Fuzzy sliding-mode control with rule adaptation for nonlinear systems

Abstract: A fuzzy sliding-mode control with rule adaptation design approach with decoupling method is proposed. It provides a simple way to achieve asymptotic stability by a decoupling method for a class of uncertain nonlinear systems. The adaptive fuzzy sliding-mode control system is composed of a fuzzy controller and a compensation controller. The fuzzy controller is the main rule regulation controller, which is used to approximate an ideal computational controller. The compensation controller is designed to compensate for the difference between the ideal computational controller and the adaptive fuzzy controller. Fuzzy regulation is used as an approximator to identify the uncertainty. The simulation results for two cart–pole systems and a ball–beam system are presented to demonstrate the effectiveness and robustness of the method. In addition, the experimental results for a tunnelling robot manipulator are given to demonstrate the effectiveness of the system.     

一类不确定多输入模糊双线性系统的鲁棒H∞控制

针对一类带有参数不确定性和干扰的多输入模糊双线性系统(FBS)的鲁棒H_∞控制问题,使用并行分布补偿算法(PDC)设计了模糊控制器,得到了整个模糊控制系统鲁棒全局稳定的充分条件,控制器的设计可以通过求解一系列线性矩阵不等式(LMI)获得.仿真例子验证了方法的有效性.     

Direct adaptive fuzzy control for a class of MIMO nonlinear systems

This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.     

Observer-based variable universe adaptive fuzzy controller without additional dynamic order

A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output (SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.     

Robust Fuzzy Control of Electrical Manipulators

Stability analysis for fuzzy control of robot manipulators has been a serious challenging problem in literature. The theoretical difficulties are highly increased due to the complexity of both manipulator dynamics and fuzzy controller structure. This paper develops a novel robust fuzzy control approach for electrical robot manipulators using the direct method of Lyapunov. We pass analytical difficulties by the use of voltage control strategy in replace of torque control strategy. Then, a normalized and decentralized Takagi–Sugeno fuzzy controller is presented in a simple structure. A simple Lyapunov candidate is proposed to apply stability analysis without knowing the explicit dynamics of system. Consequently, fuzzy control is analyzed and designed as a robust nonlinear control. Roles of scaling factors, gains in consequent parts, and membership functions in condition parts are considered in the control design. The proposed control approach is applied on a Puma560 robot arm.     

Robust fuzzy control for a plant with fuzzy linear model

A robust complexity reduced proportional-integral-derivative (PID)-like fuzzy controllers is designed for a plant with fuzzy linear model. The plant model is described with the expert's linguistic information involved. The linguistic information for the plant model is represented as fuzzy sets. In order to design a robust fuzzy controller for a plant model with fuzzy sets, an approach is developed to implement the best crisp approximation of fuzzy sets into intervals. Then, Kharitonov's Theorem is applied to construct a robust fuzzy controller for the fuzzy uncertain plant with interval model. With the linear combination of input variables as a new input variable, the complexity of the fuzzy mechanism of PID-like fuzzy controller is significantly reduced. The parameters in the robust fuzzy controller are determined to satisfy the stability conditions. The robustness of the designed fuzzy controller is discussed. Also, with the provided definition of relative robustness, the robustness of the complexity reduced fuzzy controller is compared to the classical PID controller for a second-order plant with fuzzy linear model. The simulation results are included to show the effectiveness of the designed PID-like robust fuzzy controller with the complexity reduced fuzzy mechanism.     

不确定非线性网络化系统的鲁棒H_∞控制

用T-S(Takagi-Sugeno)模糊方法研究了带有参数不确定的非线性网络化系统的鲁棒控制.首先,考虑到诱导时延和数据丢包等网络因素的影响,基于事件驱动的保持器的更新序列建立闭环反馈系统的采样模型,并将其转化为状态中附加两个时滞变量的连续T-S模糊系统.然后,利用时滞系统方法,分析不确定闭环模糊系统的鲁棒H∞性能,并设计相应的鲁棒H∞模糊控制器.最后,仿真例子表明了方法的有效性.     

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

In this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.     

一类不确定混沌系统的模糊滑模控制与同步

针对一类具有不确定项的二阶连续时间混沌系统的定值跟踪控制和自混沌同步及异结构混沌同步问题,提出了一种模糊滑模变结构控制方法,设计了模糊滑模变结构控制器,并从理论上证明了控制系统的稳定性.在该控制器的作用下,可以实现两个相同或不同结构的混沌系统的控制与同步,且不受不确定性的影响,具有很强的鲁棒性.定值跟踪和同步控制的仿真结果表明,该控制器是有效的.     

不确定Willis脑动脉瘤系统的自适应模糊滑模控制

研究了具有不确定项的非线性Willis环上脑动脉瘤系统的混沌控制和同步问题,提出了一种自适应模糊滑模变结构控制方法,设计了模糊滑模变结构控制器及自适应控制律,并从理论上证明了控制系统的稳定性。在该控制器的作用下,受控Willis脑动脉瘤系统能够达到任意目标轨道,且不受不确定性的影响,具有很强的鲁棒性。定值跟踪和同步控制的仿真结果表明了控制器的有效性。     

Robust adaptive fuzzy sliding mode trajectory tracking control for serial robotic manipulators

The ever increasingly stringent performance requirements of industrial robotic applications highlight significant importance of advanced robust control designs for serial robots that are generally subject to various uncertainties and external disturbances. Therefore, this paper proposes and investigates the design and implementation of a robust adaptive fuzzy sliding mode controller in the task space for uncertain serial robotic manipulators. The sliding mode control is well known for its robustness to system parameter variations and external disturbances, and is thus a highly desirable and cost-effective approach to achieve high precision control task for serial robots. The proposed controller is designed based on a fuzzy logic approximation to accomplish trajectory tracking with high accuracy and simultaneously attenuate effects from uncertainties. In the controller, the high-frequency uncertain term is approximated by using a fuzzy logic system while the low-frequency term is adaptively updated in real time based on a parametric adaption law. The control efficacy and effectiveness of the proposed control algorithm are comparatively verified against a recently proposed conventional controller. The test results demonstrate that the proposed controller has better trajectory tracking performances and is more robust against large disturbances than the conventional controller under the same operating conditions.     

一种基于Matlab的参数自调整模糊控制器的设计方法

本文介绍了一种在MATLAB的模糊控制工具箱中,通过编写S函数实现对量化因子和比例因子的在线自动调整来设计模糊控制器,从而有效地实现参数自调整模糊控制器的设计方法。为了验证参数自调整模糊控制器的优越性,分别进行了空调温度控制系统的PID控制、常规模糊控制和参数自调整模糊控制的仿真研究。结果表明,参数自调整模糊控制器较之常规的模糊控制器,在被控对象特性变化或较大扰动的情况下,控制系统能保持较好的性能,是一种较理想的控制方法,具有广阔的发展前景。     

Robust fuzzy neural network control for linear ceramic motor drivevia backstepping design technique

This study presents a robust fuzzy-neural-network (RFNN) control system for a linear ceramic motor (LCM) that is driven by an unipolar switching full-bridge voltage source inverter using LC resonant technique. The structure and operating principle of the LCM are introduced. Since the dynamic characteristics and motor parameters of the LCM are nonlinear and time varying, a RFNN control system is designed based on the hypothetical dynamic model to achieve high-precision position control via the backstepping design technique. In the RFNN control system a fuzzy neural network (FNN) controller is used to learn an ideal feedback linearization control law, and a robust controller is designed to compensate the shortcoming of the FNN controller. All adaptive learning algorithms in the RFNN control system are derived from the sense of Lyapunov stability analysis, so that system-tracking stability can be guaranteed in the closed-loop system. The effectiveness of the proposed RFNN control system is verified by experimental results in the presence of uncertainties. In addition, the advantages of the proposed control system are indicated in comparison with the traditional integral-proportional (IP) position control system     

A robust stabilization problem of fuzzy control systems and itsapplication to backing up control of a truck-trailer

A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions     

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H_∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H_∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.     

Fuzzy sliding mode control for an under-actuated system with mismatched uncertainties

This article presents a robust fuzzy sliding mode controller. The methodology of sliding mode control provides an easy way to control under-actuated nonlinear systems with uncertainties. The structure of the sliding surface is designed as follows. First, decouple the entire system into second-order systems so that each subsystem has a separate control target expressed in terms of a sliding surface. Second, from the sliding surface of subsystems, organize the main sliding surface system. Third, generate a control input for the main sliding surface to make whole subsystems move toward their sliding surface. A fuzzy controller is used to obtain a smooth boundary layer to the sliding surface. Finally, the fuzzy sliding mode controller presented is used to control an under-actuated nonlinear system, and confirms the validity of the proposed approach and its robustness to uncertainties.     

A Learning-Based Fault Tolerant Tracking Control of an Unmanned Quadrotor Helicopter

This paper presents a novel learning-based fault tolerant tracking control approach by using an extended Kalman filter (EKF) to optimize a Mamdani fuzzy state-feedback tracking controller. First, a robust state-feedback tracking controller is designed as the baseline controller to guarantee the expected system performance in the fault-free condition. Then, the EKF is employed to regulate the shape of membership functions and rules of fuzzy controller to adapt with the working conditions automatically after the occurrence of actuator faults. Next, based on the modified fuzzy membership functions and rules, the baseline controller is readjusted to properly compensate the adverse effects of actuator faults and asymptotically stabilize the closed-loop system. Finally, in order to verify the effectiveness of the proposed method, several groups of numerical simulations are carried out by comparing the performance of a tracking control scheme and the presented technique. Simulation results demonstrate that the proposed method is effective for optimizing the fuzzy tracking controller on-line and counteracting the side effects of actuator faults, and the control performance is significantly improved as well.     

Fuzzy approach-based optimal robust control for permanent magnet synchronous motor with experimental validation

This paper presents an optimal robust control for a permanent magnet synchronous motor (PMSM) with uncertainties and external disturbances which can be described by fuzzy approach. The fuzzy approach based on fuzzy set theory is distinguish from probability theory or fuzzy logic theory. Firstly, a dynamical model of the PMSM with uncertainties is established using a fuzzy approach. Then, a robust controller with an optimizable parameter is designed for PMSM to handle the uncertainties. The stability of the proposed control is proven using the Lyapunov theory. Furthermore, the controller gain is optimized by minimizing performance index, which contains the control performance and cost. Finally, the numerical simulations and experimental results are presented to validate the effectiveness of the proposed control with an optimal parameter.     

Robust Stabilization of the Distributed Parameter System With Time Delay via Fuzzy Control

In this paper, stabilization of the distributed parameter system (DPS) with time delay is studied using Galerkin's method and fuzzy control. With the help of Galerkin's method, the dynamics of DPS with time delay can be first converted into a group of low-order functional ordinary differential equations, which will be used for design of the robust fuzzy controller. The fuzzy controller designed can guarantee exponential stability of the closed-loop DPS. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality design approach. The effectiveness of the proposed control design methodology is demonstrated in numerical simulations.     

Hybrid compensation control for affine TSK fuzzy control systems

The paper proposes a way of designing state feedback controllers for affine Takagi-Sugeno-Kang (TSK) fuzzy models. In the approach, by combining two different control design methodologies, the proposed controller is designed to compensate all rules so that the desired control performance can appear in the overall system. Our approach treats all fuzzy rules as variations of a nominal rule and such variations are individually dealt with in a Lyapunov sense. Previous approaches have proposed a similar idea but the variations are dealt with as a whole in a robust control sense. As a consequence, when fuzzy rules are distributed in a wide range, the stability conditions may not be satisfied. In addition, the control performance of the closed-loop system cannot be anticipated in those approaches. Various examples were conducted in our study to demonstrate the effectiveness of the proposed control design approach. All results illustrate good control performances as desired.