Constrained predictive control based on T-S fuzzy model for nonlinear systems

A constrained generalized predictive control （GPC） algorithm based on the T-S fuzzy model is presented for the nonlinear system. First, a Takagi-Sugeno （T-S） fuzzy model based on the fuzzy cluster algorithm and the orthogonalleast square method is constructed to approach the nonlinear system. Since its consequence is linear, it can divide the nonlinear system into a number of linear or nearly linear subsystems. For this T-S fuzzy model, a GPC algorithm with input constraints is presented. This strategy takes into account all the constraints of the control signal and its increment, and does not require the calculation of the Diophantine equations. So it needs only a small computer memory and the computational speed is high. The simulation results show a good performance for the nonlinear systems.

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.

Controller Design for Electric Power Steering System Using T-S Fuzzy Model Approach

Pressure ripples in electric power steering （EPS） systems can be caused by the phase lag between the driver s steering torque and steer angle, the nonlinear frictions, and the disturbances from road and sensor noise especially during high-frequency maneuvers. This paper investigates the use of the robust fuzzy control method for actively reducing pressure ripples for EPS systems. Remarkable progress on steering maneuverability is achieved. The EPS dynamics is described with an eight-order nonlinear state-space model and approximated by a Takagi-Sugeno （T-S） fuzzy model with time-varying delays and external disturbances. A stabilization approach is then presented for nonlinear time-delay systems through fuzzy state feedback controller in parallel distributed compensation （PDC） structure. The closed-loop stability conditions of EPS system with the fuzzy controller are parameterized in terms of the linear matrix inequality （LMI） problem. Simulations and experiments using the proposed robust fuzzy controller and traditional PID controller have been carried out for EPS systems. Both the simulation and experiment results show that the proposed fuzzy controller can reduce the torque ripples and allow us to have a good steering feeling and stable driving.

Statistic PID Tracking Control for Non-Gaussian Stochastic Systems Based on T-S Fuzzy Model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

Modeling and Stability Analysis for Non-linear Network Control System Based on T-S Fuzzy Model

Based on the T-S fuzzy model,this paper presents a new model of non-linear network control system with stochastic transfer delay.Sufficient criterion is proposed to guarantee globally asymptotically stability of this two-levels T-S fuzzy model.Also a T-S fuzzy observer of NCS is designed base on this two-levels T-S fuzzy model.All these results present a new approach for networked control system analysis and design.

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

Fault tolerant synchronization of chaotic systems based on T-S fuzzy model with fuzzy sampled-data controller

In this paper the fault tolerant synchronization of two chaotic systems based on fuzzy model and sample data is investigated. The problem of fault tolerant synchronization is formulated to study the global asymptotical stability of the error system with the fuzzy sampled-data controller which contains a state feedback controller and a fault compensator. The synchronization can be achieved no matter whether the fault occurs or not. To investigate the stability of the error system and facilitate the design of the fuzzy sampled-data controller, a Takagi Sugeno （T-S） fuzzy model is employed to represent the chaotic system dynamics. To acquire good performance and produce a less conservative analysis result, a new parameter-dependent Lyapunov-Krasovksii functional and a relaxed stabilization technique are considered. The stability conditions based on linear matrix inequality are obtained to achieve the fault tolerant synchronization of the chaotic systems. Finally, a numerical simulation is shown to verify the results.

Impulsive Control for T-S Fuzzy Model Based Chaotic Systems Consisting of Van der Pol Oscillators Coupled to Linear Oscillators

This paper proposes an impulsive control scheme for chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators （VDPL） based on their Takagi-Sugeno （T-S） fuzzy models. A T-S fuzzy model is utilized to represent the chaotic VDPL system. By using comparison method, a general asymptotical stability criterion by means of linear matrix inequality （LMI） is derived for the T-S fuzzy model of VDPL system with impulsive effects. The simulation results demonstrate the effectiveness of the proposed scheme.

Robust State Feedback H_∞Control for Dynamic Biped Robot Based on T-S Fuzzy Model

T-S fuzzy model was applied to describe nonlinear system and global fuzzy model was expressed by the form of uncertain system.Based on robust state feedback H_∞control strategy,designed a global asymptotic steady fuzzy model.This control system can use the experimental input-output data pairs for the biped robot learning and walking with dynamic balance.It is proved by simulation result that robust state feedback H_∞control method based on T-S fuzzy model can effectively restrain the effect of model uncertainties and external disturbance acting on biped robot.From these works,we showed the satisfactory performance of joint tracking without any chattering.

Fuzzy identification of T-S model for beam stability control for electron gun

In this paper, Takagi-Sugeno(T-S) fuzzy control is proposed for stabilizing the output beam of accelerators. To model the nonlinear system, we proposed a hybrid optimization algorithm based on quantum-inspired differential evolution and genetic algorithm. Based on the T-S model identified, the corresponding statefeedback fuzzy controller is designed. The method is applied to the La B6 electron gun system in the industrial radiation accelerator and the simulation results show its effectiveness.

FUZZY ROBUST H_∞ CONTROL OF UNCERTAIN NONLINEAR SYSTEM WITH TIME-DEALY

This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. Some sufficient conditions are derived for the existence of fuzzy H ∞ state feedback controllers such that the closed loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.

基于T-S模糊模型的PLZT驱动器的本构建模及伺服驱动控制

针对目前ON-OFF控制策略在PLZT驱动器光致应变位移的闭环伺服控制系统中的缺点,提出了一种基于T-S模糊模型的PLZT驱动器应变位移的动态模型及预测控制方法。首先,建立了PLZT驱动器光致应变位移的T-S模糊模型,该模型利用基于减法聚类的模糊C均值聚类算法进行前件辨识,并利用奇异值分解(singular value decomposition, SVD)算法进行后件辨识,所建立模型的有效性通过拟合度仿真加以验证。随后,在所建立的T-S模糊模型的基础上结合预测控制方法对PLZT驱动器的光致应变位移进行闭环控制,并对该算法进行仿真验证。仿真结果显示,在PLZT驱动器微位移的控制中,该文控制算法减小了基于ON-OFF控制策略下的抖振,且具有更好的控制效果。

基于改进T-S模糊模型的弧焊机器人轨迹实时跟踪

针对弧焊机器人在实际作业中受到诸多不确定因素的影响,导致弧焊机器人焊接轨迹偏离预期轨迹的问题,提出一种基于改进T-S(Takagi-Sugeno)模糊模型的弧焊机器人轨迹实时跟踪方法。采用图像识别技术识别并定位焊缝,通过坐标转换,确定焊缝中心线在机器人坐标系中的位置坐标。利用蚁群算法根据焊缝中心线在机器人坐标系中的坐标,搜索从起始位置到目标位置的最优焊接路径。设计了一种改进区间二型T-S模糊模型,通过视觉传感器实时获取新的焊缝信息,计算轨迹误差,以此为输入,利用改进T-S模糊模型对机器人的运动轨迹进行实时调整。实验结果表明,采用改进T-S模糊模型后,机器人轨迹跟踪离散度均降至1 mm以下,弧焊机器人轨迹与预期轨迹高度重合,比传统方法跟踪离散度大大降低。

基于模糊T-S型内模PID控制算法的无刷直流电机仿真分析

针对无刷直流电机(BLDCM)双闭环控制调速系统的控制响应速度慢、转速波动较大等问题,提出一种模糊神经网络与内模控制相结合的驱动方式。该方式利用Matlab/Simulink来构建一种基于BLDCM和控制器的电梯一体式限速器仿真模型,得到BLDCM的速度、转矩响应曲线。仿真分析和实验结果均表明,模糊T-S型内模PID控制算法在响应速度、转速误差、抗干扰能力和控制精度等性能方面优于内模PID控制算法与常规双闭环PID控制系统。该研究可为模糊神经网络T-S型内模PID算法在电梯一体式限速器上的应用积累经验。

基于T-S模糊建模的气动肌肉拮抗关节预测角度控制

目的:为了提升气动肌肉拮抗关节的控制精度。方法:提出了一种用于气动肌肉拮抗关节角度跟踪的T-S模糊模型预测控制方法。建立了拮抗关节的T-S模糊模型,并对模型进行了离散化处理;基于离散后的T-S模糊模型,设计了拮抗关节的模型预测控制器,通过特征值法验证了系统的稳定性。结果:仿真实验表明,T-S模糊模型预测控制器跟踪±15°和±10°的角度时,相对于传统模型预测控制,平均绝对误差分别降低了29.05%和44.11%。结论:设计的T-S模糊模型预测控制器提高了气动肌肉拮抗关节的控制精度。

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.

Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Robust Stabilization of Nonlinear Time Delay Discrete-time Systems Based on T-S Model

A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.