From Continuous-Time Design to Sampled-Data Design of Observers

In this work, a sampled-data nonlinear observer is designed using a continuous-time design coupled with an inter-sample output predictor. The proposed sampled-data observer is a hybrid system. It is shown that under certain conditions, the robustness properties of the continuous-time design are inherited by the sampled-data design, as long as the sampling period is not too large. The approach is applied to linear systems and to triangular globally Lipschitz systems.     

Inter-sample output predictor based sampled-data ADRC supporting high precision control of VCM servo systems

Ultra high precision servo control systems usually require fast sampling rate to achieve desired digital control performance, where output sampling restrictions (such as sensor bandwidth) pose major challenges for such applications. In this paper, we propose a novel sampled-data multi-rate active disturbance rejection control (ADRC) architecture under sampling rate restrictions, where a digital extended state observer (ESO) with inter-sample output prediction structure is employed to construct inter-sample dynamics between two consecutive sampling instants, such that high frequency disturbances can be better rejected. The convergence of the estimation and the stability of the closed-loop system are analyzed based on Lyapunov function method and separation principle. The proposed control architecture is implemented on a voice coil motor (VCM) actuated micro–nano servo gantry, demonstrating significant performance improvement over existing single-rate or multi-rate ADRC methods.     

非线性微分-代数系统的输出反馈镇定:基于线性采样控制

对满足指数1和线性增长条件的非线性微分-代数系统,本文证明其采样输出反馈镇 定控制问题可解.首先,给出一个线性显式非初始化状态观测器设计;然后,构造出线性的采样输出 反馈控制器,使得整个闭环系统渐近稳定.仿真结果表明了所提控制方法的有效性.     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Semi-global sampled-data output feedback disturbance rejection control for a class of uncertain nonlinear systems

This paper investigates the semi-global output feedback disturbance rejection control problem for a class of uncertain nonlinear systems with additive disturbances using linear sampled-data control. Aiming to reject the adverse effects caused by the uncertainties and unknown nonlinear perturbations which may not satisfy the strict feedback or feedforward structure, a new generalised discrete-time extended state observer is proposed to estimate the disturbance at sampling points. An output feedback disturbance rejection control law is then constructed in a sampled-data form which facilitates digital implementations. By selecting adequate control gains and a sufficiently small sampling period to restrain the state growth under a zero-order-hold input, the semi-global asymptotic stability of the hybrid closed-loop system and the disturbance rejection ability are proved. Both numerical example and an application of a single-link robot arm system demonstrate the feasibility and efficacy of the proposed method.     

Continuous–discrete-time adaptive observers for nonlinear systems with sampled output measurements

This paper considers the continuous–discrete-time adaptive observer (CDAO) design for a class of nonlinear systems with unknown constant parameters and sampled output measurements. The proposed observer is actually an impulsive system, since the observer state flows according to a set of differential equations and with instantaneous state jumps corresponding to measured samples and their estimates, and an inter-sample output predictor is used to predict the output during sampling intervals. By assuming appropriate persistent excitation conditions and following a technical lemma, an upper bound of the sampling intervals is derived, with which the convergence of the observer state and unknown parameters can be ensured. Finally, the proposed observer is used in examples of chaotic oscillators and single-link flexible-joint robot manipulator to show the effectiveness.     

Disturbance-observer-based sampled-data adaptive output feedback control for a class of uncertain nonlinear systems

In this paper, a sampled-data adaptive output feedback controller is proposed for a class of uncertain nonlinear systems with unmeasured states, unknown dynamics and unknown time-varying external disturbances. To approximate uncertain nonlinear functions, radial basis function neural networks (RBFNNs) are employed. The state observer and the disturbance observer (DO) are constructed to estimate the unmeasured state and the external disturbance, respectively. Then, the sampled-data adaptive output feedback controller and adaptive laws are designed by using the backstepping design technique. The allowable sampling period T is derived to guarantee that all states of the resulting closed-loop system are semi-globally uniformly ultimately bounded. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed approach.     

Cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control

This paper studies the problem of cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control. To dominate the unknown nonlinear perturbing terms, a scaling gain is introduced by a change in coordinates. Then, we construct a reduced-order sampled-data observer and use the backstepping method to design a linear sampled-data controller. By using combined graph theory with feedback domination approach, an explicit formula for the sampling period can be obtained under the proposed controller with appropriate gains such that all outputs of the agents in the network can be synchronised. Finally, two examples are provided to verify the effectiveness of the proposed method.     

An output delay approach to fault estimation for sampled-data systems

The problem of fault estimation for a class of non-uniformly sampled-data systems is investigated from the time delay point of view in this paper.Firstly,the output delay approach is employed to model the sampled-data system as a continuous-time one with time-varying delay output.Then,based on the analysis of the inapplicability of the adaptive fault diagnosis observer in such class of time-delay systems,a novel augmented fault estimation observer design method is proposed to guarantee the exponential convergence of the estimation errors.Furthermore,an extension to the case of time varying fault estimation for the noisy sampled-data systems is studied.Finally,simulation results of a flight control system are presented to demonstrate the effectiveness of the proposed method.     

Actuator fault detection and performance recovery with Kalman filter-based adaptive observer

A novel Kalman filter-based adaptive observer for the sampled-data nonlinear time-varying system is proposed in this paper. With the high gain property of Kalman filter, it is applicable to a large variation of unknown parameters, which can be estimated optimally. Then a method of actuator fault detection is proposed. With the estimated faults, one can use the proposed input compensation method to solve actuator faults. Additionally, the optimal linearization technique is used to obtain the locally optimal linear model for a nonlinear system at each sampled state, so that the actuator fault detection and performance recovery of a sampled-data nonlinear time-varying system is accomplished. In this paper, we also introduce a prediction-based digital redesign method to develop the corresponding sampled-data controller.     

Formulas relating stability estimates of discrete-time and sampled-data nonlinear systems

We provide an explicit stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the estimate for the corresponding discrete-time system and a function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [[Reference to 1]] or extend some results in [[Reference to 4]] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.     

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.     

Global practical tracking of a class of nonlinear systems using linear sampled-data control

This paper considers the problem of global practical tracking via sampled-data control for a class of uncertain nonlinear systems. Under a lower triangular linear growth condition, a sampled-data state feedback controller is first constructed such that the states are globally bounded and the error between the system output and the reference signal will be rendered smaller than a given tolerance. When only the output of the system is measurable, a sampled-data output feedback controller, whose observer and control law are both linear, is constructed to solve the global practical tracking problem.     

线性/非线性切换扩张状态观测器的收敛性和稳定性分析

线性/非线性切换扩张状态观测器(linear/nonlinear switching extended state observer,SESO)是为追求更高的控制精度和抗扰能力,在进行状态估计时根据状态误差大小在线性扩张状态观测器(linear extended state observer,LESO)和非线性扩张状态观测器(nonlinear extended state observer,NLESO)之间进行切换的一种扩张状态观测器.但由于该算法存在非线性结构,目前还没有从频域角度对该方法进行收敛性和控制系统稳定性分析的相关研究.针对此问题,以二阶系统为研究对象,首先对SESO的结构及参数选择进行了介绍,然后,分别采用等效增益法和描述函数法,从频域角度对了其状态估计误差的收敛性和基于SESO的自抗扰控制系统的稳定性进行了研究.结果表明,三阶SESO具有良好的收敛性,能实现对系统状态和"总扰动"的误差估计,并且选择适当的SESO参数,可避免极限环的产生.     

On interval tracking performance evaluation and practical varying sampling ILC

This paperconsiders the evaluation of interval tracking error for sampled control performance and an associated sampling technique to enhance the tracking performance. The upper bounds of the tracking error profile of arbitrary sample interval for both the linear system and nonlinear system are first given. A practical sampled-data iterative learning control with varying sampling rates is proposed to ensure a prior given tolerant tracking error. In this control strategy, the inter-sample behaviour is checked to determine which intervals are not satisfactory when the given tracking performance at-sample time instants is satisfied, and then the sampling frequency for such intervals is increased. Both at-sample and inter-sample tracking performance are satisfied after enough learning iterations. Two examples are simulated to demonstrate the effectiveness of the proposed sampling strategy.     

时滞纳米运动系统的多速率采样预测自抗扰控制

电容型纳米位置传感器在纳米伺服系统中得到了越来越多的应用.这类超高精度模拟传感器用于反馈信号时因较长的模数转换时间将带来明显的测量时滞.而这类数字纳米伺服系统也因硬件使其采样频率在处理高频干扰时受到带宽限制.本文针对测量时滞和高频干扰的挑战,提出一种带采样预测功能的多速率自抗扰控制器设计方法.首先建立了电容式位移传感器的纳米运动平台带有时滞的动力学模型.其次,基于该模型设计多率采样预测线性扩张状态观测器和多率反馈控制器.通过设计预测型观测器,适当选取观测器增益,消除时滞对状态观测的影响.另外,将输出预估器加入预测扩张状态观测器中重构采样点间系统输出值,从而在时滞系统中更好地估计和消除高频干扰,并给出了系统的稳定性分析.最后通过压电驱动纳米运动平台的实时控制实验验证本文提出控制器的有效性.     

Adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs

In this paper, we propose an adaptive observer for a class of uniformly observable nonlinear systems with nonlinear parametrization and sampled outputs. A high gain adaptive observer is first designed under the assumption that the output is continuously measured and its exponential convergence is investigated, thanks to a well defined persistent excitation condition. Then, we address the case where the output is available only at (non uniformly spaced) sampling instants. To this end, the continuous-time output observer is redesigned leading to an impulsive observer with a corrective term involving instantaneous state impulses corresponding to the measured samples and their estimates. Moreover, it is shown that the proposed impulsive observer can be put under the form of a hybrid system composed of a continuous-time observer coupled with an inter-sample output predictor. Two design features are worth to be emphasized. Firstly, the observer calibration is achieved through the tuning of a scalar design parameter. Secondly, the exponential convergence to zero of the observation and parameter estimation errors is established under a well defined condition on the maximum value of the sampling partition diameter. More specifically, the observer design is firstly carried out in the case of linear parametrization before being extended to the nonlinear one. The theoretical results are corroborated through simulation results involving a typical bioreactor.     

State covariance assignment for sampled-data feedback control systems

This paper proposes a new performance criterion of ‘covariance’ for sampled-data systems. A covariance of sampled-data systems is defined by taking account of inter-sample behaviour. An SCA (state covariance assignment) problem for sampled-data feedback control systems is also discussed, which is the counterpart of that for purely continuous or discrete-time feedback control systems. The SCA problem for sampled-data systems will be solved as a discrete-time SCA problem, where the discretization preserves the state covariance and is in two steps. In the first step, a certain sample time performance is required to ensure the inter-sample performance, and the output signal results to be discretized. The second step is to discretize the input signal.     

基于观测器的一类连续非线性系统的采样控制

首先使用反演方法分别设计了系统的连续时间状态反馈控制器、连续时间观测器和基于连续时间观测器的连续时间控制器. 接下来, 利用零阶保持法对连续时间状态反馈控制器进行离散化, 获得了状态反馈采样控制器; 利用零阶保持法对基于连续时间观测器 的连续时间控制器离散化, 获得了基于连续时间观测器的采样控制器; 利用Euler法对连续时间观测器离散化, 同时利用零阶保持法对控制器离散化, 从而获得了采样观测器和基于采样观测器的采样控制器. 本文论证了上述状态反馈采样控制器和基于连续时间观测器的采样控制器可以保证闭环系统渐近稳定, 而基于采样观测器的采样控制器可以保证被控对象的状态是有界的, 其最终边界依赖于设计参数与采样周期. 最后, 通过选择适当的采样周期, 完成了闭环采样控制系统的设计. 一个船舶航向控制的例子表明应用本文 所提方法设计出的三种采样控制器具有良好的控制效果.     

Stabilization of a nonlinear jump system

In this paper we consider the problem of output feedback stabilization of a general nonlinear jump system. We shall show that the combination of a locally asymptotically stabilizing state feedback law and a local asymptotic observer yields a locally asymptotically stabilizing output feedback controller. Hence, the local separation principle holds for the nonlinear jump system. This result can be applied to nonlinear sampled-data systems.