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.     

Design of interval type-2 fuzzy precompensated PID controller applied to two-DOF robotic manipulator with variable payload

The interval type-2 fuzzy logic controller (IT2-FLC), with footprint of uncertainty (FOU) in membership functions (MF), has increasingly recognized for controlling uncertainties and nonlinearities. Within the ambit of this, the efficient interval type-2 fuzzy precompensated PID (IT2FP-PID) controller is designed for trajectory tracking of 2-DOF robotic manipulator with variable payload. A systematic strategy for optimizing the controller parameters along with scaling factors and the antecedent MF parameters for minimization of performance metric integral time absolute error (ITAE) is presented. Prominently, recently proposed optimization technique hybridizing grey wolf optimizer and artificial bee colony algorithm (GWO–ABC) is utilized for solving this high-dimensional constrained optimization problem. In order to witness effectiveness, the performance is compared with type-1 fuzzy precompensated PID (T1FP-PID), fuzzy PID (FPID), and conventional PID controllers. More significantly, the robustness of IT2FP-PID is examined for payload variation, model uncertainties, external disturbance, and noise cancellation. After experimental outcome, it is inferred that IT2FP-PID controller outperforms others and can be referred as a viable alternative for controlling nonlinear complex systems with higher uncertainties.     

基于正则化 AdaBound 的区间二型模糊 神经网络软测量建模

针对复杂化工过程中存在强非线性、多变量耦合、参数时变及大时滞等因素,导致监测变量软测量精度不高的问题,提 出了一种基于正则化 AdaBound 的区间二型模糊神经网络(RAIT2FNN) 软测量建模方法。 首先为了解决区间二型神经网络 (IT2FNN)结构难以确定的问题,提出了一种采用激励强度和相似度定义增长和删减指标的自组织产生规则的算法。 该算法利 用激励强度的大小决定是否产生规则,并根据相似度进行规则的删减从而确定了区间二型模糊神经网络的结构。 其次,本文提 出正则化和 AdaBound 相结合的算法对 RAIT2FNN 模型相关参数进行修正,使得不同参数具有有界的自适应学习速率。 最后将 RAIT2FNN 作为软测量模型应用于环己烷无催化氧化过程尾氧浓度预测问题中。 实验结果为测试时间为 0. 008 2,训练 RMSE 为 0. 018 2,测试 RMSE 为 0. 009 6,表明 RAIT2FNN 作为软测量模型具有预测及时且预测精度较高的优点。     

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.     

Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system

In this paper, the interval type-2 fuzzy proportional–integral–derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller.     

Parameter estimation and interval type-2 fuzzy sliding mode control of a z-axis MEMS gyroscope

This paper reports a hybrid intelligent controller for application in single axis MEMS vibratory gyroscopes. First, unknown parameters of a micro gyroscope including unknown time varying angular velocity are estimated online via normalized continuous time least mean squares algorithm. Then, an additional interval type-2 fuzzy sliding mode control is incorporated in order to match the resonant frequencies and to compensate for undesired mechanical couplings. The main advantage of this control strategy is its robustness to parameters uncertainty, external disturbance and measurement noise. Consistent estimation of parameters is guaranteed and stability of the closed-loop system is proved via the Lyapunov stability theorem. Finally, numerical simulation is done in order to validate the effectiveness of the proposed method, both for a constant and time-varying angular rate.     

Type-2 fuzzy model based controller design for neutralization processes

In this study, an inverse controller based on a type-2 fuzzy model control design strategy is introduced and this main controller is embedded within an internal model control structure. Then, the overall proposed control structure is implemented in a pH neutralization experimental setup. The inverse fuzzy control signal generation is handled as an optimization problem and solved at each sampling time in an online manner. Although, inverse fuzzy model controllers may produce perfect control in perfect model match case and/or non-existence of disturbances, this open loop control would not be sufficient in the case of modeling mismatches or disturbances. Therefore, an internal model control structure is proposed to compensate these errors in order to overcome this deficiency where the basic controller is an inverse type-2 fuzzy model. This feature improves the closed-loop performance to disturbance rejection as shown through the real-time control of the pH neutralization process. Experimental results demonstrate the superiority of the inverse type-2 fuzzy model controller structure compared to the inverse type-1 fuzzy model controller and conventional control structures.     

A novel practical control approach for rate independent hysteretic systems

A disturbance rejection based control approach, active disturbance rejection control (ADRC), is proposed for hysteretic systems with unknown characteristics. It is an appealing alternative to hysteresis compensation because it does not require a detailed model of hysteresis, by treating the nonlinear hysteresis as a common disturbance and actively rejecting it. The stability characteristic of the ADRC is analyzed. It is shown that, in the face of the inherent dynamic uncertainties, the estimation and closed-loop tracking errors of ADRC are bounded, with their bounds monotonously decreasing with the observer and controller bandwidths, respectively. Simulation results on a typical hysteretic system further demonstrate the effectiveness of the proposed approach.     

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.     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.     

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.     

Robust inertia-free attitude takeover control of postcapture combined spacecraft with guaranteed prescribed performance

In this paper, a robust inertia-free attitude takeover control scheme with guaranteed prescribed performance is investigated for postcapture combined spacecraft with consideration of unmeasurable states, unknown inertial property and external disturbance torque. Firstly, to estimate the unavailable angular velocity of combination accurately, a novel finite-time-convergent tracking differentiator is developed with a quite computationally achievable structure free from the unknown nonlinear dynamics of combined spacecraft. Then, a robust inertia-free prescribed performance control scheme is proposed, wherein, the transient and steady-state performance of combined spacecraft is first quantitatively studied by stabilizing the filtered attitude tracking errors. Compared with the existing works, the prominent advantage is that no parameter identifications and no neural or fuzzy nonlinear approximations are needed, which decreases the complexity of robust controller design dramatically. Moreover, the prescribed performance of combined spacecraft is guaranteed a priori without resorting to repeated regulations of the controller parameters. Finally, four illustrative examples are employed to validate the effectiveness of the proposed control scheme and tracking differentiator.     

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.     

Fixed-time output feedback trajectory tracking control of marine surface vessels subject to unknown external disturbances and uncertainties

This paper proposes a novel fixed-time output feedback control scheme for trajectory tracking of marine surface vessels (MSVs) subject to unknown external disturbances and uncertainties. A fixed-time extended state observer (FESO) is proposed to estimate unknown lumped disturbances and unmeasured velocities, and the observation errors will converge to zero in fixed time. Based on the estimated values, a novel fixed-time trajectory tracking controller is designed for an MSV to track a time-varying reference trajectory by the extension of an adding a power integrator (API), and the tracking errors can converge to zero in fixed time as well. Additionally, the convergence time of the controller and the FESO is independent of initial state values. Finally, simulation results and comparisons illustrate the superiority of the proposed control scheme.     

Finite-time extended dissipative control for fuzzy systems with nonlinear perturbations via sampled-data and quantized controller

This paper investigates the problem of finite-time extended dissipative control for T–S fuzzy time-varying delay systems with nonlinear perturbations via sampled-data and quantized controller. The definition of finite-time bounded mixed extended dissipative of fuzzy systems is first proposed. Based on the constructed Lyapunov–Krasovskii functional(LKF) and Peng–Parks integral inequality, some sufficient conditions are obtained in the form of linear matrix inequalities(LMIs), which are less conservative than other papers. By combining the input delay approach and dynamic quantizer, the sampled-data and quantized controller is designed to guarantee that the T–S fuzzy system is finite-time bounded mixed extended dissipative. Finally, some numerical examples and practical examples are presented to verify the feasibility and effectiveness of the proposed methods.     

车辆四轮转向控制平台研究

针对机-电-液复合结构的四轮转向平台具有非线性、快时变的特点，提出了模糊自适应PID控制策略。将模糊自适应补偿器与PID控制器并联，提高系统的鲁棒性和抗干扰能力。使用PID控制器稳定系统的线性标称部分，应用模糊自适应补偿器调节PID参数来补偿系统参数摄动、非线性和外界扰动对系统控制性能的影响。仿真和外加扰动实验结果验证了提出的控制策略对四轮转向平台的控制具有快速性、准确性、稳定性和鲁棒性。     

四相平板式TFPM模糊PID控制系统的设计

针对四相平板式横向磁场永磁电机非线性、时变性的特点,采用单一传统的PID控制无法达到满意的控制效果,提出了一种复合控制即模糊PID控制算法。借助于模块化建模仿真工具搭建系统仿真模型,进行模糊PID与传统PID控制的对比研究,仿真结果表明模糊PID控制精度高,动态响应速度快,静态误差小,对外部扰动(负载扰动)具有很强抑制能力并且对电机参数变化也具有较强的自适应性。解决了四相平板式横向磁场永磁电机非线性、时变性特点的控制问题。     

Parametric adaptive estimation and backstepping control of electro-hydraulic actuator with decayed memory filter

Some unknown parameter estimation of electro-hydraulic system (EHS) should be considered in hydraulic controller design due to many parameter uncertainties in practice. In this study, a parametric adaptive backstepping control method is proposed to improve the dynamic behavior of EHS under parametric uncertainties and unknown disturbance (i.e., hydraulic parameters and external load). The unknown parameters of EHS model are estimated by the parametric adaptive estimation law. Then the recursive backstepping controller is designed by Lyapunov technique to realize the displacement control of EHS. To avoid explosion of virtual control in traditional backstepping, a decayed memory filter is presented to re-estimate the virtual control and the dynamic external load. The effectiveness of the proposed controller has been demonstrated by comparison with the controller without adaptive and filter estimation. The comparative experimental results in critical working conditions indicate the proposed approach can achieve better dynamic performance on the motion control of Two-DOF robotic arm.     

基于环境刚度模糊自适应估计的机器人力控制

在未知环境中为实现精确的接触力控制,需要力控制器能够适应环境的变化。该文将多模型模糊控制器引入到机器人力控制中来适应未知环境的变化,针对几种典型的接触环境刚度设计相应的模糊控制器。由于在环境变化时,很难得到精确的环境刚度值,该文对环境刚度进行模糊自适应估计,进而确定各个模糊力控制器的加权系数,模糊力控制器生成机器人位置控制系统的输入指令。仿真研究表明所设计的控制器是可行和有效的。     

基于模糊神经网络的不确定机器人实时轨迹跟踪控制的研究

针对机器人建模的不精确性以及扰动的存在给机器人控制增加难度的问题,提出了一种基于模糊神经网络的不确定机器人实时轨迹跟踪控制方法。该控制方法的控制器由模糊神经网络(FNN)控制器和CMAC控制器组成,FNN控制器代替传统的计算力矩法,CMAC控制器在线补偿控制误差,有效补偿机器人存在的各种不确定性。对二自由度机器人的仿真结果表明了所提出的控制方法的可行性。