Type-2 Fuzzy Logic Controller Research Articles

A new adaptive configuration of PID type fuzzy logic controller

In this paper, an adaptive configuration for PID type fuzzy logic controller (FLC) is proposed to improve the performances of both conventional PID (C-PID) controller and conventional PID type FLC (C-PID-FLC). The proposed configuration is called adaptive because its output scaling factors (SFs) are dynamically tuned while the controller is functioning. The initial values of SFs are calculated based on its well-tuned counterpart while the proceeding values are generated using a proposed stochastic hybrid bacterial foraging particle swarm optimization (h-BF-PSO) algorithm. The performance of the proposed configuration is evaluated through extensive simulations for different operating conditions (changes in reference, load disturbance and noise signals). The results reveal that the proposed scheme performs significantly better over the C-PID controller and the C-PID-FLC in terms of several performance indices (integral absolute error (IAE), integral-of-time-multiplied absolute error (ITAE) and integral-of-time-multiplied squared error (ITSE)), overshoot and settling time for plants with and without dead time.

Higher order fuzzy logic in controlling selective catalytic reduction systems

Abstract This paper presents research on applications of fuzzy logic and higher-order fuzzy logic systems to control filters reducing air pollution [1]. The filters use Selective Catalytic Reduction (SCR) method and, as for now, this process is controlled manually by a human expert. The goal of the research is to control an SCR system responsible for emission of nitrogen oxide (NO) and nitrogen dioxide (NO2) to the air, using SCR with ammonia (NH3). There are two higher-order fuzzy logic systems presented, applying interval-valued fuzzy sets and type-2 fuzzy sets, respectively. Fuzzy sets and higher order fuzzy sets describe linguistically levels of nitrogen oxides as the input, and settings of ammonia valve in the air filter as the output. The obtained results are consistent with data provided by experts. Besides, we show that the type-2 fuzzy logic controllers allows us to obtain results much closer to desired parameters of the ammonia valve, than traditional FLS.

Direct adaptive general type‐2 fuzzy control for a class of uncertain non‐linear systems

In this study, a stable direct adaptive general type-2 fuzzy logic controller (DAG2FLC) is introduced for a class of non-linear systems. The proposed controller uses advantages of general type-2 fuzzy logic systems (GT2FLSs) in handling dynamic uncertainties to approximate unknown non-linear actions. Implementing general type-2 fuzzy systems is computationally costly; however, by using a recently introduced α-plane representation, a GT2FLS can be seen as composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the DAG2FLC controller and a H ∞ compensator is added to attenuate external disturbance and fuzzy approximation error. Also general type-2 fuzzy adaptation laws are derived using Lyapunov approach, and the stability of the closed-loop system has been proven by mathematical analysis. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller and a direct adaptive interval type-2 fuzzy logic controller, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic Gyro system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.

Robust Adaptive Type-2 Fuzzy Sliding Mode Control for Non-Linear uncertain SISO systems

This paper deals with the synthesis of adaptive type-2 fuzzy logic controller for a class of single-input single-output system. Due to its ability in serving in universal approximation, the type-2 fuzzy logic system is used to approximate the unknown system dynamics, which will be adjusted according to the on-line adaptation laws deduced from the stability analysis. To ensure the closed loop system robustness, a modified sliding mode control signal is used. In this work, variable sliding surface is replaced by type-2 fuzzy logic system in order to reduce the starting energy without deteriorating the tracking performances. Furthermore, the knowledge of the upper bounds of the external disturbances and also the approximation errors is not needed. The global stability of the closed loop system is guaranteed in the sense of Lyapunov. As well, all signals involved are uniformly bounded. Finally, experiment results are presented to show the performance of the developed approach.

Adaptive Speed Control System Based on Interval Type-2 Fuzzy Logic

This paper presents the design and simulation of adaptive control system based on an Interval Type-2 Fuzzy Logic Controller (IT2FLC) with multilevel inverter (MLI) for control of power system, and the command line programming for constructing, editing, and simulating the IT2FLC. The modification was done by considering new membership functions (MFs) for the environment of an Interval Type-2 Fuzzy Logic System (ITFLS). Two other controllers besides the designed IT2FLC, comparing their outputs: a PID Controller and a Type-1 Fuzzy Logic Controller (T1FLC). Various design phases for the fuzzy system, from initial description to final implementation. In this work, the case study is consider for brushless DC (BLDC) motor that is driven by multilevel inverter based on discrete three-phase pulse width modulation (DPWM) generator that forced-commuted the IGBT’s three-level converters using three bridges to vectored outputs 12- pulses with three levels. Using DPWM with a three-level inverter solves the

COMPARISON OF FUZZY LOGIC CONTROLLERS FOR A MULTIVARIABLE PROCESS

The Interval Type-2 Fuzzy Logic Controller (IT2FLC) for a Quadruple Tank Process (QTP) is demonstrated in this paper. Here the Interval Type-2 based Fuzzy membership function is used. The QTP is made to operate in minimum phase mode. The vertices of fuzzy membership functions are tuned with IT2FLC to minimize Integral Absolute Error. Performance of IT2FLC and Type-1 Fuzzy Logic Controller (T1FLC) are compared with decentralized PI controller, by simulation using MATLAB/Simulink. Simulation results show that satisfactory performance for both servo and regulatory responses.It has been observed that dynamic performance of IT2FLC is better than the other two controllers. Moreover, compared with the T1FLC controller, IT2FLC performs better, particularly in noisy environments.

English

In this paper, adaptive network based fuzzy inference system (ANFIS) was used in control applications of a Heat Exchanger as interval type-2 fuzzy logic controller (IT-2FL). Two adaptive networks based fuzzy inference systems were chosen to design type-2 fuzzy logic controllers for each control applications. The whole integrated system for control of Heat Exchanger is called IT2 FLC+ANFIS controller. Membership functions in interval type-2 fuzzy logic controllers were set as an area called footprint of uncertainty (FOU), which is limited by two membership functions of adaptive network based fuzzy inference systems; they were upper membership function (UMF) and lower membership function (LMF). This work deals with the design and application of an IT2 FLC+ANFIS controller for a heat exchanger. To deal with the problem of parameter adjustment, efficient neuro-fuzzy scheme known as the ANFIS (Adaptive Network-based Fuzzy Inference System) can be used. The IT2 FLC+ANFIS controller of the heat exchanger is compared with classical PID control. System behaviors were defined by Lagrange formulation and MATLAB computer simulations. The simulation results confirm that interval type2 fuzzy is one of the possibilities for successful control of heat exchangers. The advantage of this approach is that it is not a linear-model-based strategy. Comparison of the simulation results obtained using IT2 FLC+ANFIS controller and those obtained using classical PID control demonstrates the effectiveness and superiority of the proposed approach because of the smaller consumption of the heating medium

Design and Implementation of Type-2 Fuzzy Logic Controllers for the Position Control of a DC Servo Motor

Uncertainty is an inherent part in controllers for real world applications. In this paper we compare the performance differences between type-1 and interval type-2 fuzzy logic (IT2FLC) controllers, with five and three term membership functions. The controllers are used to control a PM DC motor in a closed loop real time system. The performance of system with each controller to a step is recorded. The results showed that there is a statistical difference between the fuzzy logic type-1 and type-2 controllers. It is also found that a type-2 five term controller is as good as a type-1five term or type-2 three term controller

Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller

In this paper, we derive the analytical structure of the interval type-2 fuzzy proportional – integral – derivative (IT2F-PID) controller, which consists of a parallel combination of the IT2F-PD controller and the IT2F-PI controller. The IT2F-PID controller uses the following identical elements: two interval T2 triangular input fuzzy sets for each of the two input variables, three interval triangular output fuzzy sets, the Mamdani interval type-2 fuzzy rule based, a Zadeh AND T-norm, a Lukasiewicz OR T-conorm, and a new method for type-reduction that we propose, which called simplified type-reduction method. This new method of type-reduction reduces the computational cost of the output processing for the interval type-2 fuzzy logic controller (IT2-FLC). We relate the resulting structure to conventional PID control theory and prove that the proposed IT2F-PID controller is a nonlinear PID with variable gains changing as the input variables values vary. Moreover, the sufficient conditions for the bounded-input bounded-output (BIBO) stability of the IT2F-PID control system have established using the well-known small gain theorem. The simulation results show that the IT2F-PID controller based on the proposed type-reduction method is able to improve the system performance compared with other type-reduction methods.

MOPSO-based optimal fuzzy logic control strategy for standalone hybrid diesel-wave energy conversion system

The paper proposes a Multi-Objective Particle Swarm Optimization (MOPSO)-based Fuzzy Logic Control Proportional-Integral-Derivative (MOPSO-FLC-PID) controller for stand-alone hybrid Diesel- variable speedWave Energy Conversion System (WECS).The optimal control performance can be achieved by tuning scaling factors of the FLC and gain parameters with Multi-ObjectiveParticle Swarm Optimization (MOPSO) algorithm in order to improve system dynamic performance especially when nonlinearity,uncertainty and complexity of the hybrid Diesel-WECS are involved. Number of objective functions is defined to measurethe performance of the proposed controllers such as minimize the transient DC and AC voltage and current ripples, minimizethe DC and AC voltage and current Total Harmonic Distortion (THD), minimize the absolute total control steady state errordeviations, minimize the RMS absolute voltage deviations at the DC and AC load collection buses, ensure minimal losses aswell as wave energy optimal power utilization. Since some of these objective functions are conflicting, MOPSO is used to finda Pareto front from which a desired optimal operating state can be chosen. For the purpose of comparing the improvementobtained in the system dynamic performance with the application of the MOPSO-FLC-PID procedure to tune the scaling factorsof the FLC and the PID controller gains, these results are compared with those obtained using traditional Ziegler-Nichols PIDapproach, PID type fuzzy logic controller designed with Single-Objective Particle Swarm Optimization (SOPSO-FLC-PID),traditional PID type controller optimized with SOPSO-PID and traditional PID type controller optimized with MOPSO-PID.A complete simulation model is developed for such stand-alone hybrid Diesel-WECS under variable speed operation usingMATLAB Simulink environment. Simulation results show that the proposed design approaches are efficient to find the optimalscaling factors and PID gains of the controllers and therefore improves the transient performance of the hybrid Diesel-WECSover a wide range of operating conditions, sudden load change and three-phase short circuit fault.

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.

A multi-objective optimization of type-2 fuzzy control speed in FPGAs

This paper proposes a design of multi-objective genetic optimization for the average approximation of an interval type-2 fuzzy logic controller (AT2-FLC) using linear combination of individual criteria. There has been shown, on the real case, that the proposed method can be competitive to other commonly used approaches in the design of fuzzy controllers. The AT2-FLC was tested with different levels of uncertainty and different number of bits for the VHDL codification to regulate speed in a direct current motor (ReSDCM). Comparisons were made between the type-1 fuzzy logic controller versus AT2-FLC synthesized in VHDL code for FPGA and the AT2-FLC in VHDL versus the PID controller to ReSDCM. The main contribution of the paper is the design, implementation and comparison of multi-objective GA optimization of AT2-FLC for FPGA real applications. The AT2-FLC is targeted to a Xilinx Spartan 3A XC3S700A device using the Xilinx Foundation Environment.

A controller based on Optimal Type-2 Fuzzy Logic: Systematic design, optimization and real-time implementation

A computationally-efficient systematic procedure to design an Optimal Type-2 Fuzzy Logic Controller (OT2FLC) is proposed. The main scheme is to optimize the gains of the controller using Particle Swarm Optimization (PSO), then optimize only two parameters per type-2 membership function using Genetic Algorithm (GA). The proposed OT2FLC was implemented in real-time to control the position of a DC servomotor, which is part of a robotic arm. The performance judgments were carried out based on the Integral Absolute Error (IAE), as well as the computational cost. Various type-2 defuzzification methods were investigated in real-time. A comparative analysis with an Optimal Type-1 Fuzzy Logic Controller (OT1FLC) and a PI controller, demonstrated OT2FLC׳s superiority; which is evident in handling uncertainty and imprecision induced in the system by means of noise and disturbances.

An Optimized Interval Type-2 Fuzzy Logic Control Scheme based on Optimal Defuzzification

In this paper, a new way of optimizing fuzzy logic is introduced. This way is used to optimize the output of Interval Type-2 Fuzzy Logic controller by replacing the Defuzzification stage by the Optimization algorithm. The algorithm chooses the best crisp output variable from the type-reduced set which is the output of the Type-Reduction stage instead of averaging the set extremes which was performed by Defuzzification stage. Artificial Bee Colony optimization algorithm is used to optimize the Interval Type-2 Fuzzy Logic controller to manage the navigation of multiple mobile robots in indoor environments.

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.

Real-Time Implementation of Type-2 FLC–Based Shunt Active Filter Control Strategies (p–q and Id–Iq) with Different Fuzzy MFs for Power Quality Improvement

Abstract This research article proposes the shunt active filter (SHAF) control strategies (p–q and Id–Iq), which are used to improve the power quality of the electrical network by mitigating the harmonics with the help of Type-2 fuzzy logic controller (Type-2 FLC) different membership functions (MFs). Three-phase reference current waveforms generated by proposed scheme are tracked by the three-phase voltage source converter in a hysteresis band control scheme. The performance of the proposed control strategies has been evaluated in terms of harmonic mitigation and DC link voltage regulation under various source conditions. In order to maintain DC link voltage constant and to generate the compensating reference currents, we have developed Type-2 FLC with different fuzzy MFs (trapezoidal, triangular and Gaussian). The SHAF with proposed Type-2 FLC using Gaussian MF is able to eliminate the uncertainty in the system and SHAF gains outstanding compensation abilities. The detailed real-time results using real-time digital simulator are presented to support the feasibility of proposed control strategies.

On-line control of nonlinear systems using a novel type-2 fuzzy logic method

In this paper, a new type-2 fuzzy logic controller (T2FLC) is proposed for on-line control of nonlinear systems. The proposedmethod provides more flexibility in applying human thinking in control system design in comparison with the traditional or eventype-1 fuzzy logic controllers. One encounters some problems using the type-2 fuzzy logic controllers on-line because of thelarge volume of computations required. The main aim of this paper is to propose a new type-2 fuzzy controller with a smallcomputational burden so that it can be used on-line. In the proposed T2FLC, the programs related to the computation of unionof all qualified consequent T2MFs are divided into some sub-problems, and to design the T2FLC - not interval -we merge theType Reducer and Defuzzifier into one step. By doing so, the computational time reduces, and the performance of our T2FLCincreases so that it can be used on-line in dynamic systems. We study the noise concealing properties of the proposed T2FLCas well. The proposed method is applied to two non-linear dynamic systems, ball & beam and inverted pendulum. The resultsare compared with PID and type-1 fuzzy logic controllers. In the simulation results, it is also shown that the proposed controllerhas good noise cancelling properties.

Interval type-2 fuzzy neural network controller for a multivariable anesthesia system based on a hardware-in-the-loop simulation

This manuscript describes the use of a hardware-in-the-loop simulation to simulate the control of a multivariable anesthesia system based on an interval type-2 fuzzy neural network (IT2FNN) controller. The IT2FNN controller consists of an interval type-2 fuzzy linguistic process as the antecedent part and an interval neural network as the consequent part. It has been proposed that the IT2FNN controller can be used for the control of a multivariable anesthesia system to minimize the effects of surgical stimulation and to overcome the uncertainty problem introduced by the large inter-individual variability of the patient parameters. The parameters of the IT2FNN controller were trained online using a back-propagation algorithm. Three experimental cases are presented. All of the experimental results show good performance for the proposed controller over a wide range of patient parameters. Additionally, the results show better performance than the type-1 fuzzy neural network (T1FNN) controller under the effect of surgical stimulation. The response of the proposed controller has a smaller settling time and a smaller overshoot compared with the T1FNN controller and the adaptive interval type-2 fuzzy logic controller (AIT2FLC). The values of the performance indices for the proposed controller are lower than those obtained for the T1FNN controller and the AIT2FLC. The IT2FNN controller is superior to the T1FNN controller for the handling of uncertain information due to the structure of type-2 fuzzy logic systems (FLSs), which are able to model and minimize the numerical and linguistic uncertainties associated with the inputs and outputs of the FLSs.

Improved Torque and Flux Performance of Type-2 Fuzzy-based Direct Torque Control Induction Motor Using Space Vector Pulse-width Modulation

The conventional proportional integral controlled direct torque control of an induction motor using the space vector pulse-width modulation technique may provide satisfactory dynamic response. However, the proportional integral controller (PIC) does not provide efficient dynamic performance in the induction motor drive during sudden changes in the load or speed. To improve dynamic performance of the induction motor drive, the PICs are replaced by type-2 fuzzy logic control. The type-2 fuzzy improves the starting transient performance as well as the steady-state response. In addition, the type-2 fuzzy direct torque control provides lesser current total harmonic distortion, flux distortion, and torque pulsation of the induction motor drive compared to conventional direct torque control. A MATLAB Simulink (The MathWorks, Natick, Massachusetts, USA) model for direct torque control with type-2 fuzzy logic control is developed to simulate the response of an induction motor drive with different operating conditions. The space vector pulse-width modulation technique is used to drive the inverter, as it produces lesser total harmonic distortion in inverter current and voltage waveforms for a given switching transition due to the single switching frequency for the movement of each state vector. A prototype type-2 fuzzy-based direct torque control induction motor with space vector pulse-width modulation is developed to validate the simulated response. The control signals for the inverter are generated by the DSPACE DS1104 (DSPACE GmbH, Germany) to drive a two-HP induction machine.

Practical Implementation for the interval type-2 fuzzy PID controller using a low cost microcontroller

In this study, we propose an embedded real-time interval type-2 fuzzy proportional – integral – derivative (IT2F-PID) controller which is a parallel combination of the interval type-2 fuzzy proportional – integral (IT2F-PI) controller and the interval type-2 fuzzy proportional – derivative (IT2F-PD) controller. The proposed IT2F-PID controller is able to handle the effect of the system uncertainties due to the structure of the interval type-2 fuzzy logic controller. The proposed IT2F-PID controller is implemented practically using a low cost PIC microcontroller for controlling the uncertain nonlinear inverted pendulum to minimize the effect of the system uncertainties due to the uncertainty in the mass of the pendulum, the measurement error in the rotation angle of the pendulum and the structural uncertainty. The test is carried out using the hardware-in-the-loop (HIL) simulation. The experimental results show that the performance of the IT2F-PID controller improves significantly the performance over a wide range of system uncertainties.