Optimizing PID controller parameters for robust automatic voltage regulator system through indirect design approach-2

Automatic voltage regulators(AVR)are designed to manipulate a synchronous generator’s voltage level automatically.Proportional integral derivative(PID)controllers are typically used in AVR systems to regulate voltage.Although advanced PID tuning methods have been proposed,the actual voltage response differs from the theoretical predictions due to modeling errors and system uncertainties.This requires continuous fine tuning of the PID parameters.However,manual adjustment of these parameters can compromise the stability and robustness of the AVR system.This study focuses on the online self-tuning of PID controllers called indirect design approach-2(IDA-2)in AVR systems while preserving robustness.In particular,we indirectly tune the PID controller by shifting the frequency response.The new PID parameters depend on the frequency-shifting constant and the previously optimized PID parameters.Adjusting the frequency-shifting constant modifies all the PID parameters simultaneously,thereby improving the control performance and robustness.We evaluate the robustness of the proposed online PID tuning method by comparing the gain margins(GMs)and phase margins(PMs)with previously optimized PID parameters during parameter uncertainties.The proposed method is further evaluated in terms of disturbance rejection,measurement noise,and frequency response analysis during parameter uncertainty calculations against existing methods.Simulations show that the proposed method significantly improves the robustness of the controller in the AVR system.In summary,online self-tuning enables automated PID parameter adjustment in an AVR system,while maintaining stability and robustness.

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 2~3 factorial experimental design for a fractional order proportional integral and derivative controller(FOPID), integer order proportional integral and derivative controller(IOPID)and the Skogestad internal model control controller(SIMC). The factors assumed in experiment are the presence of random noise,external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.

Intelligent PID controller based on ant system algorithm and fuzzy inference and its application to bionic artificial leg

A designing method of intelligent proportional-integral-derivative(PID) controllers was proposed based on the ant system algorithm and fuzzy inference. This kind of controller is called Fuzzy-ant system PID controller. It consists of an off-line part and an on-line part. In the off-line part, for a given control system with a PID controller,by taking the overshoot, setting time and steady-state error of the system unit step response as the performance indexes and by using the ant system algorithm, a group of optimal PID parameters K*p , Ti* and T*d can be obtained, which are used as the initial values for the on-line tuning of PID parameters. In the on-line part, based on Kp* , Ti*and Td* and according to the current system error e and its time derivative, a specific program is written, which is used to optimize and adjust the PID parameters on-line through a fuzzy inference mechanism to ensure that the system response has optimal transient and steady-state performance. This kind of intelligent PID controller can be used to control the motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation experiment shows that the controller has less overshoot and shorter setting time.

Application of single neuron adaptive PID controller during the process of timber drying

The paper presents a method of using single neuron adaptive PID control for adjusting system or servo system to implement timber drying process control, which combines the thought of parameter adaptive PID control and the character of neural network on exactly describing nonlinear and uncertainty dynamic process organically. The method implements functions of adaptive and self-learning by adjusting weighting parameters. Adaptive neural network can make some output trail given hoping value to decouple in static state. The simulation result indicates the validity, veracity and robustness of the method used in the timber drying process

PID Controller Optimization by GA and Its Performances on the Electro-hydraulic Servo Control System

A proportional integral derivative （PID） controller is designed and attached to electro-hydraulic servo actuator system （EHSAS） to control the angular position of the rotary actuator which control the movable surface of space vehicles. The PID gain parameters are optimized by the genetic algorithm （GA）. The controller is verified on the new state-space model of servo-valves attached to the physical rotary actuator by SIMULINK program. The controller and the state-space model are verified experimentally. Simulation and experimental results verify the effectiveness of the PID controller adaptive by GA to control the angular position of the rotary actuator as compared with the classical PID controller and the compensator controller.

Design of PID controller with incomplete derivation based on differential evolution algorithm

To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution （DE） algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.

Tuning of fuzzy PID controller for Smith predictor

An analytical tuning method was proposed for fuzzy PID controller used in Smith predictor in order to extend its application and improve its robustness. The fuzzy PID controller was expressed as a sliding mode control. Based on Lyapunov theory, Smith predictor was analyzed in time domain. The parameters of the fuzzy PID controller can be obtained using traditional linear control theory and sliding mode control theory. The simulation experiments were implemented. The simulation results show that the control performance, robustness and stability of the fuzzy PID controller are better than those of the PID controller in Smith predictor.

Design of PID controller with incomplete derivation based on ant system algorithm

A new and intelligent design method for PID controller with incomplete derivation is proposed based on the ant system algorithm ( ASA) . For a given control system with this kind of PID controller, a group of optimal PID controller parameters K p * , T i * , and T d * can be obtained by taking the overshoot, settling time, and steady-state error of the system's unit step response as the performance indexes and by use of our improved ant system algorithm. K p * , T i * , and T d * can be used in real-time control. This kind of controller is called the ASA-PID controller with incomplete derivation. To verify the performance of the ASA-PID controller, three different typical transfer functions were tested, and three existing typical tuning methods of PID controller parameters, including the Ziegler-Nichols method (ZN),the genetic algorithm (GA),and the simulated annealing (SA), were adopted for comparison. The simulation results showed that the ASA-PID controller can be used to control different objects and has better performance compared with the ZN-PID and GA-PID controllers, and comparable performance compared with the SA-PID controller.

IMC based robust PID controller tuning for disturbance rejection

It is well-known that the IMC-PID controller tuning gives fast and improved set point response but slow disturbance rejection. A modification has been proposed in IMC-PID tuning rule for the improved disturbance rejection. For the modified IMC-PID tuning rule, a method has been developed to obtain the IMC-PID setting in closed-loop mode without acquiring detailed information of the process. The proposed method is based on the closed-loop step set point experiment using a proportional only controller with gain K_(c0). It is the direct approach to find the PID controller setting similar to classical Ziegler-Nichols closed-loop method. Based on simulations of a wide range of first-order with delay processes, a simple correlation has been derived to obtain the modified IMC-PID controller settings from closed-loop experiment. In this method, controller gain is a function of the overshoot obtained in the closed loop set point experiment. The integral and derivative time is mainly a function of the time to reach the first peak(overshoot). Simulation has been conducted for the broad class of processes and the controllers were tuned to have the same degree of robustness by measuring the maximum sensitivity, Ms, in order to obtain a reasonable comparison. The PID controller settings obtained in the proposed tuning method show better performance and robustness with other two-step tuning methods for the broad class of processes. It has also been applied to temperature control loop in distillation column model. The result has been compared to the open loop tuning method where it gives robust and fast response.

Robust PID controller design for time delay processes with peak of maximum sensitivity criteria

The motivation of this work is to obtain single PI/PID tuning formula for different types of processes with enhanced disturbance rejection performance. The proposed tuning formula consistently gives better performance in comparison to several well-known methods at the same degree of robustness for stable, integrating and unstable processes. For the selection of the closed-loop time constant(τc), a guideline is provided over a broad range of time-delay/time-constant ratios on the basis of the peak of maximum sensitivity(Ms). An analysis has been performed for the uncertainty margin with the different process parameters for the robust controller design. It gives the guideline of the Ms-value settings for the PI controller designs based on the process parameters uncertainty. Furthermore, a relationship has been developed between Ms-value and uncertainty margin with the different process parameters(k, τ and θ). Simulation study has been conducted for the broad class of processes and the controllers are tuned to have the same degree of robustness by measuring the maximum sensitivity, Ms, in order to obtain a reasonable comparison.

Application of PID controller to 2D differential geometric guidance problem

This paper presents the application of the proportional-integral-derivative （PID） controller to the flight control system （FCS） for two-dimensional （2D） differential geometric （DG） guidance and control problem. In particular, the performance of the designed FCS is investigated. To this end, the commanded angle-of-attack is firstly developed in the time domain using the classical DG formulations. Then, the classical PID controller is introduced to develop a FCS so as to form the 2D DG guidance and control system, and the PID controller parameters are determined by the Ziegler-Nichols method as well as the Routh-Hurwitz stability algorithm to guarantee the convergence of the system error. The results demonstrate that the designed controller yields a fast responding system, and the resulting DG guidance and control system is viable and effective in a realistic missile defense engagement.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

Design and Experimental Evaluation of PID Controller for Digital Electro-Pneumatic Cabin Pressure Control System

The performance of the designed digital electro-pneumatic cabin pressure control system for the cabin pressure schedule of transport aircraft is investigated.For the purpose of this study,an experimental setup consisting of a simulated hermetic cabin and altitude simulation chamber is configured for cabin pressure control system operation.A series of experimental tests are executed to evaluate the performance of the cabin pressure control system.The parameters of the PID controller are optimized.In the optimization process,the variation regularity of the rate of cabin pressure change under various conditions is considered.An approach to prioritize the control of the rate of change of cabin pressure based on the flight status model is proposed and verified experimentally.The experimental results indicate that the proposed approach can be adopted for the designed digital electro-pneumatic cabin pressure control system to obtain a better cabin pressure schedule and rate of cabin pressure change.

Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

Digital implementation of fractional order PID controller and its application

A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.

Application of PID Controller Based on BP Neural Network in Export Steam’s Temperature Control System

By combining the Back-Propagation （BP） neural network with conventional proportional Integral Derivative （PID） controller, a new temperature control strategy of the export steam in supercritical electric power plant is put forward. This scheme can effectively overcome the large time delay, inertia of the export steam and the influencee of object in varying operational parameters. Thus excellent control quality is obtaitud. The present paper describes the development and application of neural network based controller to control the temperature of the boiler＇s export steam. Through simulation in various situations, it validates that the control quality of this control system is apparently superior to the conventional PID control system.

Optimal fuzzy PID controller with adjustable factors based on flexible polyhedron search algorithm

A new kind of optimal fuzzy PID controller is proposed, which contains two parts. One is an on line fuzzy inference system, and the other is a conventional PID controller. In the fuzzy inference system, three adjustable factors x p, x i , and x d are introduced. Their functions are to further modify and optimize the result of the fuzzy inference so as to make the controller have the optimal control effect on a given object. The optimal values of these adjustable factors are determined based on the ITAE criterion and the Nelder and Mead′s flexible polyhedron search algorithm. This optimal fuzzy PID controller has been used to control the executive motor of the intelligent artificial leg designed by the authors. The result of computer simulation indicates that this controller is very effective and can be widely used to control different kinds of objects and processes.

ACS algorithm-based adaptive fuzzy PID controller and its application to CIP-I intelligent leg

Based on the ant colony system （ACS） algorithm and fuzzy logic control, a new design method for optimal fuzzy PID controller was proposed. In this method, the ACS algorithm was used to optimize the input/output scaling factors of fuzzy PID controller to generate the optimal fuzzy control rules and optimal real-time control action on a given controlled object. The designed controller, called the Fuzzy-ACS PID controller, was used to control the CIP-Ⅰ intelligent leg. The simulation experiments demonstrate that this controller has good control performance. Compared with other three optimal PID controllers designed respectively by using the differential evolution algorithm, the real-coded genetic algorithm, and the simulated annealing, it was verified that the Fuzzy-ACS PID controller has better control performance. Furthermore, the simulation results also verify that the proposed ACS algorithm has quick convergence speed, small solution variation, good dynamic convergence behavior, and high computation efficiency in searching for the optimal input/output scaling factors.

Multi-objective optimization based on Genetic Algorithm for PID controller tuning

To get the satisfying performance of a PID controller, this paper presents a novel Pareto-based multi-objective genetic algorithm (MOGA), which can be used to find the appropriate setting of the PID controller by analyzing the pareto optimal surfaces. Rated settings of the controller by two criteria, the error between output and reference signals and control moves, are listed on the pareto surface. Appropriate setting can be chosen under a balance between two criteria for different control purposes. A controller tuning problem for a plant with high order and time delay is chosen as an example. Simulation results show that the method of MOGA is more efficient compared with traditional tuning methods.

Metaheuristics Algorithm for Tuning of PID Controller of Mobile Robot System

Robots in the medical industry are becoming more common in daily life because of various advantages such as quick response,less human interference,high dependability,improved hygiene,and reduced aging effects.That is why,in recent years,robotic aid has emerged as a blossoming solution to many challenges in the medical industry.In this manuscript,meta-heuristics(MH)algorithms,specifically the Firefly Algorithm(FF)and Genetic Algorithm(GA),are applied to tune PID controller constraints such as Proportional gain Kp Integral gain Ki and Derivative gain Kd.The controller is used to control Mobile Robot System(MRS)at the required set point.The FF arrangements are made based on various pre-analysis.A detailed simulation study indicates that the proposed PID controller tuned with Firefly Algorithm(FF-PID)for MRSis beneficial and suitable to achieve desired closed-loop system response.The FF is touted as providing an easy,reliable,and efficient tuning technique for PID controllers.The most suitable ideal performance is accomplished with FF-PID,according to the display in the time response.Further,the observed response is compared to those received by applying GA and conventional off-line tuning techniques.The comparison of all tuning methods exhibits supremacy of FF-PID tuning of the given nonlinear Mobile Robot System than GA-PID tuning and conventional controller.