的状态反馈,前馈和具有记忆的控制项以及时滞补偿序列的极限组成.通过截取时滞补偿序列的有限项,可以得到系统的次优减振控制律.仿真结果表明,该方法容易实现,设计的控制器对正弦扰动有较强的抑制能力.     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

Analysis and design of chattering‐free discrete‐time sliding mode control

In this paper, the disturbance observer–based chattering‐free discrete‐time sliding mode control (DSMC) approach is proposed for systems with external disturbances. The proposed disturbance observer, which makes full use of the state and input information at the current and last steps, improves the estimation accuracy and achieves accurate compensation for disturbances. Then, with the help of disturbance observer, a new reaching law, which contains not only a nonsmooth term with a dynamically adjusted gain parameter but also a second order difference of the disturbance, is proposed to reduce the range of the quasi‐sliding mode band and eliminate chattering. The proposed DSMC approach realizes the active disturbance rejection and strong robustness. Finally, a simulation example is presented to verify the effectiveness of the proposed method.     

Robust optimal tracking control for multiplayer systems by off‐policy Q‐learning approach

In this article, a novel off‐policy cooperative game Q‐learning algorithm is proposed for achieving optimal tracking control of linear discrete‐time multiplayer systems suffering from exogenous dynamic disturbance. The key strategy, for the first time, is to integrate reinforcement learning, cooperative games with output regulation under the discrete‐time sampling framework for achieving data‐driven optimal tracking control and disturbance rejection. Without the information of state and input matrices of multiplayer systems, as well as the dynamics of exogenous disturbance and command generator, the coordination equilibrium solution and the steady‐state control laws are learned using data by a novel off‐policy Q‐learning approach, such that multiplayer systems have the capability of tolerating disturbance and follow the reference signal via the optimal approach. Moreover, the rigorous theoretical proofs of unbiasedness of coordination equilibrium solution and convergence of the proposed algorithm are presented. Simulation results are given to show the efficacy of the developed approach.     

A LADRC based fuzzy PID approach to contour error control of networked motion control system with time‐varying delays

This paper investigate the contour error control problem for networked multi‐axis motion system (NMAMS) with time‐varying delays. Firstly, the uncertainties induced by the delays are modeled as a part of the total disturbance, and a linear active disturbance rejection controller (LADRC) is designed for the uniaxial trajectory tracking control. In the LADRC, a linear extended state observer (LESO) is designed to estimate the system state and the total disturbance simultaneously, and the effect of the total disturbance is eliminated by the designed linear feedback error control law. Then, the classical contour error estimation method is adopted, and a fuzzy PID controller is designed to compensate the contour error to achieve a better contour tracking performance. Finally, experiments are provided to verify the effectiveness of the proposed method.     

Passivity‐based control for large‐signal stability of high‐order switching converters

This article presents a new passivity‐based control law that stabilizes the output voltage of a high‐order DC‐DC converter. Such nonlinear control law assures robust large‐signal stability, provides zero steady‐state error despite uncertainty in converter parameters and has enough degree of freedom to satisfy the usual transient specifications of DC‐DC converters. This new integral control is derived in three steps. First, a static law is obtained. Second, a positive semidefinite storage function is synthesized to guarantee zero steady‐state error of the output voltage. Finally, the storage functions of the first two steps are combined to derive the new control law for high‐order DC‐DC converters. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Disturbance‐prediction–based control of input time delay systems for rejection of unknown frequency disturbances

In this paper, a novel disturbance rejection approach is presented for a class of input time‐delay systems subject to sinusoidal disturbances with unknown frequency. In particular, an auxiliary observer is proposed to represent the periodic disturbance in a parametric uncertainty form, where the unknown factor related to disturbance frequency can be estimated. Furthermore, the correlation between the future disturbance and the auxiliary observer output is analyzed, such that the future disturbances can be predicted and rejected through the input channel. Based on the aforementioned observer and predictor structure, the overall control architecture can be established as a framework of disturbance‐prediction–based control for systems with input time delays, where the conditions on the asymptotic stability of the closed‐loop systems are also derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed control approach.     

Stabilization and Tracking Control of X‐Z Inverted Pendulum Using Flatness Based Active Disturbance Rejection Control

A flatness based robust active disturbance rejection control technique scheme with tracking differentiator is proposed for the problem of stabilization and tracking control of the X‐Z inverted pendulum known as a special underactuated, non‐feedback linearizable mechanical system. The differential parameterization on the basis of linearizing the system around an arbitrary equilibrium decouples the underactuated system into two lower order systems, resulting in two lower‐order extended state observers. Using a tracking differentiator to arrange the transient process utilizes the problem of stabilization and tracking control and gives a relatively small initial estimation error, which enlarges the range of the controller parameters. The convincing analysis of the proposed modified linear extended state observer is presented to show its high effectiveness on estimating the states and the extended states known as the total disturbances consisting of the unknown external disturbances and the nonlinearities neglected by the linearization. Simulation results on the stabilization and tracking control of the X‐Z inverted pendulum, including a comparative simulation with an all‐state‐feedback sliding mode controller are presented to show the advantages of the combination of flatness and active disturbance rejection control techniques.     

Asymptotic rejection of sinusoidal disturbances based voltage balance control in back‐to‐back power converters

This paper addresses the imbalance problem of the dc‐link capacitor voltages in the three‐level diode‐clamped back‐to‐back power converter. In order to cope with it, a mathematical analysis of the capacitor voltage difference dynamics, based on a continuous model of the converter, is first carried out. It leads to an approximated model that contains explicitly several sinusoidal functions of time. In view of this result, the voltage imbalance phenomenon can be addressed as an output regulation problem, considering the sinusoidal functions of time as exogenous disturbances. Thus, a novel approach to deal with the mentioned problem in the back‐to‐back converter is presented. Then, the particular features of the disturbances are used to design several controllers. They all follow an asymptotic disturbance rejection approach. In this way, the estimates of the disturbances are used to apply a control law that cancels them while regulating the capacitor voltage balance as well. Finally, the performance of the proposed control laws is evaluated, presenting the simulation results obtained when the different controllers are implemented. Copyright © 2013 John Wiley & Sons, Ltd.     

An Efficient Finite Difference Method for The Time‐Delay Optimal Control Problems With Time‐Varying Delay

In this paper, an efficient finite difference method is presented for the solution of time‐delay optimal control problems with time‐varying delay in the state. By using the Pontryagin's maximum principle, the original time‐delay optimal control problem is first transformed into a system of coupled two‐point boundary value problems involving both delay and advance terms. Then the derived system is converted into a system of linear algebraic equations by using a second‐order finite difference formula and a Hermite interpolation polynomial for the first‐order derivatives and delay terms, respectively. The convergence analysis of the proposed approach is provided. The new scheme is also successful for the optimal control of time‐delay systems affected by external persistent disturbances. Numerical examples are included to demonstrate the validity and applicability of the new technique. Some comparative results are included to illustrate the effectiveness of the proposed method.