Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

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.     

Distributed guaranteed cost control for aperiodic sampled-data networked interconnected systems: a switched system approach

This paper investigates the distributed guaranteed cost control problem for a class of networked interconnected control systems (NICSs) under aperiodic sampling. The NICSs with missing data and time-varying delay are modelled as an aperiodic sampled-data switched system with uncertainties. Then, sufficient conditions ensuring the exponential stability and guaranteed cost quadratic performance are presented by using the average dwell time approach. The distributed state feedback controller is designed by solving a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

Stabilization of Sampled-Data Control Systems With Control Inputs Missing

This note is concerned with the stabilization problem for sampled-data control systems with control inputs missing. A sufficient condition is derived for the existence of exponentially stabilizing state feedback controllers via the switched system approach. The obtained condition establishes several quantitative relations among some system parameters (such as the sampling period and the exponential decay rate), the actual data missing rate, and the admissible data missing rate bound. Two illustrative examples are given to show the effectiveness of the proposed results.      

A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems

In this paper, we consider the H/sub 2/ sampled-data control for uncertain linear systems by the impulse response interpretation of the H/sub 2/ norm. Two H/sub 2/ measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H/sub 2/ criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.     

ROBUST SAMPLED-DATA CONTROL SYSTEMS ANALYSIS BY APPROXIMATE Z-TRANSFORM USING HIGHER-ORDER INTEGRATORS

In this paper, robust sampled-data control systems are analyzed in the frequency domain. Stability analysis of a sampled-data control system using higher-order integrators was proposed by Wang et al. in 1990 [1] and adopted in the approximate Z-transform by Wang et al. in 1997 [2]. We further apply the approximate Z-transform to analyze the stability boundary of a sampled-data control system in which the plant transfer function has bounds prescribed on its parameters.     

Robust global stabilisability by means of sampled-data control with positive sampling rate

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global stabilisation of non-linear sampled data systems with positive sampling rate. Sufficient conditions for robust reachability of one set from another under constant control are also provided. The proposed method is illustrated through a number of examples, including the study of the sampled-data stabilisation problem of the chemostat.     

Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

Controlling aliased dynamics in motion systems? An identification for sampled-data control approach

Sampled-data control systems occasionally exhibit aliased resonance phenomena within the control bandwidth. The aim of this paper is to investigate the aspect of these aliased dynamics with application to a high performance industrial nano-positioning machine. This necessitates a full sampled-data control design approach, since these aliased dynamics endanger both the at-sample performance and the intersample behaviour. The proposed framework comprises both system identification and sampled-data control. In particular, the sampled-data control objective necessitates models that encompass the intersample behaviour, i.e., ideally continuous time models. Application of the proposed approach on an industrial wafer stage system provides a thorough insight and new control design guidelines for controlling aliased dynamics.     

Robust reliable sampled-data control for switched systems with application to flight control

This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.     

不确定非线性网络化系统的鲁棒H_∞控制

用T-S(Takagi-Sugeno)模糊方法研究了带有参数不确定的非线性网络化系统的鲁棒控制.首先,考虑到诱导时延和数据丢包等网络因素的影响,基于事件驱动的保持器的更新序列建立闭环反馈系统的采样模型,并将其转化为状态中附加两个时滞变量的连续T-S模糊系统.然后,利用时滞系统方法,分析不确定闭环模糊系统的鲁棒H∞性能,并设计相应的鲁棒H∞模糊控制器.最后,仿真例子表明了方法的有效性.     

切换非线性系统采样控制的研究现状与进展

切换非线性系统由于其广泛的工程应用背景以及重要的理论研究价值引起各行业学者的广泛关注.近年来,随着计算机技术的快速发展,切换非线性系统采样控制问题成为研究热点.对目前切换非线性系统采样控制领域的研究现状进行综述.首先介绍了切换非线性系统的基本问题,并梳理了切换非线性系统几个常用控制方法的基本思想.然后从时间触发采样控制和事件触发采样控制两个方面对切换非线性系统采样控制的国内外研究现状进行了论述.最后进行了总结并提出切换非线性系统采样控制领域未来值得关注的研究方向.     

Design of H 2 Controllers for Sampled-Data Systems with Input Time Delays

This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H ₂ sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H ₂ sampled-data controller for the sampled-data systems with the various input time delays.     

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.     

Generalized predictive control for non-uniformly sampled systems

In this paper, we study digital control systems with non-uniform updating and sampling patterns, which include multirate sampled-data systems as special cases. We derive lifted models in the state-space domain. The main obstacle for generalized predictive control (GPC) design using the lifted models is the so-called causality constraint. Taking into account this design constraint, we propose a new GPC algorithm, which results in optimal causal control laws for the non-uniformly sampled systems. The solution applies immediately to multirate sampled-data systems where rates are integer multiples of some base period.     

Robust sampled-data H∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals

In this paper, the problem of robust sampled-data H_∞ control of linear uncertain singularly perturbed systems is investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Two types of controller design are considered: (1) with a fast sampling in the fast state and a slow one in the slow state, and (2) with a fast sampling in both states. For each type, a time-dependent Lyapunov functional associated with the sampling pattern is introduced to analyse the exponential stability and L₂-gain performance of the closed-loop system. Linear matrix inequalities based solutions of the robust sampled-data H_∞ control problem are derived. The new results are proved theoretically to be less conservative than the existing results. An illustrative example is given which substantiates the usefulness of the proposed method.     

基于分段连续Lyapunov函数的采样系统鲁棒保性能控制

针对不确定采样控制系统的鲁棒保性能控制问题,首先将采样系统描述为跳变线性系统,基于矩阵凸组合思想构造了分段连续Lyapunov函数,进而在线性矩阵不等式框架内给出了不确定采样系统鲁棒稳定的条件.针对范数有界参数不确定采样系统,提出了鲁棒保性能控制器设计的在线算法,在每个采样周期内通过求解一组线性矩阵不等式的可行解来构造出状态反馈增益矩阵.最后的仿真算例验证了所提设计方法的有效性.     

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．     

线滞后系统的控制算法比较

本文介绍了用于时滞系统的Smith预估补偿控制、采样PI控制和预测控制方法的原理,并对一阶纯滞后对象,采用Matlab工具对其控制性能进行仿真比较.仿真结果表明,Smith预估补偿算法在滞后被控对象模型已知的情况下能够取得较好的控制效果,而在模型参数未知或不准确情况下,适合采用采样PI控制或预测控制.