A fuzzy decentralized variable structure tracking control with optimal and improved robustness designs: theory and applications

To begin with, each subsystem of a nonlinear interconnected system was approximated by a weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the mth subsystem, a dead-beat to its switching surface was first designed. The output disturbance of the mth LPTFS included the interconnections coming from the other subsystems, the approximation error of the mth subsystem, and the interactions resulting from the other LPTFSs. In general, this output disturbance was not small and contains various frequencies. Under this circumstances, the H/sup /spl infin//-norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized. In addition, an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance. Although the effect of the output disturbance is attenuated and partially rejected, a better performance could be enhanced by a switching control based on the Lyapunov redesign. In addition, the stability of the overall system was verified by Lyapunov stability theory. The simulations for the LPTFSs with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control. Finally, the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control.     

一类非线性系统的积分变结构模糊自适应跟踪控制

针对一类具有未知常数控制增益的不确定非线性系统,基于变结构控制原理,并利用具有非线性可调参数的模糊系统逼近等价控制,提出一种具有监督控制器的积分变结构模糊自适应跟踪控制策略.该策略通过监督控制器保证闭环系统所有信号有界.进一步,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响.理论分析证明了跟踪误差能够收敛到零.仿真结果表明了该方法的有效性.     

Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach

The output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied. Our approach is based on the Takagi-Sugeno (T-S) fuzzy modeling method and a variable structure control (VSC) technique. Therefore, the systems considered are not and need not be in the triangular and parametric strict-feedback form, which are prevalent among adaptive model following control for nonlinear systems, or in the normal form, which pervades almost all existing results in neuro-fuzzy model following control approach. We first study the problem of stabilization of T-S fuzzy systems by using a VSC technique. A method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed. Then, the method is extended to design controllers for output tracking of T-S fuzzy nonlinear systems in two cases, i.e. systems which possess the so-called strong passive subsystems and strong stable zero dynamics, respectively. Finally, illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers. Simulation results show that the goal of output tracking can be achieved by the proposed controllers.     

A data-driven controller for position tracking of a long-stroke piezoelectric actuator

Microsystem Technologies - Hysteresis and other nonlinearities exhibited by piezoelectric materials significantly limit the tracking capability of piezoelectric actuators (PAs). To eliminate these...     

Self-learning active vibration control of a flexible plate structure with piezoelectric actuator

In this paper, an active vibration control (AVC) incorporating active piezoelectric actuator and self-learning control for a flexible plate structure is presented. The flexible plate system is first modelled and simulated via a finite difference (FD) method. Then, the validity of the obtained model is investigated by comparing the plate natural frequencies predicted by the model with the reported values obtained from literature. After validating the model, a proportional or P-type iterative learning (IL) algorithm combined with a feedback controller is applied to the plate dynamics via the FD simulation platform. The algorithms were then coded in MATLAB to evaluate the performance of the control system. An optimized value of the learning parameter and an appropriate stopping criterion for the IL algorithm were also proposed. Different types of disturbances were employed to excite the plate system at different excitation points and the controller ability to attenuate the vibration of observation point was investigated. The simulation results clearly demonstrate an effective vibration suppression capability that can be achieved using piezoelectric actuator with the incorporated self-learning feedback controller.     

压电式精密驱动器及其闭环控制系统设计

提出了一种以压电叠堆作为驱动源的新型步进直线精密驱动器,设计了直线驱动器的整体结构,分析了直线驱动器的工作原理。制作了直线驱动器样机并进行试验测试,试验结果表明:步距与电压间具有良好的线性关系,但驱动器存在步距误差。采用PCI—6229NI数据采集卡,使用LabVIEW软件设计了驱动器闭环反馈控制系统,对比试验结果表明:驱动器定位精度显著提高,可达到0.06μm。     

Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi–Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T–S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T–S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

A robust adaptive fuzzy variable structure tracking control for the wheeled mobile robot: Simulation and experimental results

In this paper an adaptive fuzzy variable structure control (kinematic control) integrated with a proportional plus derivative control (dynamic control) is proposed as a robust solution to the trajectory tracking control problem for a differential wheeled mobile robot. The variable structure controller, based on the sliding mode theory, is a well known, proven control method, fit to deal with uncertainties and disturbances (e.g., structural and parameter uncertainties, external disturbances and operating limitations). To minimize the problems found in practical implementations of the classical variable structure controllers, an adaptive fuzzy logic controller replaces the discontinuous portion of the control signals (avoiding the chattering), causing the loss of invariance, but still ensuring the robustness to uncertainties and disturbances without having any a priori knowledge of their boundaries. Moreover, the adaptive fuzzy logic controller is a feasible tool to approximate any real continuous nonlinear system to arbitrary accuracy, and has a simple structure by using triangular membership functions, a low number of rules that must be evaluated, resulting in a lower computational load for execution, making it feasible for real time implementation. Stability analysis and the convergence of tracking errors as well as the adaptation laws are guaranteed with basis on the Lyapunov theory. Simulation and experimental results are explored to show the verification and validation of the proposed control strategy.     

Intelligent tracking control for robot manipulator including actuator dynamics via TSK-type fuzzy neural network

In this paper, a Takagi-Sugeno-Kang-type fuzzy-neural-network control (T-FNNC) scheme is constructed for an n-link robot manipulator to achieve high-precision position tracking. According to the concepts of mechanical geometry and motion dynamics, the dynamic model of an n-link robot manipulator including actuator dynamics is introduced initially. However, it is difficult to design a suitable model-based control scheme due to the uncertainties in practical applications, such as friction forces, external disturbances and parameter variations. In order to cope with this problem, a T-FNNC system without the requirement of prior system information and auxiliary control design is investigated to the joint position control of an n-link robot manipulator for periodic motion. In this model-free control scheme, a five-layer fuzzy-neural-network is utilized for the major control role, and the adaptive tuning laws of network parameters are established in the sense of projection algorithm and Lyapunov stability theorem to ensure the network convergence as well as stable control performance. In addition, experimental results of a two-link robot manipulator actuated by dc servomotors are provided to verify the effectiveness and robustness of the proposed T-FNNC methodology.     

Decentralized variable structure control design for a two-pendulum system

This note presents a decentralized variable structure control design for a nonlinear state model of two coupled pendulums. This was motivated by the swing equation model of a two-machine power system whose behavior is similar. The control objective is to drive the pendulum motion from one equilibrium point to another.     

Adaptive impedance control of a variable stiffness actuator

This paper proposes an optimal impedance control method for a variable stiffness actuator (VSA), in which a variable stiffness mechanism and an actuator are aligned in series. First, we introduce a circuit expression of the robotic system and provide a unified framework to determine an optimal index of robots driven by VSAs, irrespective of the presence or absence of the environment. Next, we design a torque controller for a one-degree-of-freedom (DOF) robot and find the optimal condition of the stiffness in the VSA for a given task. Then, we design a stiffness control law for the VSA exploiting the intrinsic indivisible property between motion and passive impedance. This stiffness control law adaptively tunes the passive stiffness to minimize the energy consumption without defining any explicit desired impedance, which is usually required in impedance controllers. The stability of the closed loop system is proved using Lyapunov’s analysis. Simulations and experimental results validate the effectiveness of the proposed method and the robustness in response to parameter changes.     

Optimal boundary control of a tracking problem for a parabolic distributed parameter system

A comparative study is made of five methods for calculating the optimal control function for a linear parabolic tracking problem with boundary control. Questions of computational instability, numerical accuracy and economic computer usage are investigated. Open-loop methods based upon the variational equations are shown to have the advantages of efficiency, accuracy and ease of programming. Methods based on the method of lines and the Riccati equation are shown to be less straightforward in use. The fourth-order explicit Runge-Kutta algorithm has little scope for application because of its restricted stability range. The Kalman-Englar algorithm is much more robust but a Crank-Nicholson algorithm for the associated auxiliary equation is not very satisfactory in some cases. The auxiliary variable method may then confer some benefits.     

Optimal tracking design for stochastic fuzzy systems

In general, fuzzy control design for stochastic nonlinear systems is still difficult since the fuzzy bases are stochastic so as to increase the difficulty and complexity of the fuzzy tracking control design. In this study, a fuzzy stochastic moving-average model with control input (fuzzy ARMAX model) is introduced to describe nonlinear stochastic systems. From the fuzzy ARMAX model, a fuzzy one-step ahead prediction model is developed. Based on a fuzzy one-step ahead prediction stochastic model, optimal design algorithms are proposed to achieve the optimal tracking of nonlinear stochastic systems. In this study, the minimum variance tracking control, generalized minimum variance tracking control, and the optimal model reference tracking control are developed for stochastic fuzzy systems. We construct some basic stability conditions for general stochastic fuzzy systems and use these conditions to verify the stability of the fuzzy tracking control systems. Finally, two simulation examples are given to indicate the performance of the proposed methods.     

基于图像的双臂模糊自适应轨迹跟踪控制

在固定相机的监视下,随机位姿的目标物体在双臂系统的控制下执行轨迹跟踪控制任务时,既要考虑目标随机位姿引起的运动学和动力学不确定性问题,还要考虑运动学和动力学的协同问题.针对上述问题,分别采用自适应方法估计目标质心和特征点的位置信息,利用模糊逻辑系统逼近系统的动力学模型,使用分散控制策略处理双臂的协同问题,最后基于位置/力混合控制方法设计基于图像的双臂模糊自适应轨迹跟踪控制器,并采用李亚普诺夫方法证明系统的稳定性.仿真实验验证了所设计控制器的有效性.     

Necessary and sufficient conditions for robust perfect tracking under variable structure control

The tracking control of linear MIMO systems with structured uncertainty is considered. A necessary and sufficient condition for robust asymptotic tracking employing variable structure techniques in the presence of multiplicative uncertainty is derived. The constructive proof of the theorem provides an explicit formula for controller synthesis. Copyright © 2002 John Wiley & Sons, Ltd.     

Output tracking control of nonlinear switched cascade systems using a variable structure control method

This article is concerned with the output tracking control problem for a class of nonlinear switched cascade systems under some average dwell-time-based switching laws. Firstly, stabilisation problem of this class of switched systems is considered. Then, the result is extended to the output tracking control problem. Based on the variable structure control technique and the characteristic of the system, the variable structure controllers and the average dwell-time are designed. The effectiveness of the proposed design approach is illustrated with simulation results.     

聚焦式模糊变结构控制及其在主汽温控制中的应用

针对具有纯滞后、大惯性、参数漂移大的非线性复杂系统,本文提出一种聚焦式模糊变结构控制算法,使系统在多种干扰下具有较强鲁棒性的同时,具有较快的响应速度．控制器采用偏差e、偏差变化速率de/dt和偏差累积∫edt作为输入信号,利用聚焦式量化算法对这3个输入论域进行离散化,模糊化后采用模糊变结构算法对三维输入进行二维的模糊推理,大大简化了模糊推理的过程．仿真结果表明:新算法具有很好的动态品质,可以有效地消除系统的稳态误差．该算法在广东某电厂2#机组锅炉的汽温控制系统中得到成功的应用,其控制效果良好．     

pH值系统变论域模糊控制器的设计及性能分析

针对pH值非线性控制系统,设计了一种实时简化变论域模糊控制器.将变论域思想与实时模糊推理策略相结合:一方面论域随着误差的减小而收缩,而论域的收缩相当于控制规则的增加,从而增加了控制精度;另一方面采用实时模糊推理方法,即对于一个二入一出的模糊控制器,一次推理过程中最多只激活4条控制规则,在控制的过程中只考虑这4条控制规则.这2种思想的结合使得控制规则的设计大大简化,可以采用批处理的方式设计控制器,不仅加快了系统的动态响应,也提高了控制精度.仿真结果证实了这种控制方法的有效性.