Designing Discrete Predictor-Based Controllers for Networked Control Systems with Time-varying Delays: Application to A Visual Servo Inverted Pendulum System

A discrete predictor-based control method is developed for a class of linear time-invariant networked control systems with a sensor-to-controller time-varying delay and a controller-to-actuator uncertain constant delay, which can be potentially applied to vision-based control systems. The control scheme is composed of a state prediction and a discrete predictor-based controller. The state prediction is used to compensate for the effect of the sensor-to-controller delay, and the system can be stabilized by the discrete predictor-based controller. Moreover, it is shown that the control scheme is also robust with respect to slight message rejections. Finally, the main theoretical results are illustrated by simulation results and experimental results based on a networked visual servo inverted pendulum system.      

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

The problem of output stabilization and disturbance rejection for input‐delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov‐Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed‐loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.     

Predictor-based stabilisation for discrete nonlinear systems with state-dependent input delays

We consider predictor-based stabilisation for discrete nonlinear systems with state-dependent input delays. The key design is how to determine the prediction horizon and the predictor state. Sufficient conditions for stabilisation of the closed-loop system are obtained. An explicit feedback law is presented for compensating state-dependent input delay. Since input delay is dependent on state, a region of attraction is estimated for the closed-loop system. The proposed predictor-based design can be applied in controlling the yaw angular displacement of a four-rotor mini-helicopter.     

Modified Smith predictor with a robust disturbance reduction scheme for linear systems with small time delays

This paper presents a robust disturbance reduction scheme using an artificial neural network (ANN) for linear systems with small time delays. It is assumed that the nominal linear systems are stable, minimum phase and relative degree one systems. The proposed structure is an integration of a modified Smith predictor and an ANN‐based disturbance reduction scheme. Unlike other disturbance rejection methods, the proposed approach does not require information about unknown load disturbance frequencies. An ANN is used to approximate the unknown load disturbances and to enhance the robustness of the proposed disturbance reduction scheme against modelling errors in the estimated time delay and the process model. Connective weights of the ANN are trained on‐line using a back‐propagation algorithm until uncertainties resulting from unknown load disturbances and modelling errors are minimized. The simulation results show the effectiveness of the presented disturbance reduction scheme for controlling linear delay systems subjected to step or periodic unknown load disturbances.     

Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch

We consider LTI finite-dimensional, completely controllable, but possibly open-loop unstable, plants, with arbitrarily long actuator delay, and the corresponding predictor-based feedback for delay compensation. We study the problem of inverse-optimal re-design of the predictor-based feedback law. We obtain a simple modification of the basic predictor-based controller, which employs a low-pass filter, and has been proposed previously by Mondie and Michiels for achieving robustness to discretization of the integral term in the predictor feedback law. The key element in our work is the employment of an infinite-dimensional “backstepping” transformation, and the resulting Lyapunov function, for the infinite dimensional systems consisting of the state of the ODE plant and the delay state. The Lyapunov function allows us to quantify the Lyapunov stability properties under the modified feedback, the inverse optimality of the feedback, and its disturbance attenuation properties. For the basic predictor feedback, the availability of the Lyapunov function also allows us to prove robustness to small delay mismatch (in both positive and negative directions).     

Computation delay compensation for real time implementation of robust model predictive control

The implementation of model predictive control (MPC) requires to solve an optimization problem online. The computation time, often not negligible especially for nonlinear MPC (NMPC), introduces a delay in the feedback loop. Moreover, it impedes fast sampling rate setting for the controller to react to uncertainties quickly. In this paper, a dual time scale control scheme is proposed for linear/nonlinear systems with external disturbances. A pre-compensator works at fast sampling rate to suppress uncertainty, while the outer MPC controller updates the open loop input sequence at a slower rate. The computation delay is explicitly considered and compensated in the MPC design. Four robust MPC algorithms for linear/nonlinear systems in the literature are adopted and tailored for the proposed control scheme. The recursive feasibility and stability are rigorously analysed. Three simulation examples are provided to validate the proposed approaches.     

Disturbance‐prediction–based control of input time delay systems for rejection of unknown frequency disturbances

In this paper, a novel disturbance rejection approach is presented for a class of input time‐delay systems subject to sinusoidal disturbances with unknown frequency. In particular, an auxiliary observer is proposed to represent the periodic disturbance in a parametric uncertainty form, where the unknown factor related to disturbance frequency can be estimated. Furthermore, the correlation between the future disturbance and the auxiliary observer output is analyzed, such that the future disturbances can be predicted and rejected through the input channel. Based on the aforementioned observer and predictor structure, the overall control architecture can be established as a framework of disturbance‐prediction–based control for systems with input time delays, where the conditions on the asymptotic stability of the closed‐loop systems are also derived. Finally, numerical examples are provided to illustrate the effectiveness of the proposed control approach.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

具有输入饱和的近空间飞行器鲁棒控制

针对近空间飞行器这一类存在外部扰动,输入饱和和参数不确定的多输入多输出线性系统,提出了一种基于干扰观测器的抗饱和鲁棒控制方案.将干扰观测器与抗饱和控制技术相结合,从而消除系统存在的未知外部扰动、输入饱和和不确定性对系统控制的影响.首先,设计干扰观测器对线性外部系统产生的未知扰动进行估计.然后根据干扰观测器输出,通过超前抗饱和方法设计抗饱和补偿器,并将其加入到鲁棒控制器的设计中,保证闭环系统存在输入饱和、未知外部扰动和参数不确定情况下的稳定性.为便于设计,干扰观测器、抗饱和补偿器和控制器设计矩阵均通过求解线性矩阵不等式得到.最后,将提出的鲁棒抗饱和控制方法应用于近空间飞行器,仿真结果验证了该控制方案的有效性.     

Robust predictor feedback for discrete-time systems with input delays

This work studies the design problem of feedback stabilisers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping coincides with the predictor-based feedback law used in continuous-time systems with input delays. However, simple examples demonstrate that the sensitivity of the closed-loop system with respect to modelling errors increases as the value of the delay increases. The paper proposes a Lyapunov redesign procedure that can minimise the effect of the uncertainty. Specific results are provided for linear single-input discrete-time systems with multiplicative uncertainty. The feedback law that guarantees robust global exponential stability is a nonlinear, homogeneous of degree 1 feedback law.     

Pseudo-Predictor Feedback Control for Multiagent Systems with Both State and Input Delays

This paper is concerned with the consensus problem for high-order continuous-time multiagent systems with both state and input delays. A novel approach referred to as pseudo-predictor feedback protocol is proposed. Unlike the predictor-based feedback protocol which utilizes the open-loop dynamics to predict the future states, the pseudo-predictor feedback protocol uses the closed-loop dynamics of the multiagent systems to predict the future agent states. Full-order/reduced-order observer-based pseudo-predictor feedback protocols are proposed, and it is shown that the consensus is achieved and the input delay is compensated by the proposed protocols. Necessary and sufficient conditions guaranteeing the stability of the integral delay systems are provided in terms of the stability of the series of retarded-type time-delay systems. Furthermore, compared with the existing predictor-based protocols, the proposed pseudo-predictor feedback protocol is independent of the input signals of the neighboring agents and is easier to implement. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approaches.      

Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust stability of predictor-based control systems with delayed control

This article deals with the delay-dependent robust stability of predictor-based control systems with a delayed control and non-linear parameter perturbations. The uncertainty terms do not require the matching condition but are norm-bounded. The predictor-based controller includes a predictor to compensate for time delay. The problem treated here is to determine an allowable delay bound to ensure the robust stability of the delayed control systems under the predictor-based control. A delay bound for memoryless state feedback control systems is also derived for comparisons of their delay bounds. It is shown that the predictor-based control can maximize the allowable delay bound to a greater degree than the memoryless state feedback via an illustrative example.     

可反馈线性化系统的鲁棒自适应容错控制设计

针对存在不确定执行器故障和未知不匹配干扰的可反馈线性化非线性系统, 提出一种鲁棒自适应容错控 制策略. 首先分别给出系统输入和扰动关于系统输出的相对阶, 针对两种相对阶之间的不同关系设计鲁棒控制器, 抑制干扰对系统输出的影响; 然后针对各故障情况分别设计容错控制器; 最后将各控制器进行融合得到一个综合 故障补偿控制器, 从而有效解决故障模式、类型、大小、时间和外界干扰等多重不确定性, 保证闭环系统稳定和渐近 输出跟踪性能. 仿真结果验证了所设计控制方案的可行性与有效性.     

无线通讯网络功率和流量的预联合控制

To mitigate the loop delay in distributed wireless networks, a predictive power and rate control scheme is proposed for the system model that also accounts for the congestion levels and input delay instead of state-delayed in a network. A measurement feedback control problem with input delay is formulated by minimizing the energy of the difference between the actual and the desired signal-to-interference-plus-noise ratio (SNR) levels, as well as the energy of the control sequence. To solve this problem, we present two Riccati equations for the control and the estimation for the time delay systems. A complete analytical optimal controller is obtained by using the separation principle and solving two Riccati equations, where one is backward equation for stochastic linear quadratic regulation and the other is the standard filtering Riccati equation. Simulation results illustrate the performance of the proposed power and the rate control scheme.     

Study on the sliding mode fault tolerant predictive control based on multi agent particle swarm optimization

For a class of uncertain discrete-time systems with time varying delay, the problem of robust fault-tolerant control for such systems is studied by combining the design of sliding mode control (SMC) and model predictive control (MPC). A sliding mode fault tolerant predictive control based on multi agent particle swarm optimization (PSO) is presented, and the design, analysis and proof of the scheme are given in detail. Firstly, the sliding mode prediction model of the system is designed by assigning poles of the output error of the system. The model has time varying characteristics, and it can improve the motion quality of the system while ensuring the sliding mode is stable. Secondly, a new discrete reference trajectory considering time-delay systems subjected simultaneously to parameter perturbations and disturbances is proposed, which not only can ensure that the state of the system has good robustness and fast convergence in the process of approaching sliding mode surface, but also can inhibit chattering phenomenon. Thirdly, the multi agent PSO improves the receding-horizon optimization, which can quickly and accurately solve the control laws satisfying the input constraints, and can effectively avoid falling into local extrema problem of the traditional PSO. Finally, the theoretical proof of robust stability of the proposed control scheme is given. Experimental results of quad-rotor helicopter semi physical simulation platform show that the state of uncertain discrete-time systems with time varying delay is stable under the action of the proposed control scheme in this paper. The advantages of fast response, less overshoot and small control chattering prove the feasibility and effectiveness of the proposed control scheme.     

Nonlinear tracking and input disturbance rejection with application to pH control

This paper presents a nonlinear observer-based controller configuration for a class of nonlinear single-input single-output systems with certain observability and stability properties. Particular attention is paid to the effect of input disturbances typically present in chemical processes. It is pointed out that conventional feedback linearizing internal model controllers reject output disturbances linearly, but that they can experience significant performance degradation in the presence of input disturbances. This problem is shown to originate in the lack of the linear superposition property. It is proven that the proposed control architecture rejects constant input disturbances from the control signal and then recovers linear reference tracking. The convenient tuning and improved performance are illustrated for pH neutralization.     

Fault tolerant control with disturbance rejection and attenuation performance for systems with multiple disturbances

It is difficult to diagnose and accommodate the faults if disturbances and faults exist simultaneously in the controlled plants. In this paper, an anti‐disturbance fault tolerant control (FTC) scheme is presented for a class of nonlinear systems with both faults and multiple disturbances. The multiple disturbances are supposed to include two types including the uncertain modeled disturbances and norm bounded uncertain disturbances. A composite fault tolerant controller is constructed by integrating a fault accommodation from diagnosis observer with additional disturbance rejection and attenuation performance for two different types of disturbances. As a result, the fault can be accommodated and the multiple disturbances can be rejected and attenuated simultaneously. Simulations for a flight control system are given to show the efficiency of the proposed approach. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于等价输入干扰滑模观测器的磁悬浮球系统模型预测控制

本文针对系统不确定性和外部干扰引起的磁悬浮球系统控制性能下降的问题,提出了一种基于等价输入干扰滑模观测器的模型预测控制(MPC+EIDSMO)方法.首先将原系统转化为EID系统,采用等价输入干扰滑模观测器对EID系统状态变量及等价输入干扰进行估计;然后基于状态估计值设计模型预测控制器,并将等价输入干扰估计值以前馈的方式...     

Predictor-based control for an uncertain Euler–Lagrange system with input delay

Controlling a nonlinear system with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics. Developing a predictor-based controller for an uncertain system is especially challenging. In this paper, tracking controllers are developed for an Euler–Lagrange system with time-delayed actuation, parametric uncertainty, and additive bounded disturbances. The developed controllers represent the first input delayed controllers developed for uncertain nonlinear systems that use a predictor to compensate for the delay. The results are obtained through the development of a novel predictor-like method to address the time delay in the control input. Lyapunov–Krasovskii functionals are used within a Lyapunov-based stability analysis to prove semi-globally uniformly ultimately bounded tracking. Experimental results illustrate the performance and robustness of the developed control methods.