Interval Type-2 Fuzzy PID Controller Research Articles

Optimization of a fractional-order interval type-2 fuzzy PID controller based on BBO for real-time applications

This paper addresses the development of a robust controller for a nonlinear system to minimize the tracking errors and reduce the effects of external noise and disturbances. To achieve this, the biogeography-based optimization (BBO) algorithm is utilized for an optimally robust interval type 2 fractional-order fuzzy proportional integral derivative controller (BB0-IT2FO-FPID) is proposed. The proposed method offers several advantages. Firstly, the proposed controller is optimized to achieve robustness and minimize tracking errors. Secondly, it effectively handles external noise and disturbances, making it suitable for real-world applications. Thirdly, the use of the BBO algorithm enhances the controller's performance by dynamically adjusting its parameters based on system requirements. The performance of the proposed controller is validated by applying it to control a robotic manipulator, which presents challenges due to its nonlinear characteristics and interacting multi-input multi-output (MIMO) dynamics. Additionally, a real-time evaluation of the proposed controller is conducted by applying it to the speed control of a direct current (DC) machine. The effectiveness of the proposed controller is verified through simulation and practical experiments and comparisons with other optimized controllers, namely FO fuzzy type 1 PID (T1FO-FPID) and FOPID. The simulation and practical results demonstrate the superior performance of the BBO-IT2FO-FPID controller in the presence of system uncertainties and different types of disturbances.

An interval type-3 fuzzy PID control system design and its application in solid oxide fuel cells power plant

Compared with type-2 fuzzy sets, the secondary membership degree of interval type-3 fuzzy sets is an interval rather than crisp value, which makes interval type-3 fuzzy sets can obtain more degree of freedoms. This article studies an interval type-3 fuzzy PID controller based on interval type-3 fuzz sets. The framework of interval type-3 fuzzy PID controller is identical with type-2 fuzzy PID controller, but it contains more adjustment controller parameters and its type reduction procedure is more complex. In this paper, type reduction of interval type-3 fuzzy sets is derived from general type-2 fuzzy sets represented by α-plane and a direct NT type reduction algorithm is applied. The control effects of interval type-3 fuzzy PID controller are firstly tested by 2 nonlinear plants, the simulation results show that interval type-3 fuzzy PID controller has better control performance indexes than PID controller, type-1 fuzzy PID controller, interval type-2 fuzzy PID controller and general type-2 fuzzy PID controller. Furthermore, the interval type-3 fuzzy PID controller will be applied in rated voltage control of solid oxide fuel cells (SOFC) power plant. The output voltage control of SOFC is quite challenging because of the strong nonlinearity, limited fuel flow, and rapid variation of the load disturbance. The simulation results demonstrate the advantages and robustness of proposed interval type-3 fuzzy PID controller.

Modified Flower Pollination Optimization Based Design of Interval Type-2 Fuzzy PID Controller for Rotary Inverted Pendulum System

The Type 2 Fuzzy Logic System (T2FLS) is an enhanced form of the classical Fuzzy Logic System (FLS). The T2FLS based control technics demonstrated a lot of improvements for the past few decades. This is based on the advantage of its membership function (MF). Many experimental studies indicated the superiority of Type 2 Fuzzy Logic Controller (T2FLC) over the ordinary Type 1 Fuzzy Logic Controller (T1FLC), particularly in the event of non-linearities and complex uncertainties. However, the organized design method of T2FLCs is still an interesting problem in the control engineering community. This is due to the difficulties in computing the parameters associated it. A novel application of the Modified Flower Pollination (MFP) optimization algorithm in the design of T2FL is presented. The optimized Cascade Interval Type 2 Fuzzy PID Controller (IT2FPIDC) structure is proposed in this study. The best values of the parameters of the antecedent MFs and the PID gains of IT2FPIDC are found using the MFP algorithm. The MFP optimization technique was used because of its lower computational effort and high convergence speed, in view of the higher number of variables to be optimized in cascaded IT2FPIDC. The MFP-based Type-1 Fuzzy Proportional Integral Derivative Controller (T1FPIDC) is compared with the proposed MFP-based cascade-optimized IT2FPIDC. The rotary inverted pendulum (RIP) which is a non-minimum phase, non-linear, and unstable system is employed as a benchmark for testing the proposed controller. Balance and trajectory-tracking controls of the RIP are considered. Furthermore, the disturbance rejection ability of the proposed controller is analysed. The presented control methos is evaluated on the RIP manufactured by Quanser over many simulations and real-world experiments. The performance characteristics considered are steady state error (Ess), settling time (ts), maximum overshoot (Mp) and rise time (tr). The improvement of the effectiveness and robustness proposed controller in the presence of load disturbance, noise effects and parameter variation is shown.

Real-Time Interval Type-2 Fuzzy Control of an Unmanned Aerial Vehicle with Flexible Cable-Connected Payload

This study presents the design and real-time applications of an Interval Type-2 Fuzzy PID (IT2-FPID) control system on an unmanned aerial vehicle (UAV) with a flexible cable-connected payload in comparison to the PID and Type-1 Fuzzy PID (T1-FPID) counterparts. The IT2-FPID control has significant stability, disturbance rejection, and response time advantages. To prove and show these advantages, the DJI Tello, a commercial UAV, is used with a flexible cable-connected payload to test the robustness of PID, T1-FPID, and IT2-FPID controllers. First, the optimal coefficients of the compared controllers are found using the Big Bang–Big Crunch algorithm via the nonlinear UAV model without the payload. Second, once optimised, the controllers are tested using several scenarios, including disturbing the payload and the coverage path planning area to examine their robustness. Third, the controller performance results are evaluated according to reference achievement and point-based tracking under disturbances. Finally, the superiority of the IT2-FPID controller is shown via simulations and real-time experiments with a better overshoot, a faster settling time, and good properties of disturbance rejection compared with the PID and the T1-FPID controllers.

Input-output scaling factors tuning of type-2 fuzzy PID controller using multi-objective optimization technique

<abstract><p>The PID controller is a popular controller that is widely used in various industrial applications. On the other hand, the control problems in microgrids (MGs) are so challenging, because of natural disturbances such as wind speed changes, load variation, and changes in other sources. This paper proposes an input-output scaling factor tuning of interval type-2 fuzzy (IT2F) PID controller using a multi-objective optimization technique. The suggested controller is applied to an MG frequency regulation problem. In the introduced controller the effect of variations of renewable energies (REs) and other disturbances are taken into account, and the robustness is investigated. In the multi-objective scheme, some factors such as least overshoot, and minimum settling/rising time are considered. The simulations show that by considering the suitable adjustment the desired regulation accuracy is achieved, such that the frequency trajectory shows the desired overshoot, and settling/rising time.</p></abstract>

A simple modelling strategy for integer order and fractional order interval type-2 fuzzy PID controllers with their simulation and real-time implementation

This paper presents a simple approach to the mathematical modelling of the Integer Order (IO) and Fractional Order (FO) Interval Type-2 Fuzzy Proportional Integral Derivative (IT2FPID) controllers. In this approach, the control effort produced by the IT2FPID controller is obtained by combining the individual control efforts generated by the Interval Type-2 Fuzzy Proportional (IT2FP), Interval Type-2 Fuzzy Integral (IT2FI), and Interval Type-2 Fuzzy Derivative (IT2FD) controllers. The analytical structures of each of the IT2FPID components are unveiled using one-dimensional (1D) input space and without using any AND or OR operator. To the best of the authors’ knowledge, such a strategy was never used and is completely new for the modelling of the IT2FPID controllers. Properties, computational issues, and design guidelines of the newly obtained controllers are discussed, and their applicability is delineated using five simulation examples and one experimental case study. A chemical reactor plant, two fractional order plants, a nonlinear plant, and a Twin Rotor Multi Input Multi Output System (TRMS) are considered in the simulation study. The experimental study is conducted on an unstable nonlinear Magnetic Levitation System (MLS). Moreover, to exhibit the usefulness of the newly derived controllers, simulation and real-time results are also compared with the existing results available in the literature. As the proposed controllers are plant model-free, they can be used for other control applications also.

Development, experimental validation, and comparison of interval type-2 Mamdani fuzzy PID controllers with different footprints of uncertainty

Interval Type-2 Fuzzy PID (IT2FPID) controllers use Interval Type-2 Fuzzy Sets (IT2FSs). The difference between Type-1 Fuzzy PID (T1FPID) controllers and IT2FPID controllers is the Footprint of Uncertainty (FOU) which occurs due to the use of IT2FSs. FOU gives an extra degree of freedom to the controller structure, which is capable of handling uncertainty in the plant. However, the effect of FOU on the analytical structures of the IT2FPID controllers is not yet explored when uniformly/non-uniformly distributed multiple IT2FSs are used on the input side and uniformly/non-uniformly distributed multiple singleton fuzzy sets are considered on the output side of the controller. In this paper, controllers with three different types of FOUs and two different defuzzification methods are considered, and their analytical structures are derived. The suitability of the controllers is examined, and the properties of the suitable controllers are explored. Effects of FOU on the nonlinearity, gain, and computational aspects of the suitable controllers are studied. The applicability of proposed IT2FPID controllers is shown through simulation and real-time studies. The effectiveness of the proposed controllers is depicted by comparing their performances with that of the recently developed Integer Order Fuzzy PID (IOFPID) and Fractional Order Fuzzy PID (FOFPID) controllers.

Design of interval type-2 fuzzy fractional order PID controller based on particle swarm optimization

Abstract In this paper, an interval type-2 fuzzy fractional order PID controller (IT2F-FOPIDC) based on particle swarm optimization is proposed. The proposed controller has two adjustable degree of freedom parameters, so the control range of the controller parameters becomes larger and can control the controlled object more flexibly. Aiming at the difficult problem of many controller parameters and tuning, this paper introduces particle swarm optimization algorithm to optimize the controller parameters. In order to avoid the problems of long iteration time and high computational cost caused by Karnik-Mendel reduction algorithm, the enhanced iterative with stop condition algorithm is selected for the proposed controller. Finally, the proposed controller is applied to the second order systems with time delays. Simulation results show that the proposed strategy has faster response time and smaller oscillation amplitude, and its performance is better than fuzzy controller and interval type-2 fuzzy controller.

Observer-based interval type-2 fuzzy PID controller for PEMFC air feeding system using novel hybrid neural network algorithm-differential evolution optimizer

In this paper, a novel hybrid Neural Network Algorithm-Differential Evolution (NNA-DE) optimizer which integrates both NNA and DE is proposed. The proposed hybrid NNA-DE optimizer demonstrates better performance compared to the standard NNA and the other state-of-the-art optimization algorithms. The proposed hybrid NNA-DE algorithm is then employed for optimizing an observer-based interval type-2 fuzzy PID (OB-IT2FPID) controller applied to the proton exchange membrane fuel cell (PEMFC) air feeding system. The whole design parameters of the OB-IT2FPID controller including the scaling factors, interval type-2 membership function parameters and the footprint-of-uncertainty (FOU) are optimized using the proposed hybrid NNA-DE algorithm. The results show that the proposed NNA-DE optimized OB-IT2FPID controller achieves better performance in terms of set-point tracking, disturbance rejection and the time-domain performance indices. The robustness of the proposed NNA-DE optimized OB-IT2FPID controller against parametric uncertainty in the PEMFC air-feeding system is tested. The proposed controller demonstrated better robustness against parameter uncertainty in the system. Processor-in-the-Loop (PIL) approach is adopted to validate the performance of the proposed controller on embedded control hardware.

Modelling and analysis of an interval type-2 Mamdani fuzzy PID controller

From the last decade, modelling of Interval Type-2 (IT2) fuzzy controllers has become an exciting area of research in the field of control systems engineering. The input-output relationship of the fuzzy controller gives insights into the exact structure of the controller. From the literature, it is observed that IT2 fuzzy controllers handle plant uncertainty in a better way than their Type 1 (T1) counterparts due to the presence of additional Degree of Freedom (DoF) provided by the Footprint of Uncertainty (FoU) present in the membership functions of Interval Type-2 Fuzzy Sets (IT2FSs). Further, it is also noticed that controllers obtained with non-uniformly distributed fuzzy sets control the uncertain and nonlinear plants in a better way than their uniformly distributed counterparts. To take advantage of these two, in this study, the authors have made an attempt to unveil the exact input-output relationship of an Interval Type-2 Fuzzy PID (IT2FPID) controller, where the modelling is done using a particular type of FoU and non-uniformly distributed fuzzy sets. Apart from modelling, the properties of the newly derived controller are analysed. Moreover, to justify the theoretical development made in this manuscript, the applicability of the controller is shown through simulation, where an unstable chemical reactor plant with a large time delay is controlled. Finally, the effectiveness of the proposed controller is delineated by comparing its performance with that of some recently developed controllers.

Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller

Derivation and structural analysis of a three-input interval type-2 TS fuzzy PID controller

Application of Interval Type-2 Fuzzy PID Controller for Frequency Regulation of AC Islanded Microgrid Using Modified Equilibrium Optimization Algorithm

The questionable generation of solar power, wind sources and load demand makes AC microgrids increasingly complicated and presents the frequency oscillations. It is profoundly expected to build up power balance among generation and load demand by planning a suitable controller for frequency oscillations. Thus, in this research article, a novel approach is proposed by considering a modified equilibrium optimization algorithm (MEO) Algorithm-based Interval Type-2 Fuzzy proportional integral derivative Controller (IT2FPID) structure for the frequency control of an AC microgrid. The performance of the modified algorithm is tested by comparing it with the standard EO algorithm by considering various standard benchmark test functions. Further, the genuine utilization of the MEO algorithm is tried by planning an IT2FPID controller for frequency regulation of an AC microgrid. The supremacy of the MEO-based IT2FPID controller is introduced by comparing its outcomes with MEO-based Type-1 FPID, conventional PID, EO-based PID controller and observed that the proposed MEO-based IT2FPID controller is more effective.

Non-singleton interval type-2 fuzzy PID control for high precision electro-optical tracking system

In this paper, two non-singleton interval type-2 fuzzy PID (NIT2F-PID) controllers for the high precision electro-optical tracking system (ETS) are presented to improve anti-interference ability. Specifically, two types of non-singleton fuzzifiers, including type-1 (T1) and type-2 (T2), are considered to construct the proposed NIT2F-PID (N1IT2F-PID and N2IT2F-PID) controllers. Faced with the optimization problem of parameters, particle swarm optimization (PSO), quantum-behaved PSO (QPSO), weighted QPSO (WQPSO) and improved QPSO with adaptive coefficients (LTQPSO) are employed for comparison of convergence performance to optimize the parameters of controllers. In addition, to demonstrate the superiority of the proposed NIT2F-PID controllers, PID, singleton T1 fuzzy PID (ST1F-PID), singleton interval T2 fuzzy PID (SIT2F-PID), T1 non-singleton interval T2 fuzzy (N1IT2F) and T2 non-singleton interval T2 fuzzy (N2IT2F) controllers are also designed. All of these controllers are tested under the circumstances of step disturbance and sinusoidal disturbance. At last, a series of simulation analyses and experimental results explicitly show performance of proposed NIT2F-PID controllers are superior to their counterparts.

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.

Nature-inspired and hybrid optimization algorithms on interval Type-2 fuzzy controller for servo processes: a comparative performance study

In this paper, performance evaluations of six well-known nature-inspired algorithms have been reported containing genetic algorithm, cuckoo search, particle swarm optimization, differential evolution, bee colony, and combined particle swarm optimization and differential evolution (CPSODE) algorithms. Based on these optimization algorithms, input and output scaling factors of an interval Type-2 fuzzy PID controller (IT2-FLC) are chosen for closed-loop servo tracking. Optimal values of the scaling factors are chosen by minimization of the objective function which is defined based on the closed-loop controller performance criteria. A detailed comparative analysis is reported based on the simulation and experimental results. Performance analysis reveals that improved performance, reliability, robustness, and lesser noise sensitivity are reported by IT2-FLC with the optimal values obtained by the hybrid algorithm CPSODE.

A Fractional Order General Type-2 Fuzzy PID Controller Design Algorithm

Fractional order PID controller was received attentions in control problems for it had 2 freedom adjustable parameters. Practices had proved that better results could be obtained by introduction of fractional order PID in control problems. And in recently years, fractional order PID combined with fuzzy logic system was gradually got attention, the typical of which was fractional order type-1 fuzzy PID controller. For fractional order PID and fractional order type-1 fuzzy PID controller couldn't deal with the uncertainty of system, so fractional order interval type-2 fuzzy PID controller was applied to solve this problem. But interval type-2 fuzzy sets were a simplification of type-2 fuzzy sets, and there may be have the defect of information loss. A fractional order general type-2 fuzzy PID controller was proposed in this article. The proposed controller based on general type-2 fuzzy logic system, which can make full use of the advantages of general type-2 fuzzy logic system in describing the uncertainty of the system. The fractional order general type-2 fuzzy PID controller utilized a simplified type reduction called NT type reduction algorithm. The NT type reduction algorithm can get the defuzzification result directly and avoided iterative process as KM type reduction commonly used in interval type-2 fuzzy controller. The simulations of 3 processes and a practical inverted pendulum system show that fractional order general type-2 fuzzy PID controller can reduce overshoot, improve system response speed and accelerate system stability time in comparing with other controllers. Especially, when the system has disturbance, parameters uncertainty or structure uncertainty, the fractional order general type-2 fuzzy PID controller has better control effects than other compared controllers.

Mathematical analysis of a simplified general type-2 fuzzy PID controller

For the type reduction of general type-2 fuzzy PID controller is time consuming and the mathematical expression of general type-2 fuzzy PID controller is difficult to derived. So, a simplified general type-2 fuzzy PID (SGT2-FPID) controller is studied in this article. The SGT2-FPID controller adopts triangular function as the primary and secondary membership function. Then the primary membership degree of apex for the secondary membership degree will be applied to get the output of SGT2-FPID controller, which can reduce the computation complexity of general type-2 fuzzy controller type reduction. Furthermore, the mathematical expressions of SGT2-FPID controller, type-1 fuzzy PID controller and interval type-2 fuzzy PID controller are discussed. Finally, 4 plants are applied to demonstrate the effectiveness and robustness of SGT2-FPID controller. The simulation results show that when the plants have uncertainty in model structure, measurement and external disturbance, the SGT2-FPID controller can achieve better control performances in contrast to compared controllers.

Improving Performance Parameters of PMBLDC Motor Using Fuzzy Sliding Mode Controller

This paper proposes an intelligent speed control system for PMBLDC motor drive applications. A fuzzy sliding mode controller is designed for the high speed control of BLDC motors, Efficacy of the system can be improved by FSM controller. Due to the non- linear characteristics of BLDC motors PID controllers are not relevant to it. Noise disturbances, harmonics, and antecedent or consequent uncertainties are difficult to handle by Interval Type2 fuzzy PID controller. Whereas Sliding Mode Controller is most attractive control technique for all type of uncertainties, and improves the performance of the system. An effective Mat-lab / Simulation result presents the attractive performance of proposed system.

SCA Based Interval Type-2 Fuzzy PID Controller for Solar MPPT

In this publication section, novel interval type-2 fuzzy-PID controller (T2FPID) based Maximum Power Point Tracking (MPPT) is implemented in proposed a standalone photovoltaic (PV) system, type-1 fuzzy-PID controller (FPID), and PID controller with strategic control of online set point tracking in association with DC-DC boost converter is enforced in PV system to track maximum power point (MPP) in solar PV system is depicted. The opted controllers are appropriately composed by picking sine-cosine (SCA) algorithm. The proposed T2FPID based MPPT technique is espoused to dig out maximum power under certain circumstances of temperature and irradiance. System performance is enhanced by the act of T2FPID controller. The maximum output power, voltage & current, duty cycle for DC-DC boost converter is relevantly controlled by the novel T2FPID controller tuned by SCA algorithm. The T2FPID based MPPT technique is authenticated by comparing it by P&O based technique. Finally, it is scrutinized that, the supremacy of intended controller is proved over conventional P&O technique, conventional PID & T1FPID controller; conceding the oscillation, time response, settling time and maximum values of voltage, current & power of the solar system. Robustness analysis is performed by varying the irradiance and temperature partly keeping one parameter constant. The proposed work is further validated on OPAL RT system.

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.