Approximation Optimal Vibration for Networked Nonlinear Vehicle Active Suspension with Actuator Time Delay

This paper is concerned with the modelling and vibration control problem for networked nonlinear vehicle active suspension (NNVAS) with actuator time delay. Inserting in‐vehicle communication network to active suspension, a novel model for NNVAS is established based on the Takagi‐Sugeno fuzzy fusion technology first. By introducing a transformation vector, NNVAS with actuator time delay is reformed as a delay‐free nonlinear system. Then, an approximation optimal vibration controller (AOVC) is proposed by using an iterative algorithm, which consists of suspension state item, a road disturbance state item, and a compensated item for nonlinear response. Dependant on the control performance in each iteration, the computability of proposed AOVC is realized. A reduced‐order observer is designed to solve the physical unrealizable problem of road disturbances. Finally, compared with the open‐loop system and control scheme without network setting, the capability of improving control performance under AOVC is illustrated.     

非线性互联大系统的最优控制:逐次逼近法

The optimal control problem for nonlinear interconnected large-scale dynamic systems is considered. A successive approximation approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value (TPBV) problem is transformed into a sequence of linear decoupling TPBV problems. It is proven that the TPBV problem sequence uniformly converges to the optimal control for nonlinear interconnected large-scale systems. A suboptimal control law is obtained by using a finite iterative result of the optimal control sequence.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

Teleoperation Control of a Position‐Based Impedance Force Controlled Mobile Robot by Neural Network Learning: Experimental Studies

Effective haptic performance in teleoperation control systems can be achieved by solving two major problems: the time‐delay in communication channels and the transparency of force control. The time‐delay in communication channels causes poor performance and even instability in a system. The transparency of force feedback is important for an operator to improve the performance of a given task. This article suggests a possible solution for these two problems through the implementation of a teleoperation control system between the master haptic device and the slave mobile robot. Regulation of the contact force in the slave mobile robot is achieved by introducing a position‐based impedance force control scheme in the slave robot. The time‐delay problem is addressed by forming a Smith predictor configuration in the teleoperation control environment. The configuration of the Smith predictor structure takes the time‐delay term out of the characteristic equation in order to make the system stable when the system model is given a priori. Since the Smith predictor is formulated from exact linear modeling, a neural network is employed to identify and model the slave robot system as a nonlinear model estimator. Simulation studies of several control schemes are performed. Experimental studies are conducted to verify the performance of the proposed control scheme by regulating the contact force of a mobile robot through the master haptic device.     

Dynamic anti‐windup method for a class of time‐delay control systems with input saturation

An anti‐windup‐based approach is newly attempted to deal with time‐delay control systems with input saturation. Following the anti‐windup paradigm, we assume that controllers have been designed beforehand for time‐delay control systems based on existing design techniques which will show desirable performance. Then, an additional compensator is designed to provide graceful performance degradation under control input saturation. By taking the difference of controller states in the absence and presence of input saturation as a performance index, a dynamic compensator which minimizes it is derived. The resulting anti‐windup compensator is expressed in plant and controller parameters. The proposed method not only provides graceful performance degradation, but also guarantees the stability of the overall systems. Illustrative examples are provided to show the effectiveness of the proposed method. Copyright © 2000 John Wiley & Sons, Ltd.     

非线性离散系统的近似最优跟踪控制

研究非线性离散系统的最优跟踪控制问题. 通过在由最优控制问题所导致的非线性两点边值问题中引入灵敏度参数, 并对它进行Maclaurin级数展开, 将原最优跟踪控制问题转化为一族非齐次线性两点边值问题. 得到的最优跟踪控制由解析的前馈反馈项和级数形式的补偿项组成. 解析的前馈反馈项可以由求解一个Riccati差分方程和一个矩阵差分方程得到. 级数补偿项可以由一个求解伴随向量的迭代算法近似求得. 以连续槽式反应器为例进行仿真验证了该方法的有效性．     

FPGA‐based adaptive dynamic sliding‐mode neural control for a brushless DC motor

In the adaptive neural control design, since the number of hidden neurons is finite for real‐time applications, the approximation errors introduced by the neural network cannot be inevitable. To ensure the stability of the adaptive neural control system, a switching compensator is designed to dispel the approximation error. However, it will lead to substantial chattering in the control effort. In this paper, an adaptive dynamic sliding‐mode neural control (ADSNC) system composed of a neural controller and a fuzzy compensator is proposed to tackle this problem. The neural controller, using a radial basis function neural network, is the main controller and the fuzzy compensator is designed to eliminate the approximation error introduced by the neural controller. Moreover, a proportional‐integral‐type adaptation learning algorithm is developed based on the Lyapunov function; thus not only the system stability can be guaranteed but also the convergence of the tracking error and controller parameters can speed up. Finally, the proposed ADSNC system is implemented based on a field programmable gate array chip for low‐cost and high‐performance industrial applications and is applied to control a brushless DC (BLDC) motor to show its effectiveness. The experimental results demonstrate the proposed ADSNC scheme can achieve favorable control performance without encountering chattering phenomena. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Anti‐windup design of active disturbance rejection control for sampled systems with input delay

A novel anti‐windup design of active disturbance rejection control (ADRC) is proposed for industrial sampled systems with input delay and saturation. By using a generalized predictor to estimate the delay‐free system output, a modified extended state observer is designed to simultaneously estimate the system state and disturbance, which could become an anti‐windup compensator when the input saturation occurs. Accordingly, a feedback controller is analytically designed for disturbance rejection. By proposing the desired closed‐loop transfer function for the set‐point tracking, a prefilter is designed to tune the tracking performance while guaranteeing no steady‐state output tracking error. A sufficient condition for the closed‐loop system stability is established with proof for practical application subject to the input delay variation. Illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control design.     

Design of a two‐level controller for an active suspension system

The paper focuses on a control design for a vehicle suspension system in which a balance between different performance demands is achieved. The starting point of the control design is a full–car model which contains nonlinear components, i.e. the dynamics of the dampers and springs and nonlinear actuator dynamics. In order to handle the high complexity of the problem this paper proposes the design of a two‐level controller of an active suspension system. The required control force is computed by applying a high‐level controller, which is designed using a linear parameter varying (LPV) method. For the control design the model is augmented with weighting functions specified by the performance demands and the uncertainty assumptions. The actuator generating the necessary control force is modelled as a nonlinear system for which a low‐level force‐tracking controller is designed. To obtain the low‐level controller a backstepping method is proposed. As an alternative solution a feedback linearization method is also presented. The operation of the controller is illustrated through simulation examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Design of a memory‐based prefilter supplementing a robust PID control system

For systems with uncertainties, lots of PID parameter tuning methods have been proposed from the view point of the robust stability theory. However, the control performance becomes conservative using robust PID controllers. In this paper, a new two‐degree‐of‐freedom (2DOF) controller, which can improve the tracking properties, is proposed for nonlinear systems. According to the proposed method, the prefilter is designed as the PD compensator whose control parameters are tuned by the idea of a memory‐based modeling (MBM) method. Since the MBM method is a type of local modeling methods for nonlinear systems, PD parameters can be tuned adequately in an online manner corresponding to nonlinear properties. Finally, the effectiveness of the newly proposed control scheme is numerically evaluated on a simulation example. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

This paper studies the problem of global stabilization of a family of discrete‐time feedforward time‐delay systems with bounded controls. Two classes of nonlinear control laws are established based on a special canonical form of the considered system. The proposed control laws use not only the current states but also the delayed states for feedback and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed‐loop system significantly. A practical example is given for illustration.     

Active vibration control for nonlinear vehicle suspension with actuator delay via I/O feedback linearization

The problem of nonlinear vibration control for active vehicle suspension systems with actuator delay is considered. Through feedback linearization, the open-loop nonlinearity is eliminated by the feedback nonlinear term. Based on the finite spectrum assignment, the quarter-car suspension system with actuator delay is converted into an equivalent delay-free one. The nonlinear control includes a linear feedback term, a feedforward compensator, and a control memory term, which can be derived from a Riccati equation and a Sylvester equation, so that the effects produced by the road disturbances and the actuator delay are compensated, respectively. A predictor is designed to implement the predictive state in the designed control. Moreover, a reduced-order observer is constructed to solve its physical unrealisability problem. The stability proofs for the zero dynamics and the closed-loop system are provided. Numerical simulations illustrate the effectiveness and the simplicity of the designed control.     

Observer‐Based Adaptive Output Feedback Fault Tolerant Control for Nonlinear Hydro‐Turbine Governing System with State Delay

This paper focuses on the problem of adaptive output feedback fault tolerant control for a nonlinear hydro‐turbine governing system. A dynamic mathematical model of the system is established, which aims to investigate the dynamic performance of the model under servomotor delay and actuator faults. Then, a fault estimation adaptive observer is proposed to achieve online real‐time diagnosis of system faults. Based on the online fault estimation information, an observer‐based adaptive output feedback fault tolerant controller is designed. Furthermore, under reasonable assumptions, the results demonstrate that the closed‐loop control system can achieve global asymptotic stability by Lyapunov function. Finally, the numerical simulation results are presented to indicate the satisfaction control effectiveness of the proposed scheme.     

非线性相似组合大系统最优控制的逐次逼近过程

研究一类仿射非线性相似组合大系统关于二次型性能指标的最优控制问题．首先通过模型简化,将非线性相似组合大系统化为若干个准解耦的子系统;然后利用非线性系统最优控制的逐次逼近设计方法,将求解高阶强耦合的非线性两点边值问题简化为求解一族解耦的线性两点边值问题序列．该线性两点边值问题序列的解一致收敛于非线性相似组合大系统的最优控制,得到的最优控制律由线性最优控制的解析项与非线性补偿序列的极限项组成．通过截取最优控制非线性补偿序列的有限次逼近值．得到了非线性组合大系统的次优控制律．     

Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

In this paper, a robust stabilization problem for a class of linear time‐varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time‐varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Operator‐based robust control for nonlinear plants with uncertain non‐symmetric backlash

This paper presents an operator‐based robust nonlinear control method for nonlinear plants with uncertain non‐symmetric backlash. The control design is achieved by introducing operator‐based robust right coprime factorization. In more detail, using an operator‐theoretic approach, the uncertain non‐symmetric backlash is described as a generalized Lipschitz operator and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new robust condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the uncertain backlash. As a result, based on the proposed robust condition, a stabilized plant is obtained. For eliminating the effect from the parasitic term to ensure the output tracking performance, a nonlinear tracking controller is designed. Simulation results are presented to validate the effectiveness of the proposed control design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

High‐gain nonlinear observer‐based impedance control for deformable object cooperative teleoperation with nonlinear contact model

Unmeasurable object deformation and local communication time delays between the slave robots influence the manipulation effect for multirobot multioperator teleoperation. In this article, a distributed control method based on high‐gain nonlinear observer, interactive identification, and impedance control is proposed for this problem. First, we use Hunt‐Crossley contact model and deduce the desired synchronizing object state in cooperative teleoperation. Second, an impedance item expressed by the internal position errors is presented to decrease object position tracking errors. For the unmeasurable object deformation, an interactive identification method is proposed for estimating unknown variables. Third, we consider both varying communication time delays and local time delays in the slave side. Two mirror high‐gain nonlinear observers are designed for estimating other slave robots' real‐time state. Finally, we build the system controllers and prove the stability of the closed‐loop system and the boundless of estimating errors using Lyapunov functions. Comparable simulation results executed by the physical system present that the position and internal force tracking errors of the object decrease in the designated cooperative tasks.     

Robust sampled‐data model predictive control for networked systems with time‐varying delay

In this paper, the problem of sampled‐data model predictive control (MPC) is investigated for linear networked control systems with both input delay and input saturation. The delay‐induced nonlinearity is overapproximatively modeled as a polytopic inclusion. The nonlinear behavior of input saturation is expressed as a convex polytope. The resulting closed‐loop systems are represented as linear systems with polytopic and additive norm‐bounded uncertainties. The aim is to determine a robust MPC controller that asymptotically stabilizes the uncertain system at the origin with a certain level of quadratic performance. The effectiveness of the proposed algorithm is demonstrated by a numerical example.     

Dynamic anti‐windup compensator for fractional‐order system with time‐delay

This paper describes the results of introducing an additional dynamic element to an anti‐windup compensator from control quality and stability area anslysis viewpoint. The analyzed system consists of a first‐order plant with time delay and a fractional‐order PI controller, to present the discussed approach. The controller is tuned based on Hermite‐Biehler and Pontryagin theorems. In the paper, the stability analysis and tracking performance are presented based on both simulation and experimental results. The experiments have been performed using Inteco Modular Servo System with performance evaluated on the basis of the selected performance criterion, namely the Integral of Absolute Error, to verify the applicability of the proposed method. The results have proven that use of the additional dynamic element provides a wider range of controller parameters to ensure stability of the closed‐loop system and better tracking performance in comparison to the system without anti‐windup compensation or system with a standard anti‐windup compensator. It is actually the first time that this type of analysis for dynamic element compensation in anti‐windup framework has been presented for fractional‐order systems. In addition, all the obtained results are referred to the experimental data.     

Optimal disturbance rejection control for singularly perturbed composite systems with time‐delay

The optimal control problem for a class of singularly perturbed time‐delay composite systems affected by external disturbances is investigated. The system is decomposed into a fast linear subsystem and a slow time‐delay subsystem with disturbances. For the slow subsystem, the feedforward compensation technique is proposed to reject the disturbances, and the successive approximation approach (SAA) is applied to decompose it into decoupled subsystems and solve the two‐point boundary value (TPBV) problem. By combining with the optimal control law of the fast subsystem, the feedforward and feedback composite control (FFCC) law of the original composite system is obtained. The FFCC law consists of analytic state feedback and feedforward terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. Simulation results are employed to test the validity of the proposed design algorithm. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society