Adaptive robust control of uncertain time delay systems

The problem of adaptive robust control for uncertain linear systems with multiple delays occurring in the state variables is studied in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds of the uncertainties are not necessarily known. An adaptive controller is developed based on linear matrix inequality technique and it is shown that the controller can guarantee the state variables of the closed loop system to converge, globally, uniformly and exponentially, to a ball in the state space with any pre-specified convergence rate. The effectiveness of our approach has been verified by its application in the control of river pollution process for the purpose of preserving standards of water constituents in streams.     

Abstractions of Hamiltonian control systems

Given a control system and a desired property, an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail. In previous work, abstractions of linear and nonlinear control systems were considered while preserving reachability properties. In this paper, we consider the abstraction problem for Hamiltonian control systems, where, in addition to the property of interest we also preserve the Hamiltonian structure of the control system. We show how the Hamiltonian structure of control systems can be exploited to simplify the abstraction process. We then focus on local accessibility preserving abstractions, and provide conditions under which local accessibility properties of the abstracted Hamiltonian system are equivalent to the local accessibility properties of the original Hamiltonian control system.     

An optimal control method for linear systems with time delay

An optimal control method for linear systems with time delay is developed in this paper. In the proposed control method, the differential equation with time delay of the system dynamics is first rewritten into a form without any time delay through a particular transformation. Then, the optimal controller is designed by using the classical optimal control theory. A numerical algorithm for control implementation is presented, since the obtained expression of the optimal controller contains an integral term that is not convenient for online calculation. The time delay is considered at the very beginning of the control design, and no approximation and estimation are made in the control system. Thus the system performance and stability are prone to be guaranteed. Instability in responses might occur only if a system with time delay is controlled by the optimal controller that was designed with no consideration of time delay. The effectiveness of the proposed optimal controller is demonstrated by simulation studies.     

PI stabilization of first-order systems with time delay

This paper considers the problem of stabilizing a first-order plant with dead time using a PI controller. Using a version of the Hermite–Biehler Theorem applicable to quasipolynomials, a complete and constructive characterization of all stabilizing PI gain values is obtained.     

Enhanced design of cascade control systems for unstable processes with time delay

In this paper, optimal H₂ internal model controller (IMC) is designed for control of unstable cascade processes with time delays. The proposed control structure consists of two controllers in which inner loop controller (secondary controller) is designed using IMC principles. The primary controller (master controller) is designed as a proportional-integral-derivative (PID) in series with a lead-lag filter based on IMC scheme using optimal H₂ minimisation. Selection of tuning parameter is important in any IMC based design and in the present work, maximum sensitivity is used for systematic selection of the primary loop tuning parameter. Simulation studies have been carried out on various unstable cascade processes. The present method provides significant improvement when compared to the recently reported methods in the literature particularly for disturbance rejection. The present method also provides robust closed loop performances for large uncertainties in the process parameters. Quantitative comparison has been carried out by considering integral of absolute error (IAE) and total variation (TV) as performance indices.     

All stabilizing PID controllers for time delay systems

This paper presents a method to compute the entire set of stabilizing PID controller parameters for an arbitrary (including unstable) linear time delay system. The main contribution is to handle the infinite number of stability boundaries in the (k_d,k_i)-plane for a fixed proportional gain k_p. For retarded open loops, it is shown that the stable region in the (k_d,k_i)-plane consists of convex polygons. Concerning neutral loops, a new phenomenon is introduced. For certain systems and certain k_p, the exact stable region in the (k_d,k_i)-plane can be described by the limit of a sequence of polygons with an infinite number of vertices. This sequence may be well approximated by convex polygons. Moreover, the paper describes a necessary condition for k_p-intervals potentially having a stable region in the (k_d,k_i)-plane. Thus, the set of stabilizing controller parameters can be calculated after gridding k_p in these intervals. A Matlab tool implementing the presented method is available.     

Robust integral sliding mode control for uncertain stochastic systems with time-varying delay

This paper is concerned with sliding mode control for uncertain stochastic systems with time-varying delay. Both time-varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system. An integral sliding surface is first constructed. Then, by means of linear matrix inequalities (LMIs), a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a simulation example is presented to illustrate the proposed method.     

Robust reliable control of switched uncertain systems with time-varying delay

This paper is concerned with reliable control problems for the switched uncertain systems with time varying delay. A method for designing robust reliable controller is presented by means of the multiple Lyapunov functions technique so that the energy-like functional does not have to decrease along the switching instants. The proposed controller is reliable in that it can guarantee the closed loop asymptotic stablility of switched delay systems in the case of the possible presence of failures of partial actuators. Delay independent results of the reliable controller design are presented in terms of Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the applicability of the proposed results.     

Observer-based event-triggered containment control of multi-agent systems with time delay

This paper studies the containment control of general linear multi-agent systems with or without time delay. The observer-based event-triggered control schemes will be considered. For the conventional distributed containment control protocol, we will not update the relative state continuously, i.e. the relative state will be updated by some events which happen intermittently. A completely decentralised event trigger will be designed for leader–follower systems. Under the proposed protocol, if we design some appropriate feedback gain matrices, all followers will asymptotically converge to the convex hull spanned by the dynamic leaders. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

Energy-based control for hybrid port-controlled Hamiltonian systems

In this paper we develop an energy-based hybrid control framework for hybrid port-controlled Hamiltonian systems. In particular, we obtain constructive sufficient conditions for hybrid feedback stabilization that provide a shaped energy function for the closed-loop system, while preserving a hybrid Hamiltonian structure at the closed-loop level. Furthermore, an inverse optimal hybrid feedback control framework is developed that characterizes a class of globally stabilizing energy-based controllers that guarantee hybrid sector and gain margins to multiplicative input uncertainty of hybrid Hamiltonian systems.     

Robust model predictive control of integrating time delay processes

This work focuses on the solution to the problem of model predictive control of time delay processes with both integrating and stable modes and model uncertainty. The controller is developed for the practical case of zone control and input target tracking. The method is based on a state-space model that is equivalent to the analytical form of the step response model corresponding to the system transfer function. Here, this model is extended to the time delay system. The proposed controller is evaluated through simulation of the of two control reactor systems and the results confirms the robustness of the proposed approach.     

时滞的不确定奇异摄动系统鲁棒稳定性研究

研究了带离散时滞和分布时滞的不确定奇异摄动系统的鲁棒稳定问题.首先采用广义系统模型方法,将所研究的系统转化为与之等价的广义系统;然后提出对应的Lyapunov-Krasovskii泛函,得到了时滞相关的鲁棒稳定性判据,并在此基础上给出了鲁棒控制器设计,结论以矩阵不等式形式给出;最后仿真算例说明了方法的有效性.     

Robust controller design of a class of nonlinear time delay systems via backstepping method

The robust control problem is investigated for nonlinear time delay systems with triangular structure. The uncertain delay disturbances are bounded by nonlinear functions with unknown coefficients. Via the backstepping method, we construct a state feedback controller with the help of Razumikhin lemma. Based on Lyapunov stability theory, we show that the resulting closed-loop system is UUB stable.     

Inverted decoupling internal model control for square stable multivariable time delay systems

This paper presents a new tuning methodology of the main controller of an internal model control structure for n × n stable multivariable processes with multiple time delays based on the centralized inverted decoupling structure. Independently of the system size, very simple general expressions for the controller elements are obtained. The realizability conditions are provided and the specification of the closed-loop requirements is explained. A diagonal filter is added to the proposed control structure in order to improve the disturbance rejection without modifying the nominal set-point response. The effectiveness of the method is illustrated through different simulation examples in comparison with other works.     

不确定时滞的无线网络控制系统的故障检测

研究了一类具有不确定时滞的无线网络控制系统的故障检测的问题。由于时滞是不确定的,可以通过增广向量法将系统建模为马尔科夫跳变系统。在此基础上,设计了观测滤波器,满足了滤波器在没有扰动的情况下均方指数稳定,在有扰动时,满足一定的H∞鲁棒性能。当系统发生故障时,故障检测系统立即检测出故障。所得结果通过仿真示例得到了验证。     

Exponential stabilization controller design for interconnected time delay systems

Decentralized robust control problem is investigated for a class of large scale systems with time varying delays. The considered systems have mismatches in time delay functions. A state coordinate transformation is first employed to change the original system into a cascade system. Then the virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem. By choosing new Lyapunov Krasovskii functional, we show that the designed decentralized continuous adaptive controller makes the solutions of the closed-loop system exponentially convergent to a ball, which can be rendered arbitrary small by adjusting design parameters. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed design techniques.     

Decentralized adaptive tracking control of nonaffine nonlinear large-scale systems with time delays

This paper addresses the problem of decentralized tracking control of large-scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time-varying delays. Based on Lyapunov-Krasovskii functional approach and implicit function theorem, a delay-independent decentralized tracking controller is proposed. Due to functional approximation capability of fuzzy logic systems (FLS), neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time-varying delays is required in our control design. Furthermore, transient performance of the resulting closed-loop system is also addressed under an analytical framework. Finally, two numerical examples are provided to show the effectiveness of the proposed controller.     

Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete‐time repetitive controller design for time‐delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time‐delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed‐loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low‐pass filter are required to be chosen. The closed‐loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Remarks on strong observability and detectability of linear time delay systems with disturbances

The problems of observability and detectability for linear time delay systems with (unknown) disturbances are considered. It is shown that the problems can be studied with the aid of an auxiliary time delay system without disturbances. In this way, results characterizing the concepts (introduced in the paper) of strong observability, strong final observability and strong delectability are given.