Computing stability domains in the space of time delay and controller coefficients for FOPDT and SOPDT systems

In this paper, a method is proposed to compute the maximum allowable time delay for first-order plus dead time and second-order plus dead time systems, in order to maintain stability. Designing first order controllers for such systems to preserve stability for a longer time delay is the main aim of this paper. The procedure uses the properties of the phase diagram of the open-loop transfer functions of such systems. The effects of the variation of the controller coefficients on the maximum allowable time delay of the systems are investigated and the stability domains in the space of the uncertain delay and the controller coefficients are computed. The results can be used to design first-order robust controllers for first and second order processes containing uncertain delays.     

Adaptive wavenet controller design for teleoperation systems with variable time delays using singular perturbation method

The main goal of controller design in teleoperation systems is to achieve stability and optimal operation in presence of factors such as time delays, system disturbances and modeling errors. This paper proposes a new method of controller design based on wavenet with singular perturbation method for the bilateral teleoperation of robots through the internet. The wavenet controller could overcome the variable time delay in teleoperation system. This new method introduces a reduced-order structure for control and stability of teleoperation systems. By using singular perturbation method, teleoperation system is decomposed into two fast and slow subsystems. This method is a step towards reduced-order modeling. In this method, we use a feedback linearization method in master subsystem and a wavenet controller for slave subsystem. In wavenet controller, we used a learning method so that the system was Lyapunov stable. As the stability of the model is highly dependent on the learning of the system, we use Lyapunov stability in this method. It has been tried to reduce the tracking error between the master and the slave subsystems. In this structure the position of master-slave are compared together and controlling signal is applied to the slave so that they can track each other in the least possible time. In all schemes the effectiveness of the system is shown through the simulations and they have been compared with each other.     

网络延时对PID控制系统性能影响的分析

由于网络通讯延时的存在，传统PID控制算法在网络化控制系统中的控制性能将受到影响．使用一种代价函数作为性能评估标准，并通过仿真实验分析了各种网络延时对PID控制性能的影响．利用根轨迹法分析了网络延时和PID参数对控制系统稳定性和控制性能的影响；用NetCon控制器实现了各种网络延时下对一个实验系统的控制．实验结果证明了仿真分析的正确性和有效性．     

一类时滞对象的PID控制器参数稳定域计算

针对任意阶时滞对象,通过求解控制参数的稳定边界线和判断边界线的哪侧具有更少的不稳定极点,给出一种确定PID控制器参数稳定域的准确计算方法．只要在所得到的稳定域中调节PID控制器参数,就能够保证闭环系统的稳定性,这不仅为时滞对象的PID控制器设计建立了基础,也为其在线调节提供了一条简单有效的途径．仿真实例验证了该方法的有效性,并表明该方法不仅适用于不稳定时滞对象而且也适用于非最小相位时滞对象．     

New stability conditions for systems with distributed delays

In the present paper, sufficient conditions for the exponential stability of linear systems with infinite distributed delays are presented. Such systems arise in population dynamics, in traffic flow models, in networked control systems, in PID controller design and in other engineering problems. In the early Lyapunov-based analysis of systems with distributed delays (Kolmanovskii & Myshkis, 1999), the delayed terms were treated as perturbations, where it was assumed that the system without the delayed term is asymptotically stable. Later, for the case of constant kernels and finite delays, less conservative conditions were derived under the assumption that the corresponding system with the zero-delay is stable (Chen & Zheng, 2007). We will generalize these results to the infinite delay case by extending the corresponding Jensen’s integral inequalities and Lyapunov–Krasovskii constructions. Our main challenge is the stability conditions for systems with gamma-distributed delays, where the delay is stabilizing, i.e. the corresponding system with the zero-delay as well as the system without the delayed term are not asymptotically stable. Here the results are derived by using augmented Lyapunov functionals. Polytopic uncertainties in the system matrices can be easily included in the analysis. Numerical examples illustrate the efficiency of the method. Thus, for the traffic flow model on the ring, where the delay is stabilizing, the resulting stability region is close to the theoretical one found in Michiels, Morarescu, and Niculescu (2009) via the frequency domain analysis.     

奇异时滞系统对时滞参数的自适应控制

针对一类状态时滞奇异系统,研究状态反馈控制器的设计问题。基于Lyapunov稳定性理论和线性矩阵不等式（LMI）工具,当时滞常数精确已知时,设计带有记忆的状态反馈控制器,使得相应的闭环系统渐近稳定;当时滞常数不能精确已知时,通过求解相应的线性矩阵不等式,得到满足设计要求的对时滞参数的自适应控制器,使得时滞系统镇定。最后,仿真实例表明此方法的有效性。     

网络控制系统补偿器设计及稳定性分析

为解决网络延时对网络化控制系统性能的影响, 从控制的角度提出基于系统模型的补偿器设计方案以解决网络延时问题. 通过对广义预测控制算法GPC状态空间形式的推导, 设计具有多步预测功能的网络控制器, 实现前向通道的延时补偿; 构造具有延时补偿功能的状态观测器以补偿反馈通道延时. 分析了使用上述延时补偿策略所构成的闭环网络控制系统的稳定性. 通过对不同网络延时补偿的仿真实验, 证实了该补偿算法能有效改善控制系统性能并保持系统的稳定.     

DIGITAL PID CONTROLLER DESIGN FOR DELAYED MULTIVARIABLE SYSTEMS

A new methodology is proposed to design digital PID controllers for multivariable systems with time delays. Except for a few parameters that are preliminarily selected, most of the PID parameters are systematically tuned using the developed plant state‐feedback and controller state‐feedforward LQR approach, such that satisfactory performance with guaranteed closed‐loop stability is achieved. In order to deal with the modeling error owing to the delay time rational approximation, an IMC structure is utilized, such that robust stability is achieved, without need for an observer, and with improved online tuning convenience. Using the prediction‐based digital redesign method, the digital implementation is obtained based on the above‐proposed analog controller, such that the resulting mixed‐signal system performance will closely match that of the analog controlled system. An illustrative example is given for comparison with alternative techniques.     

一类不确定Lurie时滞奇异系统的鲁棒H∞控制

研究一类具有不确定性的Lurie时滞奇异系统的鲁棒稳定性分析和H∞状态反馈控 制器设计方法.针对一类具有参数不确定性、未知时滞的奇异系统,得出了系统鲁棒稳定和 鲁棒H∞状态反馈控制器存在的充分条件,它能使得不确定Lurie时滞奇异系统的解在所容 许的范围内是正则的、无摄动的和稳定的;而且还得出了基于线性矩阵不等式(LMI)的鲁棒 H∞状态反馈控制器的设计方法,使得闭环系统具有鲁棒稳定性和H∞性能.     

Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method.     

无模型SISO时滞系统的PID参数稳定域研究

针对无精确模型的单输入单输出(SISO)时滞系统, 利用频率响应数据, 给出确定PID参数稳定域的解析方法. 首先通过继电反馈频域辨识法得到系统的频率响应数据, 然后基于该数据确定控制参数的奇异边界线和非奇异边界线, 并判断边界线的哪一侧具有更少的不稳定极点, 从而给出能使闭环系统稳定的控制参数区域. 该方法避免了模型辨识的复杂计算过程, 为无模型SISO时滞系统的PID控制器设计和调节提供了一条简单有效的途径. 仿真结果验证了方法的有效性.     

Low-Order Stabilization of LTI Systems With Time Delay

This paper considers the problem of stabilizing a single-input-single-output (SISO) linear time-invariant (LTI) plant with known time delay using a low-order controller, such as a Proportional (P), a Proportional-Integral (PI), or a proportional-integral-derivative (PID) controller. For the SISO LTI system with time delay, the closed-loop characteristic function is a quasipolynomial that possesses the following features: all its infinite roots are located on the left of certain vertical line of the complex plane, and the number of its unstable roots is finite. Necessary and sufficient conditions for the stability of LTI systems with time delay are first presented by employing an extended Hermite-Biehler Theorem applicable to quasi-polynomials. Based on the conditions, analytical algorithms are then proposed to compute the stabilizing sets of P, PI and PID controllers. The resulting characterizations of the stabilizing sets for P, PI and PID controllers are analogous to the Youla parameterization of all stabilizing controllers for plants without time delay. Numerical examples are provided to illustrate the proposed algorithm.     

Robust admissibility of time-varying singular systems with commensurate time delays

This paper addresses the problem of admissibility of time-varying singular systems with commensurate time delays. By introducing a new method to study the convergence of the fast sub-system, an admissibility condition is obtained in terms of linear matrix inequalities, which guarantees the considered time-varying singular delay system to be regular, impulse free and stable. Furthermore, a robust admissibility condition is proposed for the case when the time-varying system matrices admit the usual constant-plus-norm-bounded structure. It is theoretically established that the proposed robust admissibility condition is less conservative than the existing one in the literature. One of the important features of the results is that the inferred admissibility condition coincides with the usual stability condition for state-space delay systems. Moreover, the results are also applicable to the multiple rational delay case.     

Stabilization of remote control systems with unknown time varying delays by LMI techniques

In this paper, the stabilization of one class of remote control systems with unknown time varying delays is analysed and discussed using LMI techniques. A discrete time state space model under a static control law for remote control systems is first introduced based on some assumptions on the uncertain term. The time delay is unknown, time varying, and can be decomposed into two parts: one fixed part which is unknown and is an integer multiple of the sampling time; the other part which is randomly varying but bounded by one sampling time. Static controller designs based on delay dependent stability conditions are presented. This system is then extended to a more general case when the randomly varying part of the time delay is not limited to one sampling time. The derivative of the time delay is not limited to be bounded. Hence, the contributions are as follow: (i) for a given controller, we can use these stability criteria to test stability of the resulted system; (ii) we can design a remote controller to stabilize an unstable system. Finally, simulation examples are presented to show the effectiveness of the proposed method and to demonstrate remote stabilization of open loop unstable systems.     

STATE‐SPACE DIGITAL PID CONTROLLER DESIGN FOR MULTIVARIABLE ANALOG SYSTEMS WITH MULTIPLE TIME DELAYS

This paper presents a discrete‐time state‐space methodology for optimal design of digital PID controllers for multivariable analog systems with multiple time delays. The multiple time‐delayed multivariable analog systems are formulated in a state‐space generic form so that the exact discrete‐time state‐space model can be constructed. Then, the optimal digital PID controller is designed via a state‐feedback and state‐feedforward LQR approach. The developed PID controller can be applied to a general time‐delayed multivariable analog system represented by a semi‐proper or strictly proper transfer function matrix. Illustrative examples are given to compare the performance of the proposed approach with alternative techniques.     

Observer-based adaptive fuzzy control for a class of nonlinear time-delay systems

An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy control method based on the observed states. Both the designed observer and controller are independent of time delays. Using an appropriate Lyapunov-Krasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.     

基于通用学习网络的预估控制

利用通用学习网络具有所有节点互连，任意两节点之间可以有多重连接，且连接允许有任意延迟时间的特点，对典型非线性、大滞后系统进行了辨识．结合PID控制器对pH中和过程实现了高精度的预估控制．通过与传统的Smith预估控制的比较，证明该网络能有效地应用于大滞后系统，利用该网络进行系统辨识是对未知对象模型控制的一种有效新方法．     

Reliable control for a class of uncertain singular systems with interval time‐varying delay

This paper is concerned with the reliable controller design problem for a class of singular systems with interval time‐varying delay and norm‐bounded uncertainties. A more practical model of actuator failures than outages is considered. First, by constructing a novel Lyapunov–Krasovskii functional combined with Finsler's Lemma, an improved delay‐range‐dependent stability criterion for the nominal unforced singular time‐delay system is established in terms of linear matrix inequality (LMI). Then, based on this criterion, an LMI condition for the design of a reliable state feedback controller is presented such that, for all parameter uncertainties and actuator failures, the resultant closed‐loop system is regular, impulse‐free and stable. Numerical examples are proposed to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust model predictive control of discrete nonlinear systems with time delays and disturbances via T–S fuzzy approach

In this paper, robust fuzzy model predictive control of a class of nonlinear discrete systems subjected to time delays and persistent disturbances is investigated. Based on the modeling method of delay difference inclusions, nonlinear discrete time-delay systems can be represented by T–S fuzzy systems comprised of piecewise linear delay difference equations. Moreover, Lyapunov–Razumikhin function (LRF), instead of Lyapunov–Krasovskii functional (LKF), is employed for time-delay systems due to its ability to reflect system original state space and its advantages in controller synthesis and computation. The robust positive invariance and input-to-state stability with respect to disturbance under such circumstances are investigated. A robust constraint set is adopted that the system state is converged to this set round the desired point. In addition, the controller synthesis conditions are derived by solving a set of matrix inequalities. Simulation results show that the proposed approach can be successfully applied to the well-known continuous stirred tank reactor (CSTR) systems subjected to time delay.     

Robust stabilization for discrete‐time nonlinear singular systems with mixed time delays

This paper investigates the robust stability of discrete‐time singular systems involving nonlinear disturbance and mixed time delays. The mixed time delays are comprised of both discrete and distributed delays. The interval of discrete time delays can be divided into several subintervals, firstly. Then, in terms of linear matrix inequality (LMI), a suitable state feedback controller is designed for discrete‐time singular systems with nonlinear disturbance and mixed time delays, and the overall closed‐loop system is regular, causal and mean square asymptotically stable. Numerical examples are provided to show the usefulness and effectiveness of the proposed methods, and the results derived from our approaches are less conservative than existing ones. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society