Compensation for state‐dependent nonlinearity in a modified repetitive control system

This paper presents an estimation and compensation of state‐dependent nonlinearity for a modified repetitive control system. It is based on the equivalent‐input‐disturbance (EID) approach. The nonlinearity is estimated by an EID estimator and compensated by incorporation of the estimate into the repetitive control input. A two‐dimensional model of the EID‐based modified repetitive control system is established that enables the preferential adjustment of control and learning actions by means of 2 tuning parameters. The singular‐value‐decomposition technique and Lyapunov stability theory are used to derive a linear‐matrix‐inequality–based asymptotic stability condition. Exploiting the stability condition and an overall performance evaluation index, a design algorithm is developed. Simulation results for the tracking control of a chuck‐workpiece system show that the method not only compensates state‐dependent nonlinearity but also improves the tracking performance for the periodic reference input, thereby demonstrating the validity of the method.     

An adaptive disturbance rejection control scheme for multivariable nonlinear systems

An adaptive disturbance rejection control scheme is developed for uncertain multi-input multi-output nonlinear systems in the presence of unmatched input disturbances. The nominal output rejection scheme is first developed, for which the relative degree characterisation of the control and disturbance system models from multivariable nonlinear systems is specified as a key design condition for this disturbance output rejection design. The adaptive disturbance rejection control design is then completed by deriving an error model in terms of parameter errors and tracking error, and constructing adaptive parameter-updated laws and adaptive parameter projection algorithms. All closed-loop signals are guaranteed to be bounded and the plant output tracks a given reference output asymptotically despite the uncertainties of system and disturbance parameters. The developed adaptive disturbance rejection scheme is applied to turbulence compensation for aircraft fight control. Simulation results from a benchmark aircraft model verify the desired system performance.     

Robust disturbance rejection for repetitive control systems with time‐varying nonlinearities

This paper presents a disturbance‐rejection method for a modified repetitive control system with a nonlinearity. Taking advantage of stable inversion, an improved equivalent‐input‐disturbance (EID) estimator that is more relaxed for system design is developed to estimate and cancel out the influence of the disturbance and nonlinearity in the low‐frequency domain. The high‐frequency influence is filtered owning to the low‐pass nature of the linear part of the closed‐loop system. To avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system. Furthermore, comparisons with the generalized extended‐state observer (GESO) and conventional EID methods are conducted. A clear relation between the developed estimator and the GESO is also clarified. Finally, simulations show the effectiveness and the advantage of the developed method.     

Robust disturbance rejection in modified repetitive control system

This study concerns disturbance rejection for a modified repetitive control system (MRCS) that contains a strictly proper plant with time-varying uncertainties. Since an MRCS is affected by both periodic and aperiodic disturbances, and since the disturbances are often unknown, an equivalent-input-disturbance (EID)-based estimator was added to an MRCS to yield an EID-based MRCS that compensates for all types of disturbances. In this system, the repetitive controller ensures tracking of a periodic reference input, and the incorporation of an EID estimate into the control input enables rejection of unknown periodic and aperiodic disturbances. A robust stability condition for the MRCS was established in the form of a linear matrix inequality, and the condition was used to design the parameters of the controller. This design method handles uncertainties and enables the preferential adjustment of the tracking and control performance of the MRCS. Simulation results demonstrate the validity of the method.     

Observer‐based tracking control for switched stochastic systems based on a hybrid 2‐D model

This paper is concerned with the observer‐based output tracking problem for a class of linear switched stochastic systems with time delay and disturbance by using repetitive control approach. More precisely, a two‐dimensional hybrid model is incorporated to obtain and optimize the repetitive controller. In particular, the repetitive controller is used to improve the tracking performance through its continuous learning actions. In addition, an equivalent‐input‐disturbance estimator is incorporated into the repetitive control design approach to reduce the effect of the external disturbances. The main aim of the control design is to track the periodic reference signal with the measured output of the system under consideration even in the presence of an unknown bounded disturbance. By constructing a suitable Lyapunov‐Krasovskii functional and using average dwell time approach and Jensen inequality, sufficient conditions are obtained in terms of linear matrix inequalities to guarantee the mean‐square exponential stability of the considered system. Eventually, a numerical example is provided to demonstrate the effectiveness of the developed method.     

Active DIsturbance Rejection Control of Surface Vessels Using Composite Error Updated Extended State Observer

In this paper, a composite‐errors‐based active disturbance rejection control law is proposed for surface vessels with exogeneous disturbances. The low‐frequency disturbances from wind, wave and ocean currents are estimated by a novel composite‐errors‐based extended state observer (ESO). Since the composite errors are composed of trajectory tracking errors and estimation errors, the disturbance rejection control is feedforward‐feedback composite control. The advantages of feedforward control and feedback control are exploited to reject system disturbances. Compared with conventional ESO‐based active disturbance rejection control, smaller estimation errors and smaller tracking errors can be achieved by the proposed disturbance compensation control. The effectiveness and superiority of the designed control law are illustrated by theoretical analysis and simulation results.     

Disturbance rejection based tracking control design for fuzzy switched systems with time-varying delays and disturbances

The disturbance rejection and tracking problem of T-S fuzzy switched systems with uncertainties, input time-varying delays and disturbances is addressed in this article. For that cause, a modified repetitive control protocol based on the improved-equivalent-input-disturbance (IEID) estimator and extended Smith predictor approach has been proposed, which guarantees the perfect disturbance estimation and tracking performances with high precision. Specifically, by incorporating the transfer function of main feedback path in conventional Smith predictor block, the input time-varying delays are effectively compensated. In the direction of estimating the disturbances, an active disturbance rejection technique called IEID estimator approach is precisely considered. By exploiting the output of the IEID estimator and parallel distributed compensation strategy, the fuzzy rule based modified repetitive control system is formulated. Further, by making use of Lyapunov method together with average dwell-time approach, a set of sufficient conditions in the form of matrix inequalities are established. More respectively, by solving the developed matrix inequalities, the controller and observer gain matrices are determined. At last, the method proposed in this work is validated in terms of presenting the simulation results of two numerical examples, including boiler-turbine system.     

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.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

重复控制系统中非周期扰动的抑制

为了改善重复控制系统中的扰动抑制性能,提出一种基于曲率模型的扰动估计新方法.该方法的主要特点是扰动的估计值直接与重复控制规则结合也不影响重复控制系统的稳定性.仿真结果显示该方法可以有效地抑制扰动.     

Robust Repetitive Control and Disturbance Rejection Based on Two‐Dimensional Model and Equivalent‐Input‐Disturbance Approach

A new configuration of a modified repetitive‐control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two‐dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent‐input‐disturbance estimator; a state observer; and a state‐feedback controller. A robust‐stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC‐based repetitive control.     

重复学习控制及其在一类非线性系统中的应用

为跟踪或抑制仅周期已知的未知周期参考或扰动信号,提出一种新的重复学习控制方法,利用系统的稳态误差并通过迭代学习构造前馈补偿,实现了误差的渐近收敛,将所提出方法应用于一类常见的扰动信号和系统输出具有未知非线性关系的非线性系统,假设其满足连续里普希斯条件,利用重复学习控制器,系统的稳态误差可以减小到极低的程度,该方法控制精度高,实现简单,与传统的基于时延内模的重复控制方法相比,具有对非重复性干扰不敏感的优点,仿真结果验证了该方法的有效性。     

Quantitative feedback control for multivariable model matching and disturbance rejection

This article extends two recent contributions in the field of quantitative feedback theory to the multivariable case. They concern the model matching and the measured disturbance rejection problems. The model matching problem is a tracking control problem with specifications given as acceptable deviations from an ideal response. The measured disturbance rejection problem balances feedback and feedforward actions to reject disturbances. Both perspectives present advantages over classical quantitative feedback theory techniques in certain situations. This paper develops the necessary tools to solve both control problems in the case of multi‐input multi‐output plants. In particular, it shows how to derive nonconservative controller bounds for each of the single‐input single‐output control problems in which the overall multivariable problem is divided. The result is a systematic controller design methodology for multi‐input multi‐output plants with structured uncertainty. The application of the technique to the well‐known quadruple‐tank process illustrates the benefits of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

基于参考模型的扰动观测器控制系统

为了补偿控制系统的未知动态和外部扰动,论文提出一种基于参考模型的扰动观测器控制系统.首先,分析了二阶理想参考模型控制系统的设计,并通过闭环传递函数证明了参考模型控制系统的稳定性.然后,设计了二阶系统扰动观测器和基于参考模型的扰动观测器控制律,分析了二阶闭环控制误差系统收敛性.并推广到n阶控制系统,证明了n阶闭环控制误差系统稳定性.最后,仿真实验结果表明,与线性自抗扰控制(LADRC)系统相比,基于参考模型的扰动观测器控制系统阶跃响应的跟踪精度和抗扰性能明显优于LADRC系统,扰动的估计精度高,控制输入量小于LADRC系统;基于参考模型的扰动观测器控制系统正弦跟踪精度和扰动的估计精度也高于LADRC系统.该新型控制系统结构简单,抗扰性能好,控制效率高,具有重要的工程应用价值.     

Robust Tracking Control Of The Variable Stiffness Actuator Based On The Lever Mechanism

This paper is concerned with the design of a robust adaptive tracking control scheme for a class of variable stiffness actuators (VSAs) based on the lever mechanisms. For these VSAs based on the lever mechanisms, the AwAS‐II developed at Italian Institute of Technology (IIT) is chosen as the study object, and it is an enhanced version of the original realization AwAS (actuator with adjustable stiffness). Firstly, for the dynamic model of the AwAS‐II system in the presence of parametric uncertainties, unknown bounded friction torques, unknown bounded external disturbance and input saturation constraints, by using the coordinate transformations and the static state feedback linearization, the state space model of the AwAS‐II system with composite disturbances and input saturation constraints is transformed into an uncertain multiple‐input multiple‐output (MIMO) linear system with lumped disturbances and input saturation constraints. Subsequently, a combination of the feedback linearization, disturbance observer, sliding mode control and adaptive input saturation compensation law is adopted for the design of the robust tracking controller that simultaneously regulates the position and stiffness of the AwAS‐II system. Under the proposed controller, the semi‐global uniformly ultimately bounded stability of the closed‐loop system has been proved via Lyapunov stability analysis. Simulation results illustrate the effectiveness and the robustness of the proposed robust adaptive tracking control scheme.     

Active Disturbance Rejection Control of a Magnetic Suspension System

This paper proposes a novel output feedback control scheme for robust stabilization and tracking tasks in a magnetic suspension system. Active disturbance rejection control, differential flatness and on‐line asymptotic disturbance estimation are properly used for the proposed control synthesis. The controlled system is subjected to a wide spectrum of unknown significant matched and unmatched disturbances due to external forces and voltages, parametric uncertainties, control and state‐dependent perturbations and possibly input unmodeled dynamics. The effectiveness and robustness of the proposed active disturbance control scheme is verified by computer simulations for the robust tracking of a rest‐to‐rest reference position trajectory specified to firstly stabilize the suspended mass at a desired vertical position and next transfer it to another equilibrium position for both continuous and switched control voltage signals.     

Generalized-Extended-State-Observer and Equivalent-Input-Disturbance Methods for Active Disturbance Rejection: Deep Observation and Comparison

Active disturbance-rejection methods are effective in estimating and rejecting disturbances in both transient and steady-state responses.This paper presents a deep observation on and a comparison between two of those methods:the generalized extended-state observer(GESO) and the equivalent input disturbance(EID) from assumptions,system configurations,stability conditions,system design,disturbance-rejection performance,and extensibility.A time-domain index is introduced to assess the disturbance-r...     

Optimal Performance in Tracking Stochastic Signal Under Disturbance Rejection

The analysis method of optimal tracking performance is proposed for multiple‐input multiple‐output (MIMO) linear time‐invariant (LTI) systems under disturbance rejection. An H₂ criterion of the error signal between the output of the plant and the reference signal is used as a measure for the tracking performance. Spectral factorization is applied to obtain the optimal solution of the system tracking error. The explicit expressions are derived for this minimal tracking error with respect to random reference signals under disturbance rejection. It is shown that the nonminimum phase zeros, the zero direction, the unstable poles, the pole direction of a given plant, statistical characteristics of the reference input signal, and disturbance signal have a negative effect on a feedback system's ability to reduce the system error with disturbance rejection. The results show that the optimal tracking performance will further be damaged because of disturbance rejection. Some typical examples are given to illustrate the theoretical results.     

基于改进卡尔曼滤波器的扰动抑制无模型自适应控制方案

针对无模型自适应控制方法在测量扰动作用下控制效果不佳的问题, 本文提出了一种新的扰动抑制无模 型自适应控制方案. 首先基于受控系统的动态线性化数据模型及测量扰动的统计特性, 在最小方差估计准则下推导 了基于系统输入输出数据的改进卡尔曼滤波器. 然后基于此滤波器给出了一种新的扰动抑制无模型自适应控制方 案. 该方案仅需用到受控系统的输入输出数据, 即可实现在强测量扰动作用下系统的无模型自适应控制. 仿真结果 显示, 相比现有的扰动抑制无模型自适应控制方案, 该方案在系统跟踪常值参考信号、时变参考信号时均能有效地 抑制测量扰动, 适用性更好的同时可以获得更小的跟踪误差及更大的数据信噪比.     

Disturbance observer–based prescribed adaptive control for rate‐dependent hysteretic systems

In this paper, a disturbance observer–based prescribed adaptive control approach is proposed for ultra‐high‐precision tracking of a class of hysteretic systems with both high‐order matched and mismatched disturbances. Considering the adverse effects of asymmetric and rate‐dependent hysteresis nonlinearities, a polynomial‐based rate‐dependent Prandtl‐Ishlinskii model is first developed to characterize their behaviors, and inverse model based compensation is also constructed. Furthermore, the resulting inverse compensation error is analytically given, and a novel disturbance observer with adaptive control techniques is designed to handle the bounded disturbances, including the inverse compensation error and the high‐order matched and mismatched disturbances. Comparative experiments on a multiaxis nano servo stage are finally conducted to demonstrate the effectiveness of the proposed control architecture, where substantial performance improvement over existing results are achieved on various tracking scenarios.