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.     

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.     

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.     

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.     

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     

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.     

一种新的模糊PID控制器的优化及其仿真研究

该文提出了一种新的最优模糊PID控制器。该控制器由两部分组成,一部分是常规PID控制器,另一部分是在线模糊推理机构。在模糊推理机构中,引入了三个可调节因子Xp,Xj,和Xd,其作用是优化模糊推理结果,该模糊PID控制器用来控制智能人工腿中的一个直线电机,并已获得很好的控制效果。