Tuning and analysis of a fuzzy PI controller based on gain and phase margins

Tuning of fuzzy PI controllers based on gain/phase margin specifications and ITAE index

Aiming at the static unstable Hypersonic vehicle, a method for designing H∞ autopilot to satisfy gain margin and phase margin is proposed. Structured H∞ synthesis is used to synthesize the autopilot under the fixed structure. The gain margin and phase margin were constrained by using H∞ norm of the complementary of the scaled plant. The requirement for the gain margin and phase margin is represented by the distance between the open loop Nyquist curve and the circle that represents the gain margin and phase margin in the complex plane. The distance is adjusted by tuning the parameter of performance specifications automatically to reduce the conservatism of the controller. The present method is applicable to both static stable vehicle and static unstable vehicle, and a three loops acceleration tracking autopilot is design. The numerical simulations have demonstrated that the autopilot satisfys the performance specifications, gain margin and phase margin simultaneously.

The modified second-order sliding mode algorithm is used for controller tuning. Namely, the modified suboptimal algorithm-based test (modified SOT) and non-parametric tuning rules for proportional-integral-derivative (PID) controllers are presented in this article. In the developed method of test and tuning, the idea of coordinated selection of the test parameters and the controller tuning parameters is introduced. The proposed approach allows for the formulation of simple non-parametric tuning rules for PID controllers that provide desired amplitude or phase margins exactly. In the modified SOT, the frequency of the self-excited oscillations can be generated equal to either the phase crossover frequency or the magnitude crossover frequency of the open-loop system frequency response (including a future PID controller) – depending on the tuning method choice. The first option will provide tuning with specification on gain margin, and the second option will ensure tuning with specification on phase margin. Tuning rules for a PID controller and simulation examples are provided.

A hybrid optimization approach for PI controller tuning based on gain and phase margin specifications

In this paper, a robust fuzzy digital PID control strategy, via multiobjective genetic algorithm, based on the gain and phase margins specifications, with applications to uncertain dynamic systems with time delay, is proposed. A mathematical formulation based on the gain and phase margins, the fuzzy model and PID digital controller structures and the time delay of the uncertain dinamic system, is deduced. A multiobjective genetic strategy is defined to tune the fuzzy controller parameters so the gain and phase margins of the fuzzy control system are close to the specified ones. Computational results show the efficiency of the proposed methodology through the accuracy in the gain and phase margins of the PID control system compared to the specified ones and tracking of the reference trajectory.

This paper presents an approach for finding regions Of specified gain margins (GM) and phase margins (PM) in the parameter space of a single-input single-output (SISO) control system with adjustable parameters. The method uses the Nyquist stability criterion of encirclement of a point in the polar plot. The necessary of the specified GM or PM regions in the parameter space are fully treated by mapping a point related to specified GM or PM in the polar plane into the parameter space. A general problem with previous mapping techniques is identified where points in the parameter space do not necessarily satisfy the required GM or PM. A searchbased technique is proposed to address this problem. Three examples illustrate the theoretical development. I. Introduction G AIN margin (GM) and phase margin (PM) are perhaps the two most important and widespread accepted criteria in analysis and design of practical control systems. These criteria are related to the open-loop transfer function of systems. In the robust stabilization problem of control systems, however, parameter space methods generally consider the closed-loop characteristic equation of the system.13 Parameter space techniques were initially studied by Vishnegradesky for a third-order system using a graphical technique that was popularized by Nimark and was referred to as D-partition or D-decomposition46 in its early development. This method actually establishes a direct correlation between the variable parameters of the closed-loop characteristic equation and the various important stability regions, e.g., open left half of the complex plane (OLHP). The method is directly suitable for graphical representation, in which case it is convenient to consider two parameters at a time. The idea of correlating the free parameters of the open-loop transfer function of a system and the relative stability regions appears to have been initially given in Ref. 7. Unfortunately , the method was not developed in detail, and the idea of isolating the GM region in the parameter plane was not correct. A recent improvement to the idea was presented by introducing the gain-phase margin tester into the system,8 which attempted to isolate specified GM and PM regions in the parameter space to allow a choice of the adjustable parameters. However, it is argued here that in this latter approach all the possible of the relative stability regions are not in fact considered, and some and possibly all points in the relative stability region do not necessarily satisfy the actual specified relative stability margin. In particular, the so called singular boundaries of the D-partition method6 need to be considered. Finally, arising through frequency loci with re-entrant or convoluted characteristics also need to be considered with care. In this paper, a method for accounting for the

A robust fuzzy digital PID control methodology based on gain and phase margins specifications is proposed. A mathematical formulation based on gain and phase margins specifications, the Takagi-Sugeno fuzzy model of the process to be controlled, the structure of the digital PID controller, and the time delay uncertain system are developed. A multiobjective genetic strategy is defined to tune the fuzzy digital PID controller parameters, so the gain and phase margins specified to the fuzzy control system are found. An analysis of necessary and sufficient conditions for fuzzy digital PID controller design with robust stability, with the proposal of the two theorems, is presented. Experimental results show the efficiency of the proposed methodology in this chapter, applying a platform control in real time of a thermic process through tracking the reference and the gain and phase margins keeping closed the specified ones.

In order to meet the requirements of high precision and fast response of permanent magnet direct drive (PMDD) wind turbines, this paper proposes a fuzzy proportional integral (PI) controller associated with a new control strategy for wind turbine converters. The purpose of the control strategy is to achieve the global optimization for the quantization factors, ke and kec, and scale factors, kup and kui, of the fuzzy PI controller by an improved particle swarm optimization (PSO) method. Thus the advantages of the rapidity of the improved PSO and the robustness of the fuzzy controller can be fully applied in the control process. By conducting simulations for 2 MW PMDD wind turbines with Matlab/Simulink, the performance of the fuzzy PI controller based on the improved PSO is demonstrated to be obviously better than that of the PI controller or the fuzzy PI controller without using the improved PSO under the situation when the wind speed changes suddenly.

In this paper mathematical models of Mamdani type fuzzy PI or PD controllers via Center of Gravity (CoG) defuzzification are obtained. These controllers are called the simplest fuzzy PI or PD controllers as minimal number of fuzzy sets (two fuzzy sets on each of the two-input variables and three fuzzy sets on the output variable) are employed. The basic components of these models are L-type and Y-type membership functions on each input variable, trapezoidal or triangular membership functions on output variable, minimum / algebraic product t-norm, maximum OR operator, three linear fuzzy control rules, minimum / algebraic product inference and CoG defuzzification. Mathematical models of fuzzy controller via CoG defuzzification were not reported in the literature and are therefore presented for the first time in this paper.

Power conditioning system (PCS) is an interface between distributed generation and utility grid. It regulates voltage, current and power transmitted from the hybrid direct fuel-cell/turbine (DFC/T) power plant to utility grid. This paper presents a self-adaptive fuzzy PI controller of three phase inverter in PCS for the DFC/T power plant. One of the main tasks of PCS for distributed generations is power flow control. Traditionally, the control scheme for grid connected inverters is PI controller. However, PI control scheme would lead to large overshoot and long response time when the load increases sharply. Thus, a hybrid fuzzy PI control scheme is proposed in this paper in order to improve the power flow control. The fuzzy controllers can adjust the PI parameters according to the voltage error and the derivative of voltage error. The overall self-adaptive tuning fuzzy PI controller can update the PI parameters in real time, which makes the power flow control much more accurate than conventional PI controllers. Analysis and design methodologies of hybrid fuzzy PI controllers are presented in this paper. The model was developed in Matlab/Simulink environment. Simulation results show that the proposed control scheme can effectively reduce the overshoot and response time compared to the conventional PI controllers.

This paper presents a fuzzy PI controller as a power system stabilizer. The fuzzy PI controller has been designed in order to prepare an auxiliary signal for the excitation system of the synchronous generator. The proposed controller utilizes a combination of a fuzzy logic controller (FLC) and a PI controller, which are the most recent researches in the problem at hand. In comparison with the conventional fuzzy controllers, the proposed fuzzy PI controller takes advantage of both FLC and conventional PI controller to overcome all kind of disturbances. The damping of oscillations local modes in a power system will substantially be controlled by employing this controller as a replacement for conventional PSS. Furthermore, the presented paper considers the conventional PSS and compares its performance with respect to three proposed types of fuzzy PI controller. Correspondingly, the effects of the supplementary signals in damping oscillation have been shown. Finally, to scrutinize the effectiveness of the proposed controller in damping oscillations, a three-phase short circuit condition is studied in order to clarify the application of the developed methodology. The achieved outcomes show that the proposed controller for stabilizing power system can provide very good damping characteristic.

Focusing on the passive network, this paper analyzes the discrete mathematical model and its control strategy of the passive terminal of the VSC-HVDC system on the basis of the α-β frame of axes. The method of the functioning-fuzzy-subset inference is introduced into automatic regulation of the proportional integral (PI) parameters. Based on the digital signal processor (DSP), the fuzzy PI control method is adopted and the VSC-HVDC experiment device is constructed. The experiment of constant AC voltage control based on fuzzy adaptive PI controller in transmitting power to passive network via VSC-HVDC system is developed. The experimental results show that the fuzzy controller with adaptive PI parameters for AC voltage control of VSC-HVDC system is effective.

Problem statement: The main objective of this research is to obtain the speed control of switched reluctance motor with minimum settling time and without overshoot. Approach: A new algorithm has been developed with the combination of differential evolution and particle swarm optimization and applied for speed control of switched reluctance motor under sudden change in speed. Also speed control of switched reluctance motor was obtained by other artificial intelligence methods such as fuzzy logic controller, fuzzy PI controller and particle swarm optimization based tuning of fuzzy PI controller. Matlab/Simulink environment was used for the simulation. Results: Results are discussed and tabulated based on the performance of the controllers. Conclusion: From the comparison of all above methods, the algorithm has given better results in speed response than other controllers.

This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes (TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region (GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error (IAE) or the integral of the squared error (ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.

This paper presents a systematic design method of a controller using the discrete fuzzy PI control and the particle swarm optimization (PSO). Unlike a conventional PI controller, the discrete fuzzy PI controller has variable gains according to its input variables. Generally, it is complicated to tune the parameters of a fuzzy controller because there are too many parameters which are strongly coupled. In the discrete-time domain, the discrete fuzzy PI controller is a superset of the conventional PI controller. And the initial parameters of the fuzzy PI controller are selected by using the inclusion relationship. And, for the sake of simplicity, only four rules are used to construct a nonlinear fuzzy control surface. The tuning parameters of the discrete fuzzy PI controller are optimized by using the PSO. To verify the effectiveness of the controller designed by using the discrete fuzzy PI control and the PSO, we applied it to a wind turbine pitch controller. As a result, the proposed controller has variable gains, unlike the PI controller, and make the pitch controller operate in boarder operating regions.