Synchronization of chaotic systems and identification of nonlinear systems by using recurrent hierarchical type-2 fuzzy neural networks

This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown.     

Design of a TRFN Controller for a Nonlinear Multivariable Process

Abstract

Feedback architecture is found to be more suitable for controlling dynamic processes, as it utilizes the past information of the process variables as against a controller designed using a feedforward structure that utilizes only the present information about the process variables. A comparative analysis of having a recurrent fuzzy controller over a conventional fuzzy controller in a control loop involving a non-linear dynamic system is enunciated using a laboratory two-tank heating process. A considerable improvement in performance is obtained by employing the recurrent structure in place of the conventional fuzzy controller. In addition, this proposed control strategy is numerically more efficient than the feedforward fuzzy structure. Results illustrate the effectiveness of the proposed structure.     

Nonlinear dynamic systems identification using recurrent interval type-2 TSK fuzzy neural network – A novel structure

In this study, a novel structure of a recurrent interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy neural network (FNN) is introduced for nonlinear dynamic and time-varying systems identification. It combines the type-2 fuzzy sets (T2FSs) and a recurrent FNN to avoid the data uncertainties. The fuzzy firing strengths in the proposed structure are returned to the network input as internal variables. The interval type-2 fuzzy sets (IT2FSs) is used to describe the antecedent part for each rule while the consequent part is a TSK-type, which is a linear function of the internal variables and the external inputs with interval weights. All the type-2 fuzzy rules for the proposed RIT2TSKFNN are learned on-line based on structure and parameter learning, which are performed using the type-2 fuzzy clustering. The antecedent and consequent parameters of the proposed RIT2TSKFNN are updated based on the Lyapunov function to achieve network stability. The obtained results indicate that our proposed network has a small root mean square error (RMSE) and a small integral of square error (ISE) with a small number of rules and a small computation time compared with other type-2 FNNs.     

A novel interval type-2 fractional order fuzzy PID controller: Design,performance evaluation,and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.     

A simplified type-2 fuzzy logic controller for real-time control

Increasingly, genetic algorithms (GAs) are used to optimize the parameters of fuzzy logic controllers (FLCs). Although GAs provide a systematic design approach, the optimization process is generally performed off-line using a plant model. Differences between the model and physical plant may result in unsatisfactory control performance when the FLCs are deployed in practice. Type-2 FLCs are an attractive alternative because they can better cope with modeling uncertainties. Unfortunately, type-2 FLCs are computationally intensive. This paper presents a simplified type-2 FLC that is suitable for real-time applications. The key idea is to only replace some critical type-1 fuzzy sets by type-2 sets. Experimental results indicate that the proposed simplified type-2 FLC is as robust as a conventional type-2 FLC, while lowering the computational cost.     

Fault tolerant control for modified quadrotor via adaptive type-2 fuzzy backstepping subject to actuator faults

In this paper, a robust attitude and position control of a novel modified quadrotor unmanned aerial vehicles (UAV) which has higher drive capability as well as greater robustness against actuator faults than conventional quad-rotor UAV has been developed. A robust backstepping controller with adaptive interval type-2 fuzzy logic is proposed to control the attitude and position of the modified quadrotor under actuator faults. Besides globally stabilizing the system amid other disturbances, the insensitivity to the model errors and parametric uncertainties are the asset of the backstepping approach. The adaptive interval type-2 fuzzy logic as fault observer can effectively estimate the lumped faults without the knowledge of their bounds for the modified quadrotor UAV. Additionally, the type-2 fuzzy systems are utilized to approximate the local nonlinearities of each subsystem under actuator faults, next and in order to achieve the expected tracking performance, we used Lyapunov theory stability and convergence analysis to online adjust adaptive laws. As a result, the uniformly ultimate stability of the modified quadrotor system is proved. Finally, the performances of the proposed control method are evaluated by simulation and the results demonstrate the effectiveness of the proposed control strategy for the modified quadrotor in vertical flights in presence of actuator faults.     

Active fault tolerant control based on interval type-2 fuzzy sliding mode controller and non linear adaptive observer for 3-DOF laboratory helicopter

In this paper, a robust controller for a three degree of freedom (3 DOF) helicopter control is proposed in presence of actuator and sensor faults. For this purpose, Interval type-2 fuzzy logic control approach (IT2FLC) and sliding mode control (SMC) technique are used to design a controller, named active fault tolerant interval type-2 Fuzzy Sliding mode controller (AFTIT2FSMC) based on non-linear adaptive observer to estimate and detect the system faults for each subsystem of the 3-DOF helicopter.The proposed control scheme allows avoiding difficult modeling, attenuating the chattering effect of the SMC, reducing the rules number of the fuzzy controller.Exponential stability of the closed loop is guaranteed by using the Lyapunov method. The simulation results show that the AFTIT2FSMC can greatly alleviate the chattering effect, providing good tracking performance, even in presence of actuator and sensor faults.     

基于LabVIEW的模糊控制系统设计

图形编程语言LabVIEW和模糊控制系统凭借其各自的特点在工业生产中得到广泛的应用,但是将两者结合的应用比较少。结合LabVIEW和模糊控制系统的优点,分析了LabVIEW中实现模糊控制系统的方法,利用PID and FuzzyLogic Toolkit设计了一个基于LabVIEW的模糊控制器,并对频率为10.1 Hz,幅值为1的正弦波和三角波信号进行跟踪。结果表明:基于LabVIEW的模糊控制器结合了两者的优点,易于实现并具有良好的动态特性。     

非线性随机振动系统的阻尼模糊控制

建立了非线性随机振动阻尼模糊控制系统的力学模型;针对该模型内的模糊控制器的参数确定问题;提出了基于细菌遗传机理的局部改进遗传算法;解决了该遗传算法与模糊控制理论应用于非线性随机振动系统阻尼控制的有关问题;给出了仿真实例。     

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller.     

模糊识别在电厂送风机故障诊断中的应用

本文将模糊识别法应用到电厂送风机故障诊断系统中,建立了送风机的故障特征向量、故障模糊向量及模糊关系矩阵,通过模糊识别得出各故障的隶属度,根据最大隶属度原则确定设备具体故障。最后通过具体实例分析证明该方法效果良好。     

Trajectory and vibration control of a flexible joint manipulator using interval type-2 fuzzy logic

This study presents the development of a novel interval type-2 fuzzy logic controller for real time trajectory and vibration control of a flexible joint manipulator. The controller is designed on the Mamdani based interval type-2 fuzzy logic toolbox, which is developed by the authors, using interval triangular membership functions and Karnik–Mendel type reduction algorithm. The closed-loop stability of the system is proved based on Lyapunov stability theorem. In order to observe the effectiveness and robustness of the proposed controller to variations of system parameters (change in link length and payload), the experimental results of interval type-2 and conventional type-1 fuzzy logic controllers are compared. The results show that proposed controller clearly improves the link vibration and trajectory tracking behavior of the system.     

Soft sensor modeling of chemical process based on self-organizing recurrent interval type-2 fuzzy neural network

This study introduces a novel self-organizing recurrent interval type-2 fuzzy neural network (SRIT2FNN) for the construction of a soft sensor model for a complex chemical process. The proposed SRIT2FNN combines interval type-2 fuzzy logic systems (IT2FLSs) and recurrent neural networks (RNNs) to improve the modeling precision. The Gaussian interval type-2 membership function is used to describe the antecedent part of the SRIT2FNN fuzzy rule, and the consequent part is of the Mamdani type with an interval random number. An adaptive optimal clustering number of fuzzy kernel clustering algorithm based on a Gaussian kernel validity index (GKVI-AOCN-FKCM) is developed to determine the structure of the SRIT2FNN and fuzzy rule antecedent parameters, and the parameter learning of SRIT2FNN used the gradient descent method. Finally, the proposed SRIT2FNN is applied to the soft sensor modeling of ethylene cracking furnace yield in a typical chemical process. Comparisons between the SRIT2FNN and conventional fuzzy neural network (FNN) and interval type-2 fuzzy neural network (IT2FNN) are made via simulation experiments. The results show that the proposed SRIT2FNN performs better than the conventional FNN and IT2FNN.     

模糊控制恒压供水系统的设计

介绍了一种模糊控制的恒压供水系统软硬件的实现思想和方法。针对供水系统普遍存在的大滞后和惯性的特点,提出一种模糊控制方法,并对该控制算法进行研究和计算机仿真,给出了基于MALTLAB的系统仿真结果．仿真实验表明：模糊控制克服了传统PID控制设计中参数调整困难等问题,同时具有动态响应快、稳态性能好、超调量小和鲁棒性强等优点,实现了对供水系统中的管网压力恒值控制。     

Fuzzy logic sliding mode control for command guidance law design

Recently, the combination of sliding mode and fuzzy logic techniques has emerged as a promising methodology for dealing with nonlinear, uncertain, dynamical systems. In this paper, a sliding mode control algorithm combined with a fuzzy control scheme is developed for the trajectory control of a command guidance system. The acceleration command input is mathematically derived. The proposed controller is used to compensate for the influence of unmodeled dynamics and to alleviate chattering. Simulation results show that the proposed controller gives good system performance in the face of system parameters variation and external disturbances. In addition, they show the effectiveness of the proposed missile guidance law against different engagement scenarios where the results demonstrate better performance over the conventional sliding mode control.     

A type-2 fuzzy expert system based on a hybrid inference method for steel industry

In this paper, a novel type-2 fuzzy expert system for prediction the amount of reagents in desulfurization process of a steel industry in Canada is developed. In this model, the new interval type-2 fuzzy c-regression clustering algorithm for structure identification phase of Takagi–Sugeno (T–S) systems is presented. Gaussian Mixture Model is used to generate partition matrix in clustering algorithm. Then, an interval type-2 hybrid fuzzy system, which is the combination of Mamdani and Sugeno method, is proposed. The new hybrid inference system uses fuzzy disjunctive normal forms and fuzzy conjunctive normal forms for aggregation of antecedents. A statistical test, which uses least square method, is implemented in order to select variables. In order to validate our method, we develop three system modeling techniques and compare the results with our proposed interval type-2 fuzzy hybrid expert system. These techniques are multiple regression, type-1 fuzzy expert system, and interval type-2 fuzzy TSK expert system. For tuning parameters of the system, adaptive-network-based fuzzy inference system is used. Finally, neural network is utilized in order to reduce error of the system. The results show that our proposed method has less error and high accuracy.     

Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller’s parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.     

模糊PID控制器在电锅炉温度控制系统中的应用

电锅炉已经成为供热采暧的主要设备．它的温度控制系统由于存在非线性、大滞后以及时变性等特点,常规的PID控制器很难达到较好的控制效果。考虑到模糊控制能够对复杂的非线性、时变系统进行很好的控制。但却无法消除静态误差的特点．本文将模糊控制引入到常规PID控制中．提出了一种模糊PID参数自整定控制器。并且对电锅炉温度控制系统进行了抗扰动的实验。仿真结果表明。和常规PID控制器相比．所设计的模糊PID控制器改善了温度控制系统的动态性能。提高了系统的鲁棒性。     

Optimal adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control method for some classes of nonlinear systems

In this research, a novel adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control (AIT2FFOBSMC) method is presented for some classes of nonlinear fully-actuated and under-actuated mechanical systems with uncertainty. The AIT2FFOBSMC method exploits the advantages of backstepping and sliding mode methods to improve the performance of closed-loop control systems by lowering the tracking error and increasing robustness. To mitigate chattering and the tracking error, a fractional sliding surface is designed. In addition to the fractional sliding surface, an adaptive interval type-2 fuzzy compensator is used to estimate the uncertainty and perturbation of the nonlinear system in order to further reduce chattering caused by switching term as well as to enhance the perturbation rejection. In order to achieve an optimal performance, the multi-tracker optimization algorithm (MTOA) is used. Finally, a number of simulations and experimental tests are carried out to examine the performance of the AIT2FFOBSMC method.     

T-S region-based fuzzy control with multiple performance constraints

Takagi-Sugeno fuzzy control problems with minimizing H2/Hinfinity norm are investigated in this paper. A redesigned T-S fuzzy model and controller are called a T-S Region-based Fuzzy Model (TSRFM) and a T-S Region-based Fuzzy Controller (TSRFC), respectively, which are derived from the fuzzy region concept and the robust control technique. The fuzzy region concept is used to divide the general plant rules into several fuzzy regions and the robust control technique is used to stabilize all plant rules of each fuzzy region. In this case, the stability conditions with H2/Hinfinity performance are derived from Lyapunov criterion, which are expressed in terms of LMIs. For the fuzzy model involving large plant rules, the proposed idea greatly reduces the total number of LMIs and controller rules so that TSRFC is easy to implement with simple hardware. Although the controller rules are reduced, TSRFC is able to provide performance as good as former designs.