Comments on “Design of two-layered fractional order fuzzy logic controllers applied to robotic manipulator with variable payload”

Sharma et al. have investigated the performance of two-layered fractional order fuzzy logic controller (TL-FOFLC) for a 2-link rigid planer robotic manipulator with payload. In this work, the performance of TL-FOFLC has been compared with two-layered FLC (TL-FLC), single-layered FLC (SL-FLC) and the conventional proportional-integral-derivative (PID) controllers, for trajectory tracking, model uncertainties and disturbance rejection. In this comment, it is pointed out that this work has several missing essential parameters, and therefore, it is not possible for the reader to validate all the claimed results of Sharma et al. (2016). Six numerical values, three gains for each of the used two PID controllers are found to be unreported in addition to the six gains for each of the used two SL-FLCs. Since the performances of the PIDs and the SL-FLCs are highly dependent on their tuned gains it is concluded that the reported performances of these controllers cannot be validated.     

Symbiotic organisms search algorithm for optimal evolutionary controller tuning of fractional fuzzy controllers

With the development of technology and the practical needs of complex engineering applications, fuzzy controllers have been widely applied. In contrast to a traditional integer-order fuzzy controller, a fractional fuzzy controller can extend the integral and differential order of a fuzzy controller to any real number, which describes the controlled object more accurately and enhances its control performance. However, a fractional fuzzy controller has a larger number of control parameters, which makes it difficult to calibrate. Because the parameter controller tuning values of the fuzzy controller clearly influence its control performance, this paper proposes to optimize the parameter controller tuning process using the symbiotic organisms search algorithm. A large number of simulation tests were carried out to compare the symbiotic organisms search-based parameter controller tuning method with parameter controller tuning based on five other representative swarm intelligence algorithms. The experimental results show that the symbiotic organisms search algorithm better optimizes the parameters of the fractional fuzzy controller.     

分数阶模糊免疫PID控制器的设计

为改善分数阶PID控制器的控制性能,借鉴整数阶模糊免疫PID控制器,把模糊免疫调节与分数阶PID控制器结合起来,设计了分数阶模糊免疫PID控制器。仿真结果表明了该方法的有效性,不但提高了分数阶PID控制器跟踪性能,而且还具有良好的鲁棒性和抗干扰性。     

Fractional order [proportional derivative] controller for a class of fractional order systems

Recently, fractional order systems (FOS) have attracted more and more attention in various fields. But the control design techniques available for the FOS suffer from the lack of direct systematic approaches. In this paper, we focus on a given type of simple model of FOS. A fractional order [proportional derivative] (FO-[PD]) controller is proposed for this class of FOS, and a practical and systematic tuning procedure has been developed for the proposed FO-[PD] controller synthesis. The fairness issue in comparing with other controllers such as the traditional integer order PID (IO-PID) controller and the fractional order proportional derivative (FO-PD) controller has been addressed under the same number of design parameters and the same specifications. Fair comparisons of the three controllers (i.e., IO-PID, FO-PD and FO-[PD]) via the simulation tests illustrate that, the IO-PID controller designed may not always be stabilizing to achieve flat-phase specification while both FO-PD and FO-[PD] controllers designed are always stabilizing. Furthermore, the proposed FO-[PD] controller outperforms FO-PD controller for the class of fractional order systems.     

Design of internal model control based fractional order PID controller

This article presents a design of the internal model control(IMC)based single degree of freedom(SDF) fractional order(FO)PID controller with a desired bandwidth specification for a class of fractional order system(FOS). The drawbacks of the SDF FO-IMC are eliminated with the help of the two-degree of freedom(TDF)FO PID controller. The robust stability and robust performance of the designed controller are analyzed using an example.     

Tuning and auto-tuning of fractional order controllers for industry applications

This paper deals with the design of fractional order PI^λD^μ controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfill additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the PI^λD^μ controller is proposed in this paper to fulfill five different design specifications. Experimental results show that the requirements are totally met for the platform to be controlled. Besides, this paper proposes an auto-tuning method for this kind of controller. Specifications of gain crossover frequency and phase margin are fulfilled, together with the iso-damping property of the time response of the system. Experimental results are given to illustrate the effectiveness of this method.     

Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

A memetic algorithm applied to trajectory control by tuning of Fractional Order Proportional-Integral-Derivative controllers

This paper introduces a novel memetic algorithm namely Fractional Particle Swarm Optimization-based Memetic Algorithm (FPSOMA) to solve optimization problem using fractional calculus concept. The FC illustrates a potential for interpreting progression of the algorithm by controlling its convergence. The FPSOMA accomplishes global search over the whole search space through PSO whereas local search is performed by PSO with fractional order velocity to alter the memory of best location of the particles. To assess the performance of the proposed algorithm, firstly an empirical comparison study is presented for solving different test functions adopted from literature. Comparisons demonstrate the preference of FPSOMA than other related algorithms. Subsequently, experiments are conducted to achieve optimal gains of Fractional Order Proportional-Integral-Derivative (FO PID) controller in solving tracking problem. Results verify the efficiency of the proposed algorithm.     

Design of a PID optimized neural networks and PD fuzzy logic controllers for a two‐wheeled mobile robot

In this paper, two intelligent techniques for a two‐wheeled differential mobile robot are designed and presented: A smart PID optimized neural networks based controller (SNNPIDC) and a PD fuzzy logic controller (PDFLC). Basically, mobile robots are required to work and navigate under exigent circumstances where the environment is hostile, full of disturbances such as holes and stones. The robot navigation leads to an autonomous decision making to overcome an obstacle and/or to stop the engine to protect it. In fact, the actuators that drive the robot should in no way be damaged and should stop to change direction in case of insurmountable disturbances. In this context, two controllers are implemented and a comparative study is carried out to demonstrate the effectiveness of the proposed approaches. For the first one, neural networks are used to optimize the parameters of a PID controller and for the second a fuzzy inference system type Mamdani based controller is adopted. The goal is to implement control algorithms for safe robot navigation while avoiding damage to the motors. In these two control cases, the smart robot has to quickly perform tasks and adapt to changing environment conditions while ensuring stability and accuracy and must be autonomous with regards to decision making. Simulations results aren't done in real environments, but are obtained with the Matlab/Simulink environment in which holes and stones are modeled by different load torques and are applied as disturbances on the mobile robot environment. These simulation results and the robot performances are satisfactory and are compared to a PID controller in which parameters are tuned by the Ziegler–Nichols tuning method. The applied methods have proven to be highly robust.     

Fuzzy logic based adaptive admittance control of a redundantly actuated ankle rehabilitation robot

Ankle rehabilitation robots have recently attracted great attention since they provide various advantages in terms of rehabilitation process from the viewpoints of patients and therapists. This paper presents development and evaluation of a fuzzy logic based adaptive admittance control scheme for a developed 2-DOF redundantly actuated parallel ankle rehabilitation robot. The proposed adaptive admittance control scheme provides the robot to adapt resistance/assistance level according to patients' disability level. In addition, a fuzzy logic controller (FLC) is developed to improve the trajectory tracking ability of the rehabilitation robot subject to external disturbances which possibly occur due to human-robot interaction. The boundary scales of membership functions of the FLC are tuned using cuckoo search algorithm (CSA). A classical proportional-integral-derivative (PID) controller is also tuned using the CSA to examine the performance of the FLC. The effectiveness of the adaptive admittance control scheme is observed in the experimental results. Furthermore, the experimental results demonstrate that the optimized FLC significantly improves the tracking performance of the ankle rehabilitation robot and decreases the steady-state tracking errors about 50% compared to the optimized PID controller. The performances of the developed controllers are evaluated using common error based performance indices indicating that the FLC has roughly 50% better performance than the PID controller.     

Control of a distillation column by type-2 and type-1 fuzzy logic PID controllers

The aim of this paper is to develop a type-1 and a type-2 fuzzy logic PID controller (type-1 FLC and type-2 FLC, respectively) for the control of a binary distillation column, the mathematical model of which is characterized by both high nonlinearities and parameter uncertainties. Attention was focused on the tuning procedure proposed by the authors and representing a development of the original Jantzen [1] method for type-1 and type-2 fuzzy controllers, in particular including input type-2 Gaussian membership functions. A theoretical explanation of the differences in fuzzy controller performance was in fact provided in the light of simulation results. The performance of a type-1 FLC was then compared in simulation with the one of type-2 FLC. All the simulation results confirmed the robustness and the effective control action of each fuzzy controller, with evident advantages for the type-2 FLC.     

Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains

The popular linear PID controller is mostly effective for linear or nearly linear control problems. Nonlinear PID controllers, however, are needed in order to satisfactorily control (highly) nonlinear plants, time-varying plants, or plants with significant time delay. This paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear PI, PD, and PID controllers with variable gains that can outperform their linear counterparts. In the present paper, we study the analytical structure of an important class of two- and three-dimensional fuzzy controllers. We link the entire class, as opposed to one controller at a time, to nonlinear PI, PD, and PID controllers with variable gains by establishing the conditions for the former to structurally become the latter. Unlike the results in the literature, which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables, this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types. Our structural results are thus more general and contain the existing ones as special cases. Two concrete examples are provided to illustrate the usefulness of the new results.     

含有分数阶PID控制器的随机动力系统可靠性分析

随着粘弹性材料在工程结构中的广泛应用,刻画工程结构中粘弹性材料遗传特性和长记忆性的分数阶微积分成为研究的热点,特别是具有分数阶微积分特点的PID控制器更是从理论上和应用上受到关注.本文研究高斯白噪声激励下含有分数阶PID控制器的随机结构动力系统的可靠性问题.利用慢变过程的特征以及广义积分的性质,对分数阶PID控制器在数学上进行了近似处理,之后应用能量包络随机平均法确定了可靠性函数满足的后向Kolmogorov方程以及首次穿越时间统计矩满足的广义Pontryagin方程.结果表明：在分数阶控制器中,较小的分数阶α和较大的分数阶β均可以得到较为理想的可靠性结果,并且这些均与蒙特卡洛仿真结果一致,验证了方法的有效性和正确性.     

Optimal design of interval type 2 fuzzy controllers based on a simple tuning algorithm

Evolutionary algorithms are one of the most common choices reported in the literature for the tuning of fuzzy logic controllers based on either type-1 or type-2 fuzzy systems. An alternative to evolutionary algorithms is the simple tuning algorithm (STA-FLC), which is a methodology designed to improve the response of type-1 fuzzy logic controllers in a practical, intuitive and simple ways. This paper presents an extension of the simple tuning algorithm for fuzzy logic controllers based on the theory of type-2 fuzzy systems by using a parallel model implementation, it also includes a mechanism to calculate the feedback gain, new integral criteria parameters, and the effect of the AND/OR operator combinations on the fuzzy rules to improve the algorithm applicability and performance. All these improvements are demonstrated with experiments applied to different types of plants.     

Integration of PSO and GA for optimum design of fuzzy PID controllers in a pendubot system

In this paper, a novel auto-tuning method is proposed to design fuzzy PID controllers for asymptotical stabilization of a pendubot system. In the proposed method, a fuzzy PID controller is expressed in terms of fuzzy rules, in which the input variables are the error signals and their derivatives, while the output variables are the PID gains. In this manner, the PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than the conventional ones with fixed gains. To tune the fuzzy PID controller simultaneously, an evolutionary learning algorithm integrating particle swarm optimization (PSO) and genetic algorithm (GA) methods is proposed. The simulation results illustrate that the proposed method is indeed more efficient in improving the asymptotical stability of the pendubot system. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

自适应模糊PID控制器在跟踪器瞄准线稳定系统中的应用

针对陀螺惯性平台上的跟踪器瞄准线稳定系统中非线性不确定因素对稳定精度的影响, 设计了一种自适应模糊PID复合控制策略. 提出了改进的自适应调整因子和学习算法进行控制参数和规则的在线修正; 采用PID控制克服模糊控制固有的精度盲区. 实验结果表明该方法在一定测量噪声和速度敏感范围内, 能有效地隔离载体扰动,保证跟踪器对目标的准确瞄准, 具有动态响应快、稳定精度高、自适应抗干扰鲁棒性强等特点.     

Design and analysis of a class of self-organizing and trainable fuzzy controllers

As the applications of fuzzy-controllers become more complicated, the attributes of self-organization and trainability become increasingly important. Indeed, the specification of fuzzy rules and membership functions for systems with a large number of state variables is extremely difficult. This paper introduces a new class of self-organizing and trainable fuzzy-controllers that can be designed without specific information regarding either the membership functions or the fuzzy rules. The proposed controller derives the fuzzy rules from clusters formed in the input space, through a self-organizing process. The clustering is performed through a simple method which can adaptively allocate new clusters as more date are available to the controller. Then, the membership values of crisp inputs are determined by K-nearest-neighbor (KNN) distance measures applied to the centers of the input clusters. Finally, a KNN defuzzification processes directly estimates of the crisp output of unknown input data. An adaptation procedure for the center vector of each cluster and the corresponding output value is developed. The overall design is analyzed in terms of the existence and the uniqueness of the solution of the proposed model. The performance of the proposed controller is considered through the modeling of the Mackey—Glass time-series.     

An optimal adaptive robust PID controller subject to fuzzy rules and sliding modes for MIMO uncertain chaotic systems

In this paper, an optimal adaptive robust PID controller based on fuzzy rules and sliding modes is introduced to present a general scheme to control MIMO uncertain chaotic nonlinear systems. In this control scheme, the gains of the PID controller are updated by using an adaptive mechanism, fuzzy rules, the gradient search method, and the chain rule of differentiation in order to minimize the sliding surfaces of sliding mode control. More precisely, sliding mode control is used as a supervisory controller to provide sufficient control inputs and guarantee the stability of the control approach. To ascertain the parameters of the proposed controller and avoid trial and error, the multi-objective genetic algorithm is employed to augment the performance of proposed controller. The chaotic system of a Duffing-Holmes oscillator and an industrial robotic manipulator are the case studies to evaluate the performance of the proposed control approach. The obtained results of this study regarding both systems are compared with the outcomes of two notable studies in the literature. The results and analysis prove the efficiency of the proposed controller with regard to MIMO uncertain systems having challenging external disturbances in terms of stability, minimum tracking error and optimal control inputs.     

Efficient control of a 3-link planar rigid manipulator using self-regulated fractional-order fuzzy PID controller

A self-regulated fractional-order fuzzy proportional–integral–derivative (SRFOFPID) controller is proposed to control a highly non-linear, complex and coupled 3-link planar rigid robotic manipulator in a virtual industrial environment. Industrial environment was simulated by introducing different kind of disturbances in the system and sensor noise. Proposed SRFOFPID controller is a direct non-linear adaptive controller having self-regulating feature and has been realized using fractional-order operators i.e. integrator and differentiator in self-regulated integer-order fuzzy PID (SRIOFPID) controller. Gains of SRFOFPID and SRIOFPID controllers are optimized using Backtracking Search Algorithm by minimizing an amalgamation of integral absolute error signal and integral absolute change in control signal as cost function. Performance of SRFOFPID and SRIOFPID controllers are assessed and compared with reference path under virtually simulated industrial environment. Presented intensive simulation studies revealed that both the controllers offered decent reference trajectory tracking performance under nominal operating conditions while SRFOFPID controller offered exceptionally robust performance under industrial scenario and uncertainties. Finally, the stability analysis of overall closed loop system is performed using small gain theorem and necessary and sufficient bounded-input and bounded-output stability conditions are established.     

Performance improvement of aircraft pitch angle control using a new reduced order fractionalized PID controller

In this paper, a new optimal reduced order fractionalized PID (ROFPID) controller based on the Harris Hawks Optimization Algorithm (HHOA) is proposed for aircraft pitch angle control. Statistical tests, analysis of the index of performance, and disturbance rejection, as well as transient and frequency responses, were all used to validate the effectiveness of the proposed approach. The performance of the proposed HHOA-ROFPID and HHOA-ROFPID controllers with Oustaloup and Matsuda approximations was then compared not only to the PID controller tuned by the original HHO algorithm but also to other controllers tuned by cutting-edge meta-heuristic algorithms such as the atom search optimization algorithm (ASOA), Salp Swarm Algorithm (SSA), sine-cosine algorithm (SCA), and Grey wolf optimization algorithm (GOA). Simulation results show that the proposed controller with the Matsuda approximation provides better and more robust performance compared to the proposed controller with the Oustaloup approximation and other existing controllers in terms of percentage overshoot, settling time, rise time, and disturbance rejection.