Generalized sampled data feedback control of distributed parameter systems

In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems the necessary conditions are also known to be sufficient. We show that this equivalence extends to the infinite-dimensional case if the underlying semigroup is analytic. However, for general systems, the necessary conditions are not sufficient, nor are the sufficient conditions necessary. We prove this by a single example with a free parameter – one choice of parameter shows that the necessary conditions are too weak, and another choice shows that the sufficient conditions are too strong.     

Sensitivity of linear time invariant sampled data systems to sampling period

A technique for generation of sampling-period sensitivity functions for cyclic linear time-invariant sampled data systems is presented. The method uses some results of Rozenvasser to form the sensitivity models. The sensitivity functions are discontinuous at sampling times. Using some aspects of controllability, it is shown that integration of the model equations over one period only is sufficient to generate the sensitivity functions for all additional periods.     

Adaptive feedback control for unevenly sampled systems

This paper presents an adaptive control algorithm for a new type of discrete-time system that is unknown and is sampled unevenly. Such systems are obtained by unevenly sampling the unknown continuous time plant with two sequential sampling periods (T₁ and T₂), and are therefore referred to as unknown S(T₁, T₂) systems. This paper discusses their representation and stability when that system incorporates a known time delay. A generalized causal adaptive one-step-ahead controller is developed and it is shown to be able to stabilize the unknown S(T₁, T₂) system with respect to a uniformly bounded signal. The application to a typical S(T₁, T₂) system: the cross-directional basis weight control system in a paper making process, is described. Desirable results are obtained.     

A function space approach to sampled data control systems andtracking problems

This paper presents a new framework for hybrid sampled data control systems. Instead of considering the state only at sampling instants, this paper introduces a function piece during the sampling period as the state and gives an infinite-dimensional model with such a state space. This gives the advantage that sampled data systems with built-in intersample behavior can be regarded as linear, time-invariant, discrete-time systems. As a result, the approach makes it possible to introduce such time-invariant concepts as transfer functions, poles, and zeros to the sampled data systems even with the presence of the intersample behavior. In particular, tracking problems can be studied in this setting in a simple and unified way, and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions. This leads to the internal model principle for sampled data systems     

Polynomial modal control for sampled data systems with delay

The problem of modal sampled-data control for continuous-time linear time-invariant plant with delay is considered. The characteristic matrix of the system is constructed. An algorithm is given for generating the set of causal discrete-time controllers that place eigenvalues of the characteristic matrix at specified points of the complex plane.     

Optimal control of sampled data systems by geometric programming

The optimal control problem with constrained control and fixed terminal bounds has been the subject of extensive study by several investigators. This paper presents a simple method of determining the control sequence of a discrete data system by applying the Geometric Programming Technique. For purposes of illustration, a simple nonlinear second order sampled data system has been analysed by applying the Geometric Programming Technique. The analysis presented in this paper brings out the considerable flexibility of use which Geometric Programming has, and which in the authors' opinion makes this method one of immense future potential in the realm of optimal control.     

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network-induced delay

This paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network-induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network-induced delay and uncertain sampling periods can be incorporated from the original continuous-time state-space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete-time model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.     

Quantised and sampled output feedback for nonlinear systems

In this paper we consider the analysis and design of an output feedback controller for a perturbed nonlinear system in which the output is sampled and quantised. Using the attractive ellipsoid method, which is based on Lyapunov analysis techniques, together with the relaxation of a nonlinear optimisation problem, sufficient conditions for the design of a robust control law are obtained. Since the original conditions result in nonlinear matrix inequalities, a numerical algorithm to obtain the solution is presented. The obtained control ensures that the trajectories of the closed-loop system will converge to a minimal (in a sense to be made specific) ellipsoidal region. Finally, numerical examples are presented in order to illustrate the applicability of the proposed design method.     

On sampled data regulation of feedback linearizable systems using a realizable reconstruction filter

This paper deals with the classical problem of regulating a feedback linearizable system when only the samples of the output are available for measurement. The feedback linearization is done via an impulsive observer. The realizable reconstruction filter, which is a minimum order generalized hold device, connects the discrete controller with the continuous input of the system. The rest of the problem is similar to the classical regulator theory. An example of single link manipulator with flexible joints concludes the paper.     

网络化控制系统的时变采样及反馈调度策略

多处理器网络化控制系统中,信息传输的时延是使控制性能变差的主要原因之一。改进型混合调度算法通过在一个基本采样周期内的多次采样,形成时变的采样周期,缩减信息传输的截止期,可使信息传输的时延大为减少;同时构建网络化控制系统的反馈调度模型,通过调节基本采样周期,及时调度信息传输,能使网络的空闲时间始终保持在一个合理状态。仿真结果表明,网络利用率有所提高,网络化控制系统的动态性能有所改善。     

基于快速输出采样反馈的网络控制系统滑模控制

针对网络控制系统的网络诱导时延问题,提出了一种新的滑模控制方法。通过快速采样被控对象输出,建立了具有线性时不变被控对象的网络控制系统的离散模型。在此基础上,用极点配置法给出了滑模切换面参数,设计了输出反馈离散滑模控制器。仿真结果验证了该控制方法的有效性。     

多输出非线性系统在数据截断协议下的 时滞多采样率输出反馈镇定

本文研究一类多输出非线性系统基于一类数据截断协议的时滞多采样率输出反馈控制. 所考虑的非线性 系统的输出以异步方式进行采集, 通过网络传输到输出反馈控制端后立即用于构造输出反馈控制器. 当控制输入 信号可用时, 立即用来更新被控制系统. 这样, 就存在两种传输时滞, 一种是非线性系统输出端到输出反馈控制器端 的传输时滞, 另一种是输出反馈控制器端到非线性系统输入端的传输时滞. 从而被控系统的更新和输出反馈控制 器的更新不在同一个时间区间. 利用区间分解, 可以在同一个区间考虑被控系统和输出反馈控制器并分析闭环系 统的稳定性. 最后, 一个算例用来验证所提方法的有效性.     

Formation-containment control of second-order multi-agent systems with only sampled position data

This paper studies the formation-containment control problem of second-order multi-agent systems with only sampled position data. It is assumed that there exist interactions among leaders and the leaders’ neighbours are only leaders. Two different control protocols with only sampled position information are proposed for followers and leaders, respectively. By the algebraic graph theory and matrix theory, sufficient conditions are given to guarantee that the leaders achieve a desired formation and the followers asymptotically converge into the convex hull formed by the corresponding states of the leaders, i.e. the multi-agent systems achieve formation-containment. Moreover, an explicit expression of the formation position function is given for each leader. Finally, a numerical simulation is provided to illustrate the effectiveness of theoretical results.     

Simplification of the characteristic equation of multirate sampled data control systems

A method of simplifying the characteristic equation of two classes of linear time invariant multirate sampled data systems to a form similar to that of the analogous single-rate system is developed. The resulting equations are useful for multirate system design.     

Observer-based output feedback control of networked control systems with non-uniform sampling and time-varying delay

This paper investigates the problem of observer-based output feedback control for networked control systems with non-uniform sampling and time-varying transmission delay. The sampling intervals are assumed to vary within a given interval. The transmission delay belongs to a known interval. A discrete-time model is first established, which contains time-varying delay and norm-bounded uncertainties coming from non-uniform sampling intervals. It is then converted to an interconnection of two subsystems in which the forward channel is delay-free. The scaled small gain theorem is used to derive the stability condition for the closed-loop system. Moreover, the observer-based output feedback controller design method is proposed by utilising a modified cone complementary linearisation algorithm. Finally, numerical examples illustrate the validity and superiority of the proposed method.     

Control of asynchronous sampled data systems

This paper is concerned with the problem of controller design in the case of asynchronous sampled data systems. Optimal LQG controllers are obtained for the class of two-rate systems where all the control inputs are held at a rate which is asynchronously related to the rate with which all of the outputs are sampled. Furthermore for this class, a parameterization of all stabilizing controllers is provided     

时延与丢包情形下的网络控制系统量化反馈镇定

网络控制系统是通过实时网络来形成闭环反馈的控制系统。网络的介入会带来许多不确定因素,包括网络诱导时延和数据包丢失以及量化误差,它们会影响系统的稳定性,严重时甚至会导致系统失稳。本文针对短时延网络控制系统,考虑传感器-控制器和控制器-执行器两个通道都存在数据包丢失,在传感器到控制器端设立量化器,将系统建模为一个异步动态系统,利用异步动态系统指数稳定性理论、线性矩阵不等式工具分析了闭环系统稳定性,并基于MATLAB软件的线性矩阵不等式(LMI)工具箱实验仿真进行有效性验证,结果证明了方案的可行性,最后给出控制器参数的设计方法。     

The design of stochastic sampled data control systems containing a discrete actuator

A numerical method is outlined for synthesizing optimum impulse compensators in the mean-square error sense for feedback systems containing a coarse quantization actuator element where thesigma/qratio must be specified not only to ensure a valid estimate of the quantization error but also to limit the delay errors caused by the finite rate of actuator operation.     

Stability condition for sampled data based control of linear continuous switched systems

Most practical systems are continuous in nature but with discrete (sampled) feedback when digital control is utilized. This paper investigates the stabilization problem of switched linear continuous-time systems with sampled data based control. For both known and unknown arbitrary switching processes, on the basis of Lyapunov stability theory, a sufficient global exponential stability condition related to Dwell time and sampling period is established. For the latter case, on-line one-step adaptive estimation algorithm is derived and integrated with sampled feedback for control design. Validation and verification of the established result are conducted through cruise control of train systems.