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.     

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 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.     

Practical disturbance rejection of a class of nonlinear systems via sampled output

This paper presents a sampled-data control scheme for the disturbance rejection of nonlinear systems in the output feedback form. The continuous-time controller is designed first using a filtered transformation and the internal model technique. Using the emulation approach, the proposed sampled-data control uses the sampled output and a discretetime implementation of the filter, and the internal model is involved. The proposed control is shown to render the overall system stable in a spirit of fast sampling. In particular, the disturbance is practically rejected in the sense that the ultimate bound of the output is allowed to be arbitrarily small by choosing appropriate gain parameters.     

Robustness With Respect to Sampling for Stabilization of Riesz Spectral Systems

We suppose that a continuous-time feedback is input–output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying idealized sample-and-hold to this continuous-time feedback is also input–output stabilizing if the sampling time is small enough. This question has been previously addressed for fairly general systems under various conditions. In this note, we restrict our attention to Riesz spectral systems, for which we generalize the existing results. Specifically, we give two relatively simple conditions which, combined, are sufficient for the sampled-data controller to be stabilizing. The first condition is a spectrum decomposition for the open-loop system generator, which by itself is necessary, but not sufficient, for the system to be stabilizable by sampled-data control. The second is a summability condition relating the real part of the spectrum of the generator and the expansion coefficients for the input and feedback operators.     

Multi-rate digital redesign of cascaded and dynamic output feedback systems

In this paper, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analogue controllers are often pre-designed based on desirable frequency specifications, such as bandwidth, natural angular frequency, etc. To take advantage of the digital controller over the analogue controller, digital implementation of these analogue controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilised to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analogue controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.     

Stability of sampled-data piecewise-affine systems under state feedback

This paper addresses stability of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant and a discrete-time emulation of a continuous-time state feedback controller. The paper presents conditions under which the trajectories of the sampled-data closed-loop system will exponentially converge to a neighborhood of the origin. Moreover, the size of this neighborhood will be related to bounds on perturbation parameters related to the sampling procedure, in particular, related to the sampling period. Finally, it will be shown that when the sampling period converges to zero the performance of the stabilizing continuous-time PWA state feedback controller can be recovered by the emulated controller.     

Adaptive control of continuous-time overmodeled plants

This paper presents an adaptive controller that will stabilize and asymptotically regulate any continuous-time, linear time-invariant plant which has one input and one output. The only assumptions on the plant are observability, controllability, and the a priori knowledge of an upper bound on the plant order. The adaptive control concept combines continuous-time state observation and sampled-data control with a generalized, plant-dependent hold function. The feedback gains and the hold function are adaptively tuned     

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.     

Stability of sampled-data piecewise affine systems: A time-delay approach

This paper addresses the stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant in feedback connection with a discrete-time emulation of a continuous-time state feedback controller. The sampled-data system is first considered as a continuous-time system with a variable time delay. Conditions under which the trajectories of the sampled-data closed-loop system will converge to an attracting invariant set are then presented. It is also shown that when the sampling period converges to zero, these conditions coincide with sufficient conditions for non-fragility of the stabilizing continuous-time PWA state feedback controller. The results are successfully applied to a helicopter example.     

Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

The problem of output feedback stabilization of nonlinear sampled-data control systems is considered under the low measurement rate constraint. A dual-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the missing output values between measured output samples. It is shown that if an observer-based output feedback controller that semiglobally practically asymptotically (SPA) stabilizes the single-rate sampled-data plant model is given, then the SPA stability property will be preserved for the closed-loop dual-rate sampled-data system, on the basis of the proposed dual-rate control scheme under standard assumptions. A numerical example is given to illustrate the design method.     

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.     

Sufficient stability condition for a sampled-data system withdigital controller

A quantitative stability condition for a sampled-data feedback system is formulated. The system is obtained from a stable continuous-time feedback system by digitalization of the controller. The condition shows how to determine a sampling frequency f₀ such that for all f larger than f₀ the discrete-time system remains stable     

Stability and stabilization of linear sampled-data systems with multi-rate samplers and time driven zero order holds

In multi-rate sampled-data systems, a continuous-time plant is controlled by a discrete-time controller which is located in the feedback loop between sensors with different sampling rates and actuators with different refresh rates. The main contribution of this paper is to propose sufficient Krasovskii-based stability and stabilization criteria for linear sampled-data systems, with multi-rate samplers and time driven zero order holds. For stability analysis, it is assumed that an exponentially stabilizing controller is already designed in continuous-time and is implemented as a discrete-time controller. For each sensor (or actuator), the problem of finding an upper bound on the lowest sampling frequency (or refresh rate) that guarantees exponential stability is cast as an optimization problem in terms of linear matrix inequalities (LMIs). Furthermore, sufficient conditions for controller synthesis are formulated as LMIs. It is shown through examples that choosing the right sensors (or actuators) with adequate sampling frequencies (or refresh rates) has a considerable impact on stability of the closed-loop system.     

Continuous-time controller redesign for digital implementation: A trajectory based approach

Given a continuous-time nonlinear closed loop system, we investigate sampled-data feedback laws for which the trajectories of the sampled-data closed loop system converge to the continuous-time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero. We derive necessary and sufficient conditions for the existence of such sampled-data feedback laws and—in case of existence—provide explicit redesign formulas and algorithms for these controllers.     

时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

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.     

Indirect sampled-data control with sampling period adaptation

It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretisation with constant sampling period is also exponentially stable, provided that the sampling period τ?>?0 is sufficiently small. In general, it is difficult to estimate how small the sampling period has to be in order to achieve the stability of the sampled-data system. In this article, we present an adaptive mechanism for adjusting the sampling period. This mechanism has the properties that, for every initial state, (i) the adaptation of the sampling period terminates after finitely many time steps and (ii) the state of the adaptive sampled-data system is integrable and converges to zero as time goes to infinity.     

Pointwise stabilisation of a string with time delay in the observation

Pointwise stabilisation is proposed in this paper for a string equation where the observation signal is subject to a time delay. Different from the boundary control, the feedback stabiliser is acting at the middle joint of the string. Well-posedness of the open-loop system and solvability of the observer are shown first. An observer system is then designed to estimate the state at the time interval when the observation is available, and a predictor system is designed to predict the state at the time interval when the observation is not available. Pointwise output feedback controller is introduced to make the closed-loop system asymptotically stable for the non-smooth initial values and exponentially stable for the smooth initial values, respectively. Simulation results demonstrate that the output feedback based on the observer and predictor effectively stabilises the pointwise control system with time delay.     

Takagi-Sugeno模糊连续系统的模糊采样控制

研究了T-S模糊连续系统的模糊采样控制问题．利用广义系统的描述方法、Lyapunov-Krasovikii泛函以及线性矩阵不等式(LMI)方法,建立了LMIs形式的依赖于采样时间间隔的模糊采样镇定条件,同时给出了模糊采样控制律的设计方法．所设计的模糊采样控制律可以镇定T-S模糊系统．而且,当连续时间模糊控制律可以镇定T-S模糊系统时,对于足够小的采样时间间隔,带有同样增益矩阵的模糊采样控制律也可以镇定T-S模糊系统．最后,通过两个仿真实例说明了所给方法的有效性．