PID-type Fuzzy Controller Research Articles

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

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

Optimal PID-type fuzzy logic controller for a multi-input multi-output active magnetic bearing system

The performance of the fuzzy controllers depends highly on the proper selection of some design parameters which is usually tuned iteratively via a trial and error process based primarily on engineering intuition. With the recent developments in the area of global optimization, it has been made possible to obtain the optimal values of the design parameters systematically. Nevertheless, it is well known that unless a priori knowledge is available about the optimization search-domain, most of the available time-domain objective functions may result in undesirable solutions. It is consequently important to provide guidelines on how these parameters affect the closed-loop behavior. As a result, some alternative objective functions are presented for the time-domain optimization of the fuzzy controllers, and the design parameters of a PID-type fuzzy controller are tuned by using the proposed time-domain objective functions. Finally, the real-time application of the optimal PID-type fuzzy controller is investigated on the robust stabilization of a laboratory active magnetic bearing system. The experimental results show that the designed PID-type fuzzy controllers provide much superior performances than the linear on-board controllers while retaining lower profiles of control signals.

A Load Frequency Control in an Off-Grid Sustainable Power System Based on a Parameter Adaptive PID-Type Fuzzy Controller

Abstract This paper presents a new implementation of a parameter adaptive PID-type fuzzy controller (PAPIDfc) for a grid-supporting inverter of battery to alleviate frequency fluctuations in a wind-diesel power system. A variable speed wind turbine that drives a permanent magnet synchronous generator is assumed for demonstrations. The PAPIDfc controller is built from a set of control rules that adopts the droop method and uses only locally measurable frequency signal. The output control signal is determined from the knowledge base and the fuzzy inference. The input-derivative gain and the output-integral gain of the PAPIDfc are tuned online. To ensure safe battery operating limits, we also propose a protection scheme called intelligent battery protection (IBP). Several simulation experiments are performed by using MATLAB®/SimPowersystems™. Next, to verify the scheme’s effectiveness, the simulation results are compared with the results of conventional controllers. The results demonstrate the effectiveness of the PAPIDfc scheme to control a grid-supporting inverter of the battery in the reduction of frequency fluctuations.

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.

R&D of Visualization Control System for Differential Reactor

An intelligent control system for Differential Reactor is proposed based on the intelligent visualization control system, in order to reduce the complexity of process and temperature control during the operation. The Man-Machine Interface Unit is developed based on touch human-machine interface, this unit can be used to monitor and test the change of the parameters during Differential Reactor operation. At last the unit in combined with the Fuzzy PID-type controller. The practical tests performed in this article show that the new system can monitor the Differential Reactor in real-time, can effectively improve the visibility of the production process, simplify the system control, and effectively reduce the system failure rate.

Optimization of a self-tuning PID type fuzzy controller and a PID controller for an inverted pendulum

By relating to the conventional PID and PID type fuzzy, an optimized PID type fuzzy controller and an optimized PID controller are designed for an inverted pendulum with two outputs. The optimized ...

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.

Stabilizing a Gimbal Platform using Self-Tuning Fuzzy PID Controller

The aim of the inertial stabilization system is to stabilize the sensor’s line of sight (LOS) toward a target while is isolating the sensor against the disturbances which are caused by the operating environment. The purpose which this paper is following is a model of control servo system for an inertially stabilized gimbal mechanism to improve the performance of system which is using only PID controller by finding a way to tune the PID gains online, for this purpose a self-tuning Fuzzy PID type controller is used. First the relationships that governs gimbals torque will be derived from Newton’s law under consideration of the dynamic mass unbalance and base angular motion. The next step is construction of stabilization loop through designing the proposed self-tuning Fuzzy-PID controller. For simulation and investigate the system performance in different cases of controller, the Matlab/Simulink is used and Based on different performance criteria a comparison study is made. Based on the results in different conditions on proposed controller the system performance is improved. The simulation result shows improvement on transient and the steady-state performance.

Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system

In this paper, the interval type-2 fuzzy proportional–integral–derivative controller (IT2F-PID) is proposed for controlling an inverted pendulum on a cart system with an uncertain model. The proposed controller is designed using a new method of type-reduction that we have proposed, which is called the simplified type-reduction method. The proposed IT2F-PID controller is able to handle the effect of structure uncertainties due to the structure of the interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller using a new method of type-reduction are compared with the other proposed IT2F-PID controller using the uncertainty bound method and the type-1 fuzzy PID controller (T1F-PID). The simulation and practical results show that the performance of the proposed controller is significantly improved compared with the T1F-PID controller.

Stabilization loop of a two axes gimbal system using self-tuning PID type fuzzy controller

The application of inertial stabilization system is to stabilize the sensor's line of sight toward a target by isolating the sensor from the disturbances induced by the operating environment. The aim of this paper is to present two axes gimbal system. The gimbals torque relationships are derived using Lagrange equation considering the base angular motion and dynamic mass unbalance. The stabilization loops are constructed with cross coupling unit utilizing proposed fuzzy PID type controller. The overall control system is simulated and validated using MATLAB. Then, the performance of proposed controller is evaluated comparing with conventional PI controller in terms of transient response analysis and quantitative study of error analysis. The simulation results obtained in different conditions prove the efficiency of the proposed fuzzy controller which offers a better response than the classical one, and improves further the transient and steady-state performance.

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.

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.

Optimization of a self-tuning PID type fuzzy controller and a PID controller for an inverted pendulum

By relating to the conventional PID and PID type fuzzy, an optimized PID type fuzzy controller and an optimized PID controller are designed for an inverted pendulum with two outputs. The optimized PID type fuzzy tunes its scaling factors on line. The optimization is done by imperialist competitive algorithm ICA. The simulation results show a better performance in overshoot, settling time, rise time, integral absolute error, and robustness in compared to the conventional and self-tuning designs.

PID-Type Fuzzy Controller for Grid-Supporting Inverter of Battery in Embedded Small Variable Speed Wind Turbine

Frequency and voltage of embedded variable speed wind turbine (VSWT) driving a permanent magnet synchronous generator (PMSG) is strongly affected by wind speed fluctuations. In practice, power imbalance between supply and demand is also common, especially when VSWT-PMSG is connected to a weak micro grid (MG). If load demand fluctuations become high, isolated MG may be unable to stabilize the frequency and voltage so that battery storage needs to be installed into the MG to adjust energy supply and demand. To allow flexible control of active and reactive power flow from/to battery storage, grid-supporting inverters are used. For a system that contains highly nonlinear components, the use of conventional linear proportional-integral-derivative (PID) controllers may cause system performance deterioration. Additionally, these controllers show slow, oscillating responses, and complex equations are required to obtain optimum responses in other controllers. To cope with these limitations, this paper proposes PID-type fuzzy controller (PIDfc) design to control grid-supporting inverter of battery. To ensure safe battery operating limits, we also propose a new controller scheme called intelligent battery protection (IBP). This IBP is integrated into PIDfc. Several simulation tests are performed to verify the scheme’s effectiveness. The results show that the proposed PIDfc controller exhibits improved performance and acceptable responses, and can be used instead of conventional controllers.

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.

Fuzzy Stabilization Loop of One Axis Gimbal System

The application of inertial stabilization system is to stabilize the sensor’s line of sight toward a target by isolating the sensor from the disturbances induced by the operating environment. The purpose of this paper is to present a model of control servo system for one axis gimbal mechanism using fuzzy PID type controller. The gimbals torque relationships are derived using Newton’s law considering the base angular motion and dynamic unbalance. Then, the stabilization loop is constructed and the proposed fuzzy controller is designed. The overall control system is simulated using MATLAB/Simulink, then the system performance is investigated in different cases for both conventional PI and fuzzy PID controller. A comparison study is made based on some performance criteria. The results obtained in different conditions confirms that a further improved system performance can be achieved using the proposed fuzzy controller as compared to the conventional PI controller. The simulation results proves the efficiency of the proposed fuzzy controller which offers a better response than PI one, and improves further the transient and the steady-state performance. General Terms Inertial stabilization systems, fuzzy control, servo systems

Velocity Control of a Spherical Rolling Robot Using a Grey-PID Type Fuzzy Controller With an Adaptive Step Size

This paper proposes a grey-PID type fuzzy controller (GPIDFC) with an adaptive step size to control the velocity of a spherical rolling robot characterized by a highly nonlinear system model. The proposed control structure consists of a grey predictor and a PID type fuzzy controller (PIDFC). Another fuzzy controller is proposed to tune the step size of the grey predictor. The simulation results show that the PIDFC coupled to a grey predictor with an adaptive step size is able to control the spherical rolling robot with a better transient response, e.g. lower overshoot, when compared to a conventional PIDFC.

Application of hybrid fuzzy PID controller for three-area power system with generation rate constraint

This paper presents a new approach for load frequency control of three-area interconnected reheat thermal power system with the consideration of generation rate constraint (GRC). The PID-type fuzzy controller is combined with a conventional PID controller to enhance the performance and robustness of the controller. The proposed controller called hybrid fuzzy PID (HFLPID) controller has been designed for a three-area connected power system. Two performance criteria were utilised for the comparison. First, settling times and overshoots of the frequency deviation were compared. Later, integral of time multiplied absolute error (ITAE) analysis was carried out to compare all the controllers. All the models were simulated by MATLAB 7.0/Simulink software. The simulation results show that the proposed controller developed in this study performs better than the other controllers. Robustness of proposed controller is checked by analysing the system response with varying system parameters.

A PLC-based modified-fuzzy controller for PWM-driven induction motor drive with constant V/Hz ratio control

In this paper, a method to develop and design a fuzzy-hybrid control on an industrial controller to control speed of an induction motor and implementing a constant V/Hz ratio control is presented. Detailed discussions on the controller for a PWM-driven induction motor drive system, the system identification for the model transfer function, and the analysis on output responses and the associated manipulated variables are presented. The control objective is to provide an effective control action to sudden changes in reference speed and/or load torque. A switching type controller consisting of two control modes are devised: a PID-type fuzzy controller consisting of a PI-type and a PD-type fuzzy controller, and a conventional PID. At the early phase of the control action, the control task is handled by the PID-type fuzzy controller. At a later phase when the absolute of error is less than a threshold value, the input of integrator at the output side is no longer given by fuzzy action but fed by the incremental PID action. In term of control action, this is an enhanced proportional and derivative action when the actual value is closed to reference. Detailed evaluations of the controller's performance based on pre-defined performance indices under several conditions are presented. The findings demonstrate the ability of the control approach to provide a viable control solution in response to the different operating conditions and requirements.