Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.     

Non-linear anti-windup for manual flight control

In this paper we address the windup problem arising from actuator magnitude and rate saturation for the linearized longitudinal short-period dynamics of a tailless aircraft model around any trim flight condition. The proposed anti-windup scheme allows for more aggressive manoeuvres than the standard “command limiting” approach. Moreover, the compensation law guarantees stability of the controlled aircraft for any pilot command and enforces flight quality specifications whenever they are achievable within the given control constraints. “Pilot-in-the-loop” simulations confirm the effectiveness of the control strategy.     

Actuator saturation and anti-windup compensation in event-triggered control

Event-triggered control aims at reducing the communication load over the feedback link in networked control systems by sending information only if certain event conditions, which guarantee a desired control performance, are satisfied. This article investigates the consequences of actuator saturation on the behavior of the event-triggered control loop in terms of its stability and information exchange. Stability properties are derived using linear matrix inequalities (LMIs) which show how the stability of the event-triggered control loop depends on the selection of the event threshold. Moreover, it is shown that a lower bound on the minimum inter-event time exists being likewise affected by the event threshold. As actuator saturation might severely degrade the performance of the event-triggered closed-loop system, the scheme is extended by incorporating an anti-windup mechanism in order to overcome this problem. The results are illustrated by simulations and experiments.     

带宽化调节下的抗扰PID退饱和控制方法

比例–积分–微分(PID)控制的抗饱和设计是一类经典非线性控制问题, 理论研究丰富, 但工程中广泛使用的 仍是积分退饱和这类简易策略. 究其原因, 现有理论方法过于依赖系统模型和状态空间理论, 稳定性条件与调参机 制之间关系复杂. 本文基于经典退饱和控制结构, 首次阐述了“退饱和带宽”概念及退饱和参数调节机理, 在此基础 上讨论了两类低阶退饱和补偿器的带宽化设计方法. 在抗扰PID反馈控制下, 结合小增益定理得到退饱和控制的稳 定性条件, 给出控制参数与退饱和带宽之间的调节关系, 实现退饱和控制的带宽化整定. 最后, 通过数值仿真验证 了所提方法的有效性.     

Introducing concepts of passivity-based control in anti-windup algorithms

This work presents a reference conditioning anti-windup scheme based on passivity control theory. The main closed-loop is controlled by a proportional–integral–derivative (PID) control, and the injection and damping assignment technique ensures that PID variables are compatible with the process input. In the proposed algorithm, a fictitious actuator, modeled as a first-order filter, is incorporated to estimate the rate of change and the output of the actuator device. Amplitude and rate constraints are weight by coefficients that shape the energy function of the anti-windup scheme. Finally, to show how the algorithm can cope with the windup problem, simulation results are presented. Even when shown the results on a linear PID, the proposal can extend to any linear or nonlinear control in the main control loop.     

Dynamic anti-windup based control method for state constrained systems

Based on the dynamic anti-windup strategy, an alternative control methodology for state constrained systems is presented. The proposed method is an a posteriori approach for state constrained systems, which is differentiated from the usual a priori approach. That is, first a linear controller is designed to show a desirable nominal performance by ignoring state constraints. Then, an additional compensator is introduced to account for state constraints. By minimizing a reasonable performance index, a dynamic compensator is derived explicitly, which is expressed in plant and controller parameters. The proposed method not only provides a graceful performance degradation, but it also guarantees the total stability of the resulting systems. An illustrative example is given to show the effectiveness of the proposed method.     

Dynamic anti-windup scheme for feedback linearizable nonlinear control systems with saturating inputs

This paper proposes a dynamic compensation scheme for input-constrained feedback linearizable nonlinear systems to cope with the windup phenomenon. Given a dynamic feedback linearizing controller designed without considering its input constraint, an additional dynamic compensator is proposed to account for the constraint. This dynamic anti-windup is based on the minimization of a reasonable performance index. The proposed strategy is a nonlinear extended version of [Park, J.-K., & Choi, C.-H. (1995). Dynamic compensation method for multivariable control systems with saturating actuators. IEEE Transactions on Automatic Control, 40(9), 1635–1640] with simplified derivation of an optimization solution under relaxed assumptions. The parameter matrices and structure of the solution are explicitly decided by mathematical optimization for infinite horizon without tuning of design parameters unlike previous schemes. During input saturation, the role of the anti-windup scheme with the proposed dynamic feedback compensator is to maintain the controller states to be exactly the same as those without input saturation. The local asymptotic stability and the total stability of the resulting systems are proved. The usefulness of the proposed design method is illustrated by comparative simulations for a constrained control system.     

Nonlinear repetitive control

Repetitive controllers are generally applied to reject periodic disturbances and to track periodic reference signals with a known period. Their design is based on the internal model principle, proposed by Francis and Wonham (1975). This paper describes a new finite-dimensional SISO repetitive controller for two different classes of nonlinear plants. Simulation results show asymptotic tracking of the periodic reference signal by the proposed repetitive controller in closed loop up to the Nth harmonic frequency. A proof of robustness of the repetitive control system to small nonlinearities, like actuator nonlinearities, is provided     

Experimental evaluation of anti-windup extremum seeking control for airside economizers

The performance of anti-windup extremum seeking control (ESC) as a model free online optimization strategy is evaluated by experimental studies for energy efficient operation of both chilled-water and direct-expansion airside economizers. For the chilled-water based system, the ESC takes the chilled-water valve control signal as the feedback, and controls the outdoor air damper (OAD) position to minimize the cooling coil load. For the direct-expansion system, the ESC takes the total electricity power consumption as the feedback, and controls the OAD position to minimize the power consumption. Experimental results verify the effectiveness of the ESC scheme for model-free operation without temperature and humidity measurements.     

以幂次吸引的离散多周期重复控制

针对一类多周期干扰的抑制问题,提出一种基于幂次吸引律的离散多周期重复控制方法.多周期干扰由多个周期已知的周期干扰叠加而成.根据周期干扰的对称特性,构造出具有干扰抑制项的幂次吸引律,据此设计出子重复控制器,并以并联方式组合成多周期重复控制器,在消除多周期干扰的同时,有效地抑制慢时变非周期干扰带来的影响,改善控制品质;推导出幂次绝对吸引层和稳态误差带的具体表达式,用于刻画系统跟踪性能.仿真结果验证了所提控制方法的有效性.     

以幂次趋近的离散变结构重复控制

本文提出一种离散变结构重复控制器设计方法,在趋近律中“嵌入”扰动抑制措施,构造理想切换动态,并据此导出重复控制器.为了进行控制器参数整定和刻画闭环系统的收敛性能,文中推导出准滑模带、单调收敛层和绝对收敛层边界的表达式.设计的离散变结构重复控制器能够完全抑制周期性扰动,控制器设计方法也适用于常值扰动下的定位控制.数值仿真及实验结果验证了所提出控制方案的有效性.     

Nonlinear repetitive control with application to trajectory control of manipulators

In this article, a new control scheme named repetitive control is proposed for a class of nonlinear systems described by x(t) = Ax(t) + Bu(t) + n(x(t)) and y(t) = Cx(t), in which the controlled variables follow periodic reference commands. The stability condition is derived by applying the passivity theorem. We show how to apply the repetitive control scheme to the trajectory control of a manipulator. A simple repetitive control scheme is developed for the trajectory control of a manipulator by using nonlinear compensation and feedbacks of position and velocity signals. Experimental results for a three link manipulator verify that the proposed repetitive control reduces the tracking error to a very low level.     

Survey on iterative learning control,repetitive control,and run-to-run control

In this paper, three control methods—iterative learning control (ILC), repetitive control (RC), and run-to-run control (R2R)—are studied and compared. Some mathematical transformations allow ILC, RC, and R2R to be described in a uniform framework that highlights their similarities. These methods, which play an important role in controlling repetitive processes and run-based processes, are collectively referred to as learning-type control in this paper. According to the classification adopted in this paper, learning-type control has two classes—direct form and indirect form. The main ideas and designing procedures for these two patterns are introduced, separately. Approximately 400 papers related to learning-type control are categorized. Statistical analysis of the resulting data reveals some promising fields for learning-type control. Finally, a flowchart based on the unique features of the different methods is presented as a guideline for choosing an appropriate learning-type control for different problems.     

Intelligent anti-windup for systems with input magnitude saturation

The paper deals with the global stabilization of linear systems with saturating actuators. A saturated state feedback control law containing an integrating action and a specific anti-windup compensator with nonlinearities of the dead-zone type are simultaneously synthesized to guarantee the global asymptotic stability of the closed-loop system. The approach is direct in the sense that both the proposed control laws are computed simply from a Lyapunov equation based on the controlled system. The controls are allowed to saturate and the steady-state error due to admissible constant perturbations can be brought to zero. © 1998 John Wiley & Sons, Ltd.     

基于扩张状态观测器的动态抗饱和补偿器设计方法

针对一类受外界扰动以及执行器饱和影响的不确定非线性系统,提出一种基于扩张状态观测器的动态抗饱和补偿器设计方法.首先通过将系统的不确定项以及外部扰动作为扩张状态,设计线性扩张状态观测器(ESO)对系统的总扰动进行估计;然后,在控制器中引入对扩张状态的估计值,对系统的总扰动进行补偿,设计了动态抗饱和补偿器,将控制器、观测器以及动态抗饱和补偿器的参数求解问题转化为基于LMI不等式组约束的优化问题,确保系统具有尽可能大的收敛域;最后通过数值仿真验证所提出设计方法的有效性.     

基于死区吸引律的离散重复控制

针对周期参考信号下的不确定离散时间系统,提出一种离散重复控制方法,利用死区函数设计新型的吸引律,将干扰补偿、抑制措施“嵌入”吸引律,构造理想误差动态,并基于此导出重复控制器。为了进行具体的控制器参数整定和表征闭环系统的误差动态行为,推导出了稳态误差带、单调减区域和绝对吸引层边界的表达式。所设计的离散重复控制器能够完全抑制周期对称干扰信号,控制器设计方法也适用于常值调节问题的定位控制。数值仿真及在电机伺服系统上的实验结果验证了所提出控制方法的有效性。     

一类饱和不确定非线性系统静态抗饱和控制设计

研究一类执行器幅值与速率饱和的不确定非线性系统静态抗饱和控制问题.采用线性微分包含的方法处理系统模型中的非线性项.给出了抗饱和补偿器设计方法,该方法能同时保证闭环鲁棒稳定及鲁棒性能.给出了此类非线性系统代数环良定的充要条件,从而将抗饱和补偿器设计问题转化为线性矩阵不等式约束的凸优化问题.最后通过仿真算例说明了所提出方法的有效性.     

Dual-mode structure digital repetitive control

A flexible repetitive control (RC) scheme named “dual-mode structure repetitive control” (DMRC) is presented in this article. A robust stability criterion for DMRC systems is derived in terms of two parameters: odd-harmonic RC gain and even-harmonic RC gain. Several useful corollaries for the stability are addressed to reveal the compatibility of DMRC. The general framework of DMRC offers the flexibility in the development of various RC controllers. Without additional complexity and loss of tracking accuracy, DMRC can achieve faster error convergence rate than conventional RCs. DMRC requires the same data memory size as that of conventional RC one. An application example of DMRC controlled PWM inverter illustrates the validity of our proposed DMRC scheme. Comparisons of DMRC, conventional RC and odd-harmonic RC highlight the advantages of the presented DMRC approach.     

Period-robust repetitive model predictive control

Repetitive model predictive control (RMPC) incorporates the idea of repetitive control (RC) into the basic formulation of model predictive control (MPC) to enable the user to take full advantage of the constraint handling, multivariable control features of MPC in controlling a periodic process. The RMPC achieves perfect asymptotic setpoint tracking/disturbance rejection in periodic processes, provided that the period length used in the control formulation matches the actual period of the reference/disturbance signal exactly. Even a small mismatch between the actual period of the process and the controller period can deteriorate the RMPCs performance significantly. The period mismatch can occur either from an inaccurate estimation of the actual frequency of disturbance due to resolution limit or from trying to force the controller period to be an integer multiple of the sampling time. For such cases, an extension of RMPC called “period-robust” repetitive model predictive control (pr-RMPC) is proposed. It is based on the idea of using weighted, multiple memory loops in RC, such that small changes in period length do not diminish the tracking/rejection properties by much. Simulation results show that, in case of a slight period mismatch, pr-RMPC achieves significant improvement over the standard RMPC in rejecting periodic disturbances.