Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

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.

Predictive Control Algorithm for Urban Rail Train Brake Control System Based on T-S Fuzzy Model

Urban rail transit has the advantages of large traffic capacity,high punctuality and zero congestion,and it plays an increasingly important role in modern urban life.Braking system is an important system of urban rail train,which directly affects the performance and safety of train operation and impacts passenger comfort.The braking performance of urban rail trains is directly related to the improvement of train speed and transportation capacity.Also,urban rail transit has the characteristics of high speed,short station distance,frequent starting,and frequent braking.This makes the braking control system constitute a time-varying,time-delaying and nonlinear control system,especially the braking force changes directly disturb the parking accuracy and comfort.To solve these issues,a predictive control algorithm based on T-S fuzzy model was proposed and applied to the train braking control system.Compared with the traditional PID control algorithm and self-adaptive fuzzy PID control algorithm,the braking capacity of urban rail train was improved by 8%.The algorithm can achieve fast and accurate synchronous braking,thereby overcoming the dynamic influence of the uncertainty,hysteresis and time-varying factors of the controlled object.Finally,the desired control objectives can be achieved,the system will have superior robustness,stability and comfort.

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。

Flatness predictive model based on T-S cloud reasoning network implemented by DSP

The accuracy of present flatness predictive method is limited and it just belongs to software simulation. In order to improve it, a novel flatness predictive model via T-S cloud reasoning network implemented by digital signal processor(DSP) is proposed. First, the combination of genetic algorithm(GA) and simulated annealing algorithm(SAA) is put forward, called GA-SA algorithm, which can make full use of the global search ability of GA and local search ability of SA. Later, based on T-S cloud reasoning neural network, flatness predictive model is designed in DSP. And it is applied to 900 HC reversible cold rolling mill. Experimental results demonstrate that the flatness predictive model via T-S cloud reasoning network can run on the hardware DSP TMS320 F2812 with high accuracy and robustness by using GA-SA algorithm to optimize the model parameter.

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.

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.

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.

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.

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.

Fuzzy Modeling of Prediction M_s Temperature for Martensitic Stainless Steel

A method of fuzzy modeling based on fuzzy clustering and Kalman filtering was proposed for predicting M s temperature from chemical composition for martensitic stainless steel. The membership degree of each sample was calculated by the fuzzy clustering algorithm. Kalman filtering was used to identify the consequent parameters. Only Grade 95 steel are available for training and validation, and the fuzzy model is valid for the following element concentration ranges (wt%): 0.01<C<0.7; 0<Si<1.0; 0.10<Mn<1.25; 11.5<Cr< 17.5; 0<Ni<2.5; 0<Mo<1.0. Compared with that of several empirical models reported, the accuracy of the fuzzy model was almost 5 times higher than that of the best empirical model. Furthermore, the compositional dependences of Ms were successfully determined and compared with those of the empirical formulae. It was found that the specific element dependences were a function of the overall composition, something could not easily be found using conventional statistics.

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.

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.

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.

Grey Prediction Fuzzy Control of the Target Tracking System in a Robot Weapon

Grey modeling can be used to predict the behavioral development of a system and find out the lead control values of the system. By using fuzzy inference, PID parameters can be adjusted on line by the fuzzy controller with PID parameters self-tuning. According to the characteristics of target tracking system in a robot weapon, grey prediction theory and fuzzy PID control ideas are combined. A grey prediction mathematical model is constructed and a fuzzy PID controller with grey prediction was developed. Simulation result shows fuzzy PID control algorithm with grey prediction is an efficient method that can improve the control equality and robustness of traditional PID control and fuzzy PID control, and has much better performance for target tracking.

Stabilization of CSTR w ith Self-tuning Sliding Mode Controller Using T-S Fuzzy Linearization

A self-tuning reaching law based sliding mode control(SMC)theory is proposed to stabilize the nonlinear continuous stirred tank reactor(CSTR).T-S fuzzy logic is used to build a global fuzzy state-space linear model.Combing the traits of SMC and CSTR,three fuzzy rules can meet the requirements of controlled system.The self-tuning switch control law which can drive the state variables to the sliding surface as soon as possible is designed to ensure the robustness of uncertain fuzzy system.Lyapunov equation is applied to proving the stability of the sliding surface.The simulations show that the proposed approach can achieve desired performance with less chattering problem.

Robust model predictive control for discrete uncertain nonlinear systems with time-delay via fuzzy model

An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the “worst-case” objective function is converted into the linear objective minimization problem in- volving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.