Interval Type-2 Fuzzy PID Research Articles

Interval type-2 fuzzy logic PID excitation control system with AVR in power system stability analysis

Interval type-2 fuzzy logic PID excitation control system with AVR in power system stability analysis

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.

Design of Interval Type-2 Fractional-Order Fuzzy Logic Controller for Redundant Robot with Artificial Bee Colony

A five-degree of freedom redundant robot manipulator is a MIMO, extremely nonlinear and dynamically coupled system wherein the parameter variations, external disturbances, and random noise adversely affect the system performances. From this, it necessitates that the controller designed for redundant robot system should efficiently handle such complexities. In this paper, the novel application of artificial bee colony (ABC) algorithm to optimize the fractional-order operators and scaling factors of interval type-2 fractional-order fuzzy PID (IT2FO-FPID) controller are proposed for redundant robotic system for trajectory tracking problem. In order to show the superiority of new IT2FO-FPID controller, the proposed controller structure is also implemented for benchmark fractional-order plants and uncertain inverted pendulum system. Further, the tuning of each controller’s parameters is done with ABC algorithm for each plant. For investigating the effectiveness of the proposed controllers, the performances of the proposed controller are compared with integer order IT2FPID, type-1 fuzzy PID (T1FPID), and traditional PID controllers. The simulation results show that the IT2FO-FPID controller produces superior results for fractional-order plants, inverted pendulum system, and redundant robot manipulator. Further, the robustness analysis is conducted for load disturbance rejection for fractional-order plants, inverted pendulum system. Moreover, the robustness analysis is also investigated for robot manipulator in the presence of model uncertainties, load disturbance, and random noise. After numerical simulations, it is found that IT2FO-FPID controller is producing superior results than its conventional counterparts in the presence of robustness.

An enhanced and auto-tuned power system stabilizer based on optimized interval type-2 fuzzy PID scheme

An enhanced and auto-tuned power system stabilizer based on optimized interval type-2 fuzzy PID scheme

Performance analysis of optimal hybrid novel interval type-2 fractional order fuzzy logic controllers for fractional order systems

The main objective of this paper is to propose the family of hybrid novel interval type-2 fractional order fuzzy PID (IT2FO-FPID) controllers, which incorporates fractional order integro-differentiator, taking into its consideration the advantages of the interval type-2 fuzzy controllers (IT2FLCs) and fractional order PID (FOPID) controllers. The incorporation of IT2FLCs with FOPID controllers has been investigated in terms of time response measure for unit set-point response and unit load disturbance. The resulting different hybrid IT2FO-FPID controller structures are examined on different fractional order processes followed by robustness analysis. It is observed that incorporation of fractional order integro-differential operators made the proposed control structures less sensitive to the parameters change. For this reason, fractional order integro-differential operators are adopted as design variables along with input/output scaling factors for designing of effective novel controllers. In order to do reasonable comparison, the tuning of the family of hybrid IT2FO-FPID controllers' parameters is done with newly Artificial Bee Colony-Genetic Algorithm (ABC-GA) optimization technique to develop optimal closed loop performance by considering the objective function as weighted sum of control loop error index and control output. The simulation analyses are executed for two different non-integer order plus time delay fractional order process plants (NIOPTD-I and NIOPTD-II). These processes represent a sensible estimation of most process plants and are employed to examine the comparative qualities of the presented hybrid IT2FO-FPID controllers. Further, the performance comparison and the significance of the different proposed hybrid controllers are investigated under unit set-point response, load disturbance rejection, and small control signal or actuators requirement. In order to test the efficacy of proposed controllers, the robustness analysis such as parameter variations is also investigated. Finally, the simulation investigations explicitly suggest that proposed different hybrid IT2FO-FPID control structures can be recommended in terms of better step response, better load disturbance rejection, small control signal response, and parameters variation.

Cuckoo search algorithm based design of interval Type-2 Fuzzy PID Controller for Furuta pendulum system

The Interval Type-2 Fuzzy Logic Controller (IT2FLC) is an advanced version of Type-1 Fuzzy Logic Controller (T1FLC) that improves the control strategies by using the advantage of its footprint of uncertainty of the Fuzzy Membership Function (MF). Numerous experimental investigations have shown the superiority of IT2FLC over T1FLC, particularly in high level of uncertainties and nonlinearities. Nevertheless, the systematic design of IT2FLCs remains an attractive problem because of the difficulty in finding the parameters associated with IT2FLCs. In this study, a novel application of Cuckoo Search (CS) algorithm in the design of an optimized cascade Interval Type-2 Fuzzy Proportional Integral Derivative Controller (IT2FPIDC) is presented. The PID gains and the parameters of the antecedent MFs of IT2FPIDC are optimized using CS algorithm. Considering the higher number of parameters to be optimized in cascade IT2FPIDC, the CS method was employed due to its high convergence speed and less computational cost. The proposed CS based cascade optimized IT2FPIDC is compared with CS-based Type-1 Fuzzy Proportional Integral Derivative Controller (T1FPIDC). The present research presents a new application of proposed CS based cascade optimized IT2FPIDC for the balancing control and trajectory tracking control of the Furuta pendulum (FP) which is a nonlinear, non-minimum phase and unstable system. Furthermore, the disturbance rejection ability of the proposed controller is analyzed. The proposed control strategies are evaluated on FP produced by Quanser through numerous experimentations in the real world as well as simulation. The performance characteristic considered for these controllers are settling time (ts), steady state error (Ess), rise time (tr) and maximum overshoot (Mp). Both the simulation and real world experiments results demonstrated the robustness and effectiveness of the proposed CS based IT2FPIDC with respect to parameter variation, noise effects and load disturbances, with an improved performance of 27.1%, 5.7% and 20.8% for tr, ts and Mp respectively over its CS based T1FPIDC counterpart.

A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.

Interval type-2 fuzzy PID controllers and an online self-tuning mechanism

Interval type-2 fuzzy PID controllers and an online self-tuning mechanism

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.

Big Bang–Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy

Fuzzy logic control is a recognized approach for handling the faced uncertainties within control applications. However, type-1 fuzzy controllers using crisp type-1 fuzzy sets might not be able to fully handle the high levels of uncertainties and nonlinear dynamics associated with real world control applications. On the other hand, interval type-2 fuzzy controllers using Interval Type-2 Fuzzy Sets (IT2-FSs) might be able to handle such uncertainties to produce a better control performance. However, the systematic design of interval type-2 fuzzy controllers is still a challenging problem due to the difficulty in determining the parameters of the IT2-FSs. In this paper, we will present the novel application of Big Bang–Big Crunch optimization (BB–BC) approach to optimize the antecedent membership parameters of Interval Type-2 Fuzzy PID (IT2-FPID) controllers in a cascade control structure. Since the IT2-FPID control structure involves more design parameters compared to its type-1 counterpart, it is beneficial to employ the BB–BC method which has a low computational cost and a high convergence speed. The presented BB–BC based optimized IT2-FPID cascade structure will be compared with its Type-1 Fuzzy PID (T1-FPID) and conventional PID controller counterparts which were also optimized with the BB–BC optimization. In addition, the proposed IT2-FPID structure will be compared with a self-tuning T1-FPID control structure. We will then present the novel application of the cascade control architecture to solve the path tracking control problem of mobile robots which inherits large amounts of uncertainties caused by the internal dynamics and/or feedback sensors of the controlled system. Several experiments were performed in simulation and in real world using the PIONEER 3-DX mobile robot which will act as a platform to evaluate the proposed control systems in this paper. The results illustrated that the IT2-FPID structure enhanced significantly the control performance even in the presence of uncertainties and disturbances when compared to the PID, T1-FPID and self-tuning T1-FPID structures. Moreover, it has been shown that the reason for the superior control performance of the IT2-FPID under high levels of uncertainty and noise is not merely for its use of extra parameters, but rather its different way of dealing with the uncertainties and noise present in real world environments by comparing with a self-tuning T1-FPID structure.

Design of Type-1 and Interval Type-2 Fuzzy PID Control for Anesthesia Using Genetic Algorithms

This paper presents the automatic drug administration for the regulation of bispectral (BIS) index in the anesthesia process during the clinical surgery by controlling the concentration target of two drugs, namely, propofol and remifentanil. To realize the automatic drug administration, real clinical data are collected for 42 patients for the construction of patients’ models consisting of pharmacokinetic and pharmacodynamic models describing the dynamics reacting to the input drugs. A nominal anesthesia model is obtained by taking the average of 42 patients’ models for the design of control scheme. Three PID controllers are employed, namely linear PID controller, type-1 (T1) fuzzy PID controller and interval type-2 (IT2) fuzzy PID controller, to regulate the BIS index using the nominal patient’s model. The PID gains and membership functions are obtained using genetic algorithm (GA) by minimizing a cost function measuring the control performance. The best trained PID controllers are tested under different scenarios and compared in terms of control performance. Simulation results show that the IT2 fuzzy PID controller offers the best control strategy regulating the BIS index while the T1 fuzzy PID controller comes the second.

Interval type-2 fuzzy PID load frequency controller using Big Bang–Big Crunch optimization

This paper proposes an optimization based design methodology of interval type-2 fuzzy PID (IT2FPID) controllers for the load frequency control (LFC) problem. Hitherto, numerous fuzzy logic control structures are proposed as a solution of LFC. However, almost all of these solutions use type-1 fuzzy sets that have a crisp grade of membership. Power systems are large scale complex systems with many different uncertainties. In order to handle these uncertainties, in this study, type-2 fuzzy sets, which have a grade of membership that is fuzzy, have been used. Interval type-2 fuzzy sets are used in the design of a load frequency controller for a four area interconnected power system, which represents a large power system. The Big Bang–Big Crunch (BB–BC) algorithm is applied to tune the scaling factors and the footprint of uncertainty (FOU) membership functions of interval type-2 fuzzy PID (IT2FPID) controllers to minimize frequency deviations of the system against load disturbances. BB–BC is a global optimization algorithm and has a low computational cost, a high convergence speed, and is therefore very efficient when the number of optimization parameters is high as presented in this study. In order to show the benefits of IT2FPID controllers, a comparison to conventional type-1 fuzzy PID (T1FPID) controllers and conventional PID controllers is given for the four-area interconnected power system. The gains of conventional PID and T1FPID controllers are also optimized using the BB–BC algorithm. Simulation results explicitly show that the performance of the proposed optimum IT2FPID load frequency controller is superior compared to the conventional T1FPID and PID controller in terms of overshoot, settling time and robustness against different load disturbances.

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.