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.     

A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots

Autonomous mobile robots navigating in changing and dynamic unstructured environments like the outdoor environments need to cope with large amounts of uncertainties that are inherent of natural environments. The traditional type-1 fuzzy logic controller (FLC) using precise type-1 fuzzy sets cannot fully handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. In this paper, we present a novel reactive control architecture for autonomous mobile robots that is based on type-2 FLC to implement the basic navigation behaviors and the coordination between these behaviors to produce a type-2 hierarchical FLC. In our experiments, we implemented this type-2 architecture in different types of mobile robots navigating in indoor and outdoor unstructured and challenging environments. The type-2-based control system dealt with the uncertainties facing mobile robots in unstructured environments and resulted in a very good performance that outperformed the type-1-based control system while achieving a significant rule reduction compared to the type-1 system.     

Type-2 fuzzy control for a flexible-joint robot using voltage control strategy

Type-1 fuzzy sets cannot fully handle the uncertainties. To overcome the problem, type-2 fuzzy sets have been proposed. The novelty of this paper is using interval type-2 fuzzy logic controller (IT2FLC) to control a flexible-joint robot with voltage control strategy. In order to take into account the whole robotic system including the dynamics of actuators and the robot manipulator, the voltages of motors are used as inputs of the system. To highlight the capabilities of the control system, a flexible joint robot which is highly nonlinear, heavily coupled and uncertain is used. In addition, to improve the control performance, the parameters of the primary membership functions of IT2FLC are optimized using particle swarm optimization (PSO). A comparative study between the proposed IT2FLC and type-1 fuzzy logic controller (T1FLC) is presented to better assess their respective performance in presence of external disturbance and unmodelled dynamics. Stability analysis is presented and the effectiveness of the proposed control approach is demonstrated by simulations using a two-link flexible-joint robot driven by permanent magnet direct current motors. Simulation results show the superiority of the IT2FLC over the T1FLC in terms of accuracy, robustness and interpretability.     

基于FPSO的电力巡检机器人的广义二型模糊逻辑控制

针对电力巡检机器人(Power-line inspection robot, PLIR)的平衡调节问题, 设计了广义二型模糊逻辑控制器(General type-2 fuzzy logic controller, GT2FLC); 针对GT2FLC中隶属函数参数难以确定的问题, 通过模糊粒子群(Fuzzy particle swarm optimization, FPSO)算法来优化隶属函数参数. 将GT2FLC的控制性能与区间二型模糊逻辑控制器(Interval type-2 fuzzy logic controller, IT2FLC)和一型模糊逻辑控制器(Type-1 fuzzy logic controller, T1FLC) 的控制性能进行对比. 除此之外, 还考虑了外部干扰对三种控制器控制效果的影响. 仿真结果表明, GT2FLC具有更好的性能和处理不确定性的能力.     

Type-2 fuzzy multi-intersection traffic signal control with differential evolution optimization

This paper proposes a multi-agent type-2 fuzzy logic control (FLC) method optimized by differential evolution (DE) for multi-intersection traffic signal control. Type-2 fuzzy sets can deal with models’ uncertainties efficiently because of its three-dimensional membership functions, but selecting suitable parameters of membership functions and rule base is not easy. DE is adopted to decide the parameters in the type-2 fuzzy system, as it is easy to understand, simple to implement and possesses low space complexity. In order to avoid the computational complexity, the expert rule base and the parameters of membership functions (MF) are optimized by turns. An eleven-intersection traffic network is studied in which each intersection is governed by the proposed controller. A secondary layer controller is set in every intersection to select the proper phase sequence. Furthermore, the communication among the adjacent intersections is implemented using multi-agent system. Simulation experiments are designed to compare communicative type-2 FLC optimized by DE with type-1 FLC, fixed-time signal control, etc. Experimental results indicate that our proposed method can enhance the vehicular throughput rate and reduce delay, queue length and parking rate efficiently.     

Type-2 FLCs: A New Generation of Fuzzy Controllers

Type-1 fuzzy logic controllers (FLCs) have been applied to date with great success to many different applications. However, for dynamic unstructured environments and many real-world applications, there is a need to cope with large amounts of uncertainties. The traditional type-1 FLC using crisp type-1 fuzzy sets cannot directly handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. Hence, type-2 FLCs will have the potential to overcome the limitations of type-1 FLCs and produce a new generation of fuzzy controllers with improved performance for many applications, which require handling high levels of uncertainty. This paper introduces briefly the interval type-2 FLC and its benefits. We also present briefly the type-2 FLC application to three challenging domains: industrial control, mobile robots control and ambient intelligent environments control     

Design of interval type-2 fuzzy sliding-mode controller

In this paper, an interval type-2 fuzzy sliding-mode controller (IT2FSMC) is proposed for linear and nonlinear systems. The proposed IT2FSMC is a combination of the interval type-2 fuzzy logic control (IT2FLC) and the sliding-mode control (SMC) which inherits the benefits of these two methods. The objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the interval type-2 fuzzy sliding-mode controller system. The design procedure of the IT2FSMC is explored in detail. A typical second order linear interval system with 50% parameter variations, an inverted pendulum with variation of pole characteristics, and a Duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method. The simulation results show that the IT2FSMC achieves the best tracking performance in comparison with the type-1 Fuzzy logic controller (T1FLC), the IT2FLC, and the type-1 fuzzy sliding-mode controller (T1FSMC).     

Interval Type-2 Fuzzy Hierarchical Adaptive Cruise Following-Control for Intelligent Vehicles

Intelligent vehicles can effectively improve traffic congestion and road traffic safety. Adaptive cruise following-control (ACFC) is a vital part of intelligent vehicles. In this paper, a new hierarchical vehicle-following control strategy is presented by synthesizing the variable time headway model, type-2 fuzzy control, feedforward + fuzzy proportion integration (PI) feedback (F+FPIF) control, and inverse longitudinal dynamics model of vehicles. Firstly, a traditional variable time headway model is improved considering the acceleration of the lead car. Secondly, an interval type-2 fuzzy logic controller (IT2 FLC) is designed for the upper structure of the ACFC system to simulate the driver’s operating habits. To reduce the nonlinear influence and improve the tracking accuracy for the desired acceleration, the control strategy of F+FPIF is given for the lower control structure. Thirdly, the lower control method proposed in this paper is compared with the fuzzy PI control and the traditional method (no lower controller for tracking desired acceleration) separately. Meanwhile, the proportion integration differentiation (PID), linear quadratic regulator (LQR), subsection function control (SFC) and type-1 fuzzy logic control (T1 FLC) are respectively compared with the IT2 FLC in control performance under different scenes. Finally, the simulation results show the effectiveness of IT2 FLC for the upper structure and F+FPIF control for the lower structure.      

A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization

In this study, we introduce the design methodology of an optimized fuzzy controller with the aid of particle swarm optimization (PSO) for ball and beam system.The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball and beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor.The fixed membership function design of type-1 based fuzzy logic controller (FLC) leads to the difficulty of rule-based control design when representing linguistic nature of knowledge. In type-2 FLC as the expanded type of type-1 FL, we can effectively improve the control characteristic by using the footprint of uncertainty (FOU) of the membership functions. Type-2 FLC exhibits some robustness when compared with type-1 FLC.Through computer simulation as well as real-world experiment, we apply optimized type-2 fuzzy cascade controllers based on PSO to ball and beam system. To evaluate performance of each controller, we consider controller characteristic parameters such as maximum overshoot, delay time, rise time, settling time, and a steady-state error. In the sequel, the optimized fuzzy cascade controller is realized and also experimented with through running two detailed comparative studies including type-1/type-2 fuzzy controller and genetic algorithms/particle swarm optimization.     

Control of a non-isothermal continuous stirred tank reactor by a feedback-feedforward structure using type-2 fuzzy logic controllers

A control system that uses type-2 fuzzy logic controllers (FLC) is proposed for the control of a non-isothermal continuous stirred tank reactor (CSTR), where a first order irreversible reaction occurs and that is characterized by the presence of bifurcations. Bifurcations due to parameter variations can bring the reactor to instability or create new working conditions which although stable are unacceptable. An extensive analysis of the uncontrolled CSTR dynamics was carried out and used for the choice of the control configuration and the development of controllers. In addition to a feedback controller, the introduction of a feedforward control loop was required to maintain effective control in the presence of disturbances. Simulation results confirmed the effectiveness and the robustness of the type-2 FLC which outperforms its type-1 counterpart particularly when system uncertainties are present.     

Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches

In this paper, the type-2 fuzzy logic system (T2FLS) controller using the feedback error learning (FEL) strategy has been proposed for load frequency control (LFC) in the restructure power system. The original FEL strategy consists of an intelligent feedforward controller (INFC) (i.e. artificial neural network (ANN)) and the conventional feedback controller (CFC). The CFC acting as a general feedback controller to guarantee the stability of the system plays a crucial role in the transient state. The INFC is adopted in forward path to take over the control problem in the steady state. In this work, to improve the performance of the FEL strategy, the T2FLS is adopted instead of ANN in the INFC part due to its ability to model uncertainties, which may exist in the rules and measured data of sensors more effectively. The proposed FEL controller has been compared with a type-1 fuzzy logic system (T1FLS) – based FEL controller and the proportional, integral and derivative (PID) controller to highlight the effectiveness of the proposed method.     

基于量子粒子群的斜坡上两轮移动机器人的广义二型模糊控制

两轮移动机器人(2WMR)本身具有多变量和非线性等特征,从而使其控制变得复杂。当2WMR在倾斜的表面上移动时,控制问题变得更加复杂。针对2WMR的非线性模型,设计2WMR的广义二型模糊逻辑平衡控制器和位置控制器。针对广义二型模糊逻辑控制器(GT2FLC)中前、后件中参数难以设定的问题,通过量子粒子群算法(QPSO)优化隶属函数中的参数。针对GT2FLC和区间二型模糊逻辑控制器(IT2FLC)在不同斜面上对移动2WMR的平衡和位置控制的效果进行进一步的对比分析,并干扰对控制效果的影响。仿真结果表明,GT2FLC具有更好的抗干扰能力。     

Interval Type-2 Fuzzy Logic PID Controller Based on Differential Evolution with Better and Nearest Option for Hydraulic Serial Elastic Actuator

Interval type-2 fuzzy logic controller (IT2FLC) owns good performance under uncertainty and nonlinearity environments while its optimization is hard and complicated. In this work, we propose an optimization method based on differential evolution with better and nearest option (NbDE) for interval type-2 fuzzy logic PID controller (IT2FL-PID-C) in order to control the position of hydraulic serial elastic actuator (SEA). Firstly, a simplified IT2FL-PID-C structure with fewer parameters is proposed to reduce the difficulty of the optimization of IT2FL-PID-C. To balance its frequency and step performance, an objective function with weighted integral time absolute error and integral square error is given. Secondly, to investigate the performance of NbDE based IT2FL-PID-C, three experiments are conducted. A set of experiments is taken to determine the weight for fitness function. Then we compare NbDE with other algorithms. In addition, NbDE-IT2FL-PID-C is also compared with other optimization methods. At last, NbDE-IT2FL-PID-C is applied to hydraulic SEA and compared with PID. And a range for the weight of fitness function is given. The results have shown the superiority of NbDE with proposed fitness function to optimize IT2FL-PID-C and the superiority of NbDE-IT2FL-PID-C to control the position of hydraulic SEA.

     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

基于改进QPSO的两轮移动机器人区间二型模糊逻辑控制

以两轮移动机器人(TWMR)为对象,针对机器人的非线性模型分别设计控制机器人平衡和位置的区间二型模糊逻辑控制器(IT2 FLC).针对区间二型模糊规则中参数难以设定的问题,通过改进的量子粒子群算法(LTQPSO)优化区间二型模糊集参数,并给出优化算法的流程图.针对区间二型模糊逻辑控制器和一型模糊逻辑控制器(T1 FLC)对平衡和位置的控制效果进行对比.进一步考虑质量不确定和位置扰动对两种控制器控制效果的影响.仿真结果表明,IT2 FLC可以有效地达到设定的控制目标,与T1 FLC相比,IT2 FLC拥有更好的处理不确定性的能力以及更强的抗扰动能力.     

Interval type 2 hierarchical FNN with the H-infinity condition for MIMO non-affine systems

To develop a controller that deals with noise-corrupted training data and rule uncertainties for interconnected multi-input–multi-output (MIMO) non-affine nonlinear systems with unmeasured states, an interval type-2 fuzzy system is integrated with an observer-based hierarchical fuzzy neural controller (IT2HFNC) in this paper. Also, an H_∞ control technique and a strictly positive real Lyapunov (SPR-Lyapunov) design approach are employed for attenuating the influence of both external disturbances and fuzzy logic approximation error on the tracking of errors. Moreover, the proposed hierarchical fuzzy structure can greatly reduce the number of adjusted parameters of the IT2HFNC, and then, the problem of online computational burden can be solved. According to the design of the interval type-2 fuzzy neural network and H_∞ control technique, the IT2HFNN controller can improve its robustness to noise, uncertainties, approximation errors, and external disturbances. Simulation results are reported to show the performance of the proposed control system mode and algorithms.     

Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems

A fuzzy logic controller equipped with a training algorithm is developed such that the H^∞ tracking performance should be satisfied for a model-free nonlinear multiple-input multiple-output (MIMO) system, with external disturbances. Due to universal approximation theorem, fuzzy control provides nonlinear controller, i.e., fuzzy logic controllers, to perform the unknown nonlinear control actions and the tracking error, because of the matching error and external disturbance is attenuated to arbitrary desired level by using H^∞ tracking design technique. In this paper, a new direct adaptive interval type-2 fuzzy controller is developed to handle the training data corrupted by noise or rule uncertainties for nonlinear MIMO systems involving external disturbances. Therefore, linguistic fuzzy control rules can be directly incorporated into the controller and combine the H^∞ attenuation technique. Simulation results show that the interval type-2 fuzzy logic system can handle unpredicted internal disturbance, data uncertainties, very well, but the adaptive type-1 fuzzy controller must spend more control effort in order to deal with noisy training data. Furthermore, the adaptive interval type-2 fuzzy controller can perform successful control and guarantee the global stability of the resulting closed-loop system and the tracking performance can be achieved.     

Robustness of fuzzy logic control for an uncertain dynamic system

Based on the similarity between prevalent fuzzy logic controllers (FLC) and the conventional robust controller, i.e., the variable structure controller, control theoretic analysis of a fuzzy control system is presented in the sense of Lyapunov. As well as the robustness of the fuzzy control system against uncertainties of a controlled process, this analysis gives an account of the relationship between control performance and the design parameters of the FLC, which has been obscure in the theory of fuzzy control     

Fuzzy sliding mode control for a robot manipulator

This work presents the design of a robust control system using a sliding mode controller that incorporates a fuzzy control scheme. The presented control law superposes a sliding mode controller and a fuzzy logic controller. A fuzzy tuning scheme is employed to improve the performance of the control system. The proposed fuzzy sliding mode control (FSMC) scheme utilizes the complementary cooperation of the traditional sliding mode control (SMC) and the fuzzy logic control (FLC). In other words, the proposed control scheme has the advantages which it can guarantee the stability in the sense of Lyapunov function theory and can ameliorate the tracking errors, compared with the FLC and SMC, respectively. Simulation results for the trajectory tracking control of a two-link robot manipulator are presented to show the feasibility and robustness of the proposed control scheme. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008