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 FEEDBACK CONTROL SYSTEMS WITH TRACKING ERRORS SQUARE

In this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.     

Fuzzy PDFF-IIR controller for PMSM drive systems

Pseudo-derivative feedback with feed-forward gain (PDFF) combines the advantages of proportional-integral (PI) and pseudo-derivative feedback (PDF) controllers. However, PDFF responds more slowly to a command than does PI. To increase the speed of response of the PDFF controller, this work presents a PDFF with moving average errors control. A low-pass IIR filter path for errors compensation that accelerates the slow response is added to a PDFF control loop. A fuzzy inferencer is utilized to adjust the feed-forward gain and integral gain of the PDFF controller to allow closed-loop poles of the transfer function to be properly placed to improve load torque disturbance rejection capability. Simulated and experimental results reveal that the response and load disturbance rejection ability of the fuzzy PDFF-IIR controller are better than those of the traditional PDFF controller.     

Output feedback tracking control for lower‐triangular nonlinear time‐delay systems with asymmetric input saturation

In this paper, the problem of output feedback tracking control is investigated for lower‐triangular nonlinear time‐delay systems in the presence of asymmetric input saturation. A novel design program based on a dynamic high gain design approach is proposed to construct an output feedback tracking controller. The innovation here is that the problem of constructing tracking controller can be transformed into the problem of constructing two dynamic equations, with one being utilized to deal with the nonlinear terms and the other one being applied to analyze the influence of asymmetric input saturation. It is proved by an appropriate Lyapunov‐Krasovskii functional that the proposed tracking controller subject to saturation can ensure that all the signals of the closed‐loop system are globally bounded and the tracking error is prescribed sufficiently small when time is long enough. A practical example is given to illustrate the effectiveness of the proposed method.     

Arbitrarily fast and robust tracking by feedback

The output of a singe-input-single-output linear feedback system with more than one pole in excess over the zeros in the loop transmission cannot track arbitrarily fast its input (by the root locus). In this work we extend the linear feedback so that some of the open loop poles may depend on the open loop gain; we call this new class quasi-linear feedback systems. We then derive time domain, pole-zero, and frequency domain conditions which ensure arbitrarily fast and robust tracking by quasi-linear feedback, for an arbitrary number of poles in excess over the zeros. We prove that in a particular case these conditions are equivalent, and that the boundedness in frequency of the closed loop transfer function is no longer necessary for achieving arbitrarily fast tracking. The robustness is to external disturbances and initial conditions, and the open loop has to be minimum phase. Some examples are presented which illustrate these results. They also show that this good performance can be obtained with a reduced control effort, and that quasi-linear feedback can alleviate the limitation on performance of non-minimum phase open loops.     

Feedback design for robust tracking and robust stiffness in flight control actuators using a modified QFT technique

The problem of dynamic stiffness of hydraulic servomechanisms has often been recognized as a significant performance issue in a variety of applications, the most notable of which includes flight control actuation. When a hydraulic actuator such as this is operated in position control, an aerodynamic flutter load on the control surface manifests itself as a force disturbance on the system. Although this would appear to be a standard disturbance rejection problem, the disturbance does not enter the system as in the classical sense (i.e. at the plant output) and hence, this problem must be considered in a modified formulation. A hydraulic servomechanism is said to be 'stiff' if it exhibits acceptable rejection of force disturbances within the control bandwidth. In this paper, an approach to feedback design for robust tracking and robust disturbance rejection is developed via the quantitative feedback theory (QFT) technique. As a result, it is shown that reasonable tracking and disturbance rejection specifications can be met by means of a fixed (i.e. non-adaptive), single loop controller. The methodology employed in this development is the sensitivity-based QFT formulation. As a result, robust tracking and robust disturbance rejection specifications are mapped into equivalent bounds on the (parametrically uncertain) sensitivity function; hence, the frequency ranges in which tracking or disturbance rejection specifications dominate become immediately obvious. In this paper, a realistic non-linear differential equation model of the hydraulic servomechanism is developed, the linear parametric frequency response properties of the open loop system are analysed, and the aforementioned QFT design procedure is carried out. Analysis of the closed loop system characteristics shows that the tracking and disturbance rejection specifications are indeed met.     

Properties of single input,two output feedback systems

We describe properties of linear multivariable feedback systems for which the plant has a single control input and two measured outputs. Particular attention is paid to 'algebraic' design tradeoffs that occur between different feedback properties at the same frequency. To describe these tradeoffs, we use concepts of plant and controller direction and alignment. We show that if plant/controller alignment is poor, then closed loop response to noise and disturbances will be large unless the loop gain is sufficiently small. Moreover, the closed loop system will exhibit large interactions. We also describe a dual set of results that are applicable to feedback systems for which the plant has two control inputs and a single measured output.     

给定值和干扰响应解耦的新型控制器设计

基于输入输出方法讨论时滞对象控制问题.在传统控制结构基础上讨论了一种新型 的控制结构,它可以使系统的给定值响应和干扰响应解耦,分别通过一个参数优化.通过期望 闭环传递函数定义了最优性能指标,然后解析地推导出控制器,保证了系统具有好的干扰抑 制能力.为了说明新的设计方法,文中给出了设计例子.     

Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance

In this paper, we are concerned with a cascade of ODE‐wave systems with the control actuator‐matched disturbance at the boundary of the wave equation. We use the sliding mode control (SMC) technique and the active disturbance rejection control method to overcome the disturbance, respectively. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of solution for the closed‐loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed‐loop system. Considering that the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an active disturbance rejection control to attenuate the disturbance. The disturbance is canceled in the feedback loop. The closed‐loop systems with constant high gain and time‐varying high gain are shown respectively to be practically stable and asymptotically stable. Then we continue to consider output feedback stabilization for this coupled ODE‐wave system, and we design a variable structure unknown input‐type state observer that is shown to be exponentially convergent. The disturbance is estimated through the extended state observer and then canceled in the feedback loop by its approximated value. These enable us to design an observer‐based output feedback stabilizing control to this uncertain coupled system. Copyright © 2016 John Wiley & Sons, Ltd.     

A hybrid frequency—time domain adaptive fuzzy control scheme for flexible link manipulators

This paper addresses the implementation of an adaptive fuzzy controller for flexible link robot arms. The design technique is a hybrid scheme involving both frequency and time domain techniques. The eigenvalues of the open loop plant can be estimated through application of a frequency domain based identification algorithm. The region of the eigenvalue space, within which the system operates, is partitioned into fuzzy cells. Membership function are assigned to the fuzzy sets of the eigenvalue universe of discourse. The degree of uncertainty on the estimated eigenvalues is encountered through these membership functions. The knowledge data base consists of feedback gains required to place the closed loop poles at predefined locations. A rule based controller infers the control input variable weighting each with the value of the membership functions at the identified eigenvalue. The afore-mentioned controller is compared through simulation with conventional techniques, namely pole placement and gain scheduling.     

An input‐output approach to achieve adaptive tracking for saturating stable systems

The problem of controlling time-invariant linear systems subject to parametric uncertainty and input saturation constraint, is dealt with using a pole placement adaptive controller. It is shown that the resulting adaptive control system can be described by a non-linear feedback scheme. Then, the l 2 -stability condition for the control system turns out to be the positive-realness of a transfer function involving the plant (estimated) model and the specified closed-loop poles. This makes it necessary to adapt on-line the desired closed-loop poles to the time-varying (estimated) model. The proposed adaptive controller keeps bounded all the closed loop sequences, whatever the initial conditions. Furthermore, it ensures a quite interesting output-reference tracking behaviour. More precisely, the quality of the tracking depends on the reference sequence rate: the slower the reference the better the tracking.     

Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

1 Introduction There are many practical systems that require the control of the shape of the output probability den- sity function rather than just their mean values and variances. These systems are seen in papermaking processes[1,2], chemical engineering, material science, combustion ?ame distribution systems and food pro- cessing industries. For example, in chemical engineer- ing the control of particle size distribution has al- ways been regarded as an important area of research[3], whilst …     

一类不确定非线性系统的指数鲁棒输出跟踪

研究一类不确定非线性系统的鲁棒输出跟踪控制问题。应用输入／输出反馈线性化法和李亚普诺夫方法,提出一种基于不确定项上界的连续型鲁棒输出跟踪控制器设计方法。该控制器不仅可确保闭环系统的状态一致最终有界,使系统输出按指数规律跟踪期望输出,而且计算简单,更易实现。仿真结果证明了该方法的可行性与有效性。     

A harmonic balance approach to robust neural control of MIMO nonlinear processes applied to a distillation column

Robust stability and performance are the two most basic features of feedback control process. The harmonic balance analysis based on the describing function technique enables to analyze the stability of limit cycles arising from a closed loop control process operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural network controller in series with a dynamic multivariable nonlinear plant under generic Lur’e configuration. The neural controller is replaced by its sinusoidal input describing function while a linearized model is derived to represent the nonlinear plant dynamics. The uncertainty induced by the high harmonics effect for the neural controller, together with the neglected nonlinear dynamics due to plant linearization are incorporated in the robustness analysis as structured norm bounded uncertainties. Stability and robustness conditions for the neural closed loop control system are discussed using the harmonic balance equation together with the structured singular values of the uncertainty. The application to a multivariable binary distillation column under feedback neurocontrol illustrates the usefulness of the robustness approach here developed to predict the absence of limit cycles, which of course is subject to the usual restrictions of the describing function method.     

冷轧机的轧辊偏心鲁棒重复控制

设计了用于冷轧机的轧辊偏心补偿的鲁棒重复控制器.首先根据对象的期望闭环特性及扰动信号频率,确定低通滤波器的截止频率,然后通过引入状态反馈来保证闭环系统的鲁棒稳定性,把重复控制器的设计问题转化为H∞状态反馈控制器的设计问题,给出了控制器参数整定算法,最后通过在控制系统中引入一个前向系数来进一步改善和提高系统的动态性能与稳态控制精度,给出了前向系数的整定方法.仿真结果表明,当系统对象参数存在摄动时,这种控制器仍然能够实现对轧辊偏心的高精度补偿.     

Prediction‐based Adaptive Robust Tracking Control of an Uncertain First‐Order Time‐Delay System

This paper considers the tracking problem of a delayed uncertain first‐order system which is simultaneously subject to (possibly large) known input delay, unknown but bounded time‐varying disturbance, and unknown plant parameter. The proposed predictor adaptive robust controller (PARC) involves prediction‐based projection type adaptation laws with model compensation and prediction‐based continuous robust feedback such that the closed loop system has global exponential convergence with an ultimate bound proportional to delay, disturbance bound, and switching gain. Further, if there are only delay and parameter uncertainties after some finite time, then semi‐global asymptotic tracking is guaranteed. The proposed design is shown to have significant closed loop performance improvement over the baseline controller.     

基于一阶不确定项估计律的机械臂鲁棒控制研究

针对多自由度机械臂控制系统的模型参数误差、关节摩擦力以及外部输入扰动等不确定项,设计了一类一阶误差估计律;结合基于机构动力学名义模型的输入输出反馈线性化控制算法,对六自由度刚性机械臂的时变轨迹跟踪控制进行了研究,理论上证明了设计的鲁棒控制器是全局渐进稳定的.仿真结果表明该控制策略对系统的各类不确定项具有很好的鲁棒性,能够实现高精度的轨迹跟踪控制.     

Suboptimal mean controllers for bounded and dynamic stochastic distributions

Based on the recently developed algorithms for the modelling and control of bounded dynamic stochastic systems (H. Wang, J. Zhang, Bounded stochastic distributions control for pseudo ARMAX stochastic systems, IEEE Transactions on Automatic control, 486–490), this paper presents the design of a subotpimal nonlinear mean controller for bounded dynamic stochastic systems with guaranteed stability. The B-spline functional expansion based square root model is used to represent the output probability density function of the system. This is then followed by the design of a mean controller of the output distribution of the system using nonlinear output tracking concept. A nonlinear quadratic optimization is performed using the well known Hamilton–Jacobi–Bellman equation. This leads to a controller which consists of a static unit, a state feedback part and an equivalent output feedback loop. In order to achieve high precision for the output tracking, the output feedback gain is determined by a learning process, where the Lyapunov stability analysis is performed to show the asymptotic stability of the closed loop system under some conditions. A simulation example is included to demonstrate the use of the algorithm and encouraging results have been obtained.     

Robust tracking in nonlinear systems

A nonlinear feedback multivariable controller is used to implement multivariable tracking in a nonlinear system. The tracking error is measured by a general function of system state and the input command. The controller is robust in the sense that the tracking error is ultimately bounded in the presence of modeling errors. Free parameters, which affect the form of the controller, allow flexibility in determining such factors as: the size of the ultimate bound, the rate of error decay, excursion of the control, conditions on the class of modeling errors, and the level of system gain. Restrictive assumptions on the structure of the model and the modeling errors are required but they are treated in a transformation framework which allows the generalization of similar conditions which appear in the prior literature. These assumptions hold for robotic manipulators. This application is investigated at some length and it appears that the resulting control scheme may have advantages over others which have been proposed in the robotics literature.     

Robust nonlinear control of atomic force microscope via immersion and invariance

This paper reports an immersion and invariance (I&I)–based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed‐loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov‐based analysis of the closed‐loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method.