STABILITY ANALYSIS OF UNCERTAIN DISCRETE‐TIME SYSTEMS WITH TIME‐VARYING STATE DELAY: A PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH

This paper presents several new robust stability conditions for linear discrete‐time systems with polytopic parameter uncertainties and time‐varying delay in the state. These stability criteria, derived by defining parameter‐dependent Lyapunov functions, are not only dependent on the maximum and minimum delay bounds, but also dependent on uncertain parameters in the sense that different Lyapunov functions are used for the entire uncertainty domain. It is established, theoretically, that these robust stability criteria for the nominal and constant‐delay case encompass some existing result as their special case. The delay‐dependent and parameter‐dependent nature of these results guarantees the proposed robust stability criteria to be potentially less conservative.     

REDUCING CONTROL LATENCY AND JITTER IN REAL‐TIME CONTROL

This paper analyses control computation latency and jitter, which have been largely ignored in the control community for real‐time (RT) control. The focus is on RT control systems with multiple control tasks running on a uniprocessor. Three strategies are proposed to reduce control latency and/or jitter: introduction of offsets into control task scheduling, decomposition of control tasks; and increasing the priority levels of output subtasks. Examples are given to demonstrate the effectiveness of the proposed methods.     

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE‐TIME SINGULAR SYSTEMS WITH TIME‐DELAY AND NONLINEAR PERTURBATION

This paper discusses a generalized quadratic stabilization problem for a class of discrete‐time singular systems with time‐delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S‐procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete‐time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non‐singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples.     

DISTURBANCE COMPENSATION FOR TIME‐DELAY PROCESSES

In this paper, a general control scheme for disturbance rejection is presented. It is an extension of the disturbance observer used in mechatronics, and made applicable to time‐delay processes. It is shown that the proposed control scheme can achieve better load response in general and reject periodic disturbance asymptotically in particular. Stability analysis and disturbance rejection performance are provided. Simulation results confirm that the proposed method yields superior load response compared to the classical feedback system.     

OPTIMAL TRACKING CONTROL FOR DISCRETE TIME‐DELAY SYSTEMS WITH PERSISTENT DISTURBANCES

Optimal tracking control (OTC) for discrete time‐delay systems affected by persistent disturbances with quadratic performance indexes is considered. Optimal tracking controller is designed based on a sensitivity approximation approach. By introducing a sensitivity parameter, we transform the original OTC problem into a series of difference equations without time‐advance on time‐delay terms. The obtained OTC law consists of analytic feedback and feedforward terms, and a compensation term, which is the sum of the infinite series of adjoint vectors. The compensation term can be obtained with an iterated formula for the adjoint vectors. A simulation example shows that the approximation approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.     

ADAPTIVE ROBUST CONTROL OF UNCERTAIN SYSTEMS WITH TIME‐VARYING STATE DELAY

In this paper, a new adaptive robust control scheme is developed for a class of uncertain dynamical systems with time‐varying state delay, unknown parameters and disturbances. By incorporating adaptive techniques into the robust control method, we propose a continuous adaptive robust controller which guarantees the uniform boundedness of the system and at the same time, the regulating error enters an arbitrarily designated zone in a finite time. The proposed controller is independent of the time‐delay, hence it is applicable to a class of dynamical systems with uncertain time delays. The paper includes simulation studies demonstrating the performance of the proposed control scheme.     

DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY

This paper deals with the problem of stability and robust control for both certain and uncertain continuous‐time singular systems with state delay. Systems with norm‐bounded parameter uncertainties are considered. Robust delay‐dependent stability criteria and linear memoryless state feedback controllers based on linear matrix inequality are obtained. By choosing some Lyapunov‐Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay‐dependent results. Finally, numerical example is provided to illustrate the effectiveness of the proposed method.     

SLIDING MODE CONTROL SYNTHESIS OF UNCERTAIN TIME‐DELAY SYSTEMS

Sliding mode control synthesis is developed for a class of uncertain time‐delay systems with nonlinear disturbances and unknown delay values whose unperturbed dynamics is linear. The synthesis is based on a new delay‐dependent stability criterion. The controller constructed proves to be robust against sufficiently small delay variations and external disturbances. An admissible upperbound such that the corresponding closedloop system remains globally asymptotically stable for each delay value less than this up‐perbound is derived. Performance issues of the controller are illustrated in a simulation study.     

SCHEDULING AND CONTROL CO‐DESIGN FOR DELAY COMPENSATION IN THE NETWORKED CONTROL SYSTEM

The networked control system (NCS) is currently receiving increasing attention from researchers. Researches on this subject, however, have not considered the co‐design of network quality of service (QoS) and control quality of performance (QoP). This paper proposes a novel NCS design framework based on scheduling and control co‐design to compensate for random network‐induced delays. In the framework, a scheduling algorithm used to find the optimal sampling regions of control loops performs rough adjustment and guarantees the network QoS, while a novel adaptive fuzzy PID controller is designed to perform accurate adjustment to guarantee the control QoP. Practical application results obtained with a multi‐loop NCS show that the framework can ensure satisfactory performance due to its robustness against network uncertainty.     

线性时滞系统依赖于时滞的H~∞状态反馈控制

对具有纯滞后输入的线性时滞系统 ,在系统的状态时滞与控制输入时滞不同时 ,研究了依赖时滞的 H∞ 状态反馈控制器设计问题 ,其控制器存在的充分条件由一个线性矩阵不等式 (L MI)的形式给出 ,并给出了相应的 H∞ 控制器的综合设计方法     

ADAPTIVE DYNAMIC MATRIX CONTROL FOR NETWORK‐BASED CONTROL SYSTEMS WITH RANDOM DELAYS

Random transfer delays in network‐based control systems (NCSs) degrade the control performance and can even destabilize the control system. To address this problem, the adaptive dynamic matrix control (DMC) algorithm is proposed. The control algorithm is derived by applying the philosophy behind DMC to a discrete time‐delay model. A method to estimate the network‐induced delays is also presented to facilitate implementation of the control algorithm. Finally, an NCS platform based on the TrueTime simulator is constructed. With it, the adaptive DMC algorithm is compared with the conventional DMC algorithm under different network conditions. Simulation results show that the proposed adaptive DMC algorithm can respond to various network conditions adaptively and achieve better control performance for NCSs with random transfer delays.     

具有随机时延的网络化控制系统基于等价空间的故障诊断

随着控制系统技术的飞速发展，把网络环节引入到传统的控制系统实现迅速准确的远 距离闭环控制是人们日益关注的课题．而网络中由信息的碰撞、重发而产生的网络延迟对控 制系统本身带来的负面影响却不容忽视．本文针对网络化控制系统(Networked Control S ystem，简称NCS)的随机延时，提出了延时估计和在线获得延时数据的两种方法，建立控制 对象的数学模型．利用z变换来处理延时，由等价关系产生残差，通过参数设计解耦干扰向 量，从而对网络化系统的控制故障进行了诊断，并提供了仿真结果．     

DELAY‐DEPENDENT ROBUST CONTROL FOR UNCERTAIN SINGULAR TIME‐DELAY SYSTEMS

The problem of delay‐dependent robust stabilization for uncertain singular time‐delay systems is investigated in this paper. The parameter uncertainty is assumed to be norm‐bounded and possibly time‐varying, while the time delay considered here is assumed to be constant but unknown. A delay‐dependent condition is presented for a singular time‐delay system to be regular, impulse free, and stable, based on which robust stability analysis and the robust stabilization problem are studied. An explicit expression for the desired state‐feedback control law is also given. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which involve no decomposition of the system matrices. Some numerical examples are given to show the efficiency of the theoretical conditions.     

CONTROL LAW FOR QUADRATIC STABILIZATION OF PERTURBED FUZZY TIME‐DELAY LARGE‐SCALE SYSTEMS VIA LMI

In this paper, the perturbed continuous‐time large‐scale system with time delays is represented by an equivalent Takagi‐Sugeno type fuzzy model. First, two types of decentralized state feedback controllers are considered in this paper. Based on the Riccati‐type inequality, the Razumikhin theorem, and the delay‐dependent Lyapunov functional approach, some controller design approaches are proposed to stabilize the whole fuzzy time‐delay system asymptotically. In these design methods, both the delay‐independent and delay‐dependent stabilization criteria are derived. By Schur complement, these sufficient conditions can be easily transformed into the problem of LMI's. Moreover, the systems with all the time‐delays τ^l_ij (t) are the same for all rules (i.e., τ^l_ij (t) = τ^m_ij (t) = τ_ij for all l =m); the authors also propose a simpler and less conservative stabilizing criteria. A numerical example is given to illustrate the control design and its effectiveness.     

TWO‐DEGREE‐OF‐FREEDOM CONTROL SCHEME FOR PROCESSES WITH LARGE TIME DELAY

In this paper, an analytical two‐degree‐of‐freedom‐control scheme is proposed for controlling processes with large time delay. The main contributions of this paper are that a setpoint response controller and an H_∞ PID load‐loop controller are developed based on optimal control theory, and control parameters are derived analytically. This structure can also be used to control integrating or unstable processes.     

DECENTRALIZED STABILIZATION OF H FUZZY CONTROL FOR NONLINEAR MULTIPLE TIME‐DELAY INTERCONNECTED SYSTEMS

A robustness design of fuzzy control is proposed in this paper to overcome the effect of modeling errors between nonlinear multiple time‐delay systems and fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the UUB (uniformly ultimately bounded) stability of nonlinear multiple time‐delay interconnected systems with disturbances. Based on this criterion and the decentralized control scheme, a set of fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time‐delay interconnected systems and the Hcontrol performance is achieved in the mean time.     

LMI OPTIMIZATION APPROACH FOR DELAY‐DEPENDENT H∞ CONTROL OF TIME‐VARYING DELAY SYSTEMS

In this paper, the robust delay‐dependent H_∞ control for a class of uncertain systems with time‐varying delay is considered. An improved state feedback H_∞ control is proposed to minimize the H_∞‐norm bound via the LMI optimization approach. Based on the proposed result, delay‐dependent criteria are obtained without using the model transformation technique or bounded inequalities on cross product terms. The linear matrix inequality (LMI) optimization approach is used to design the robust H_∞ state feedback control. Some numerical examples are given to illustrate the effectiveness of the approach.     

一阶时滞不稳定过程的复合PID控制

针对一阶时滞不稳定过程讨论了一类复合ＰＩＤ控制及其参数整定公式．该方法基于分步设计的思想，在比例控制器镇定基础上对闭环所构成的广义稳定对象，设计二级ＰＩＤ控制器．在二级控制器设计中，通过引入时滞二阶稳定模型优化ＰＩＤ参数．本文同时讨论了等价的二自由度ＰＩＤ控制器．     

OPTIMAL REJECTION WITH ZERO STEADY‐STATE ERROR OF SINUSOIDAL DISTURBANCES FOR TIME‐DELAY SYSTEMS

This paper studies the problem of optimal rejection with zero steady‐state error of sinusoidal disturbances for linear systems with time‐delay. Based on the internal model principle, a disturbance compensator is constructed to counterbalance the external sinusoidal disturbances, so that the original system can be transformed into an augmented system without disturbances. Then, with the introduction of a sensitivity parameter and expanding power series around it, the optimal disturbance rejection problem can be simplified to the problem of solving an infinite sum of a linear optimal control series without time‐delay or disturbance. The optimal control law for disturbance rejection with zero steady‐state error consists of accurate linear state feedback terms and a time‐delay compensating term, which is an infinite sum of an adjoint vector series. In the presented approach, iteration is required only for the time‐delay compensation series. By intercepting a finite sum of the compensation series, we obtain an approximate physically realizable optimal control law that avoids complex calculation. A numerical simulation shows that the algorithm is effective and easy to implement.