Optimal Proportional-integral-derivative Controller Research Articles

Optimization of PID controller for water level control of the nuclear steam generator using PSO and GA

Abstract The water level control system implicated in the nuclear steam generator has played an essential role in unexpected shutdowns of the power plant. According to reports, about 25% of the emergency power blackouts are caused by improper level control systems. The effectiveness of optimization methods in designing a controller is currently proved in different disciplines. The novelty of this paper is the proportional integral derivative (PID) controller tuning of nuclear steam generator by particle swarm optimization (PSO) and genetic algorithm (GA) for the lowest steady-state error, overshoot, undershoot, and settling time. Different types of the cost function are employed to obtain the controller gains. The integral of the absolute error (IAE), square error (ISE), time-weighted average error (ITAE), time-weighted square error (ITSE), and a weighted function based on overshoot, undershoot, and settling time are used. The gain scheduling of optimized PIDs is used to have an entire operating range control system. The desired load-following and stability of the optimized PID controller are investigated under both time and frequency domains using trajectory tracking, disturbance rejection, and Nichols chart criterion.

The effect of an evolutionary algorithm's rapid convergence on improving DC motor response using a PID controller

Mobile robots experience a lot of challenges with path tracking because of the significant problem with DC motor speed control. The particle swarm optimization (PSO) tuned proportional integral derivative (PID) controller is commonly used to control DC motor speed. However, it fails to reach the optimal solution quickly. Therefore, this paper demonstrates the application of the artificial bee colony (ABC) algorithm to tune a PID controller for speed regulation of a DC motor. The proposed approach was used to obtain the optimal PID controller gains (proportional, integral, and derivative) by minimizing the integral of time absolute error (ITAE) as the objective function. The analysis of statistical tests, transients, and frequency responses was conducted to test the rapid convergence of the proposed approach. Also, the performance of the proposed ABC-tuned PID controller has been compared with three variants of the PSO-tuned PID controller. The conducted simulation results and comparison with the proposed ABC controller and variant PSO controllers have shown that the proposed ABC-PID controller is more effective and robust than the variant PSO-PID controllers for the speed control of a DC motor.

Parameter optimization of PID controller for water and fertilizer control system based on partial attraction adaptive firefly algorithm

Proportional Integral Derivative (PID) control is the main control method in the process of agricultural water and fertilizer regulation, and its parameter setting directly affects the control effect of water and fertilizer regulation. However, the traditional PID parameters are adjusted manually such as using the critical proportionality method, which is time-consuming and difficult to achieve optimal control effects. To solve the optimal combination of PID control parameters and improve the control effect of water and fertilizer regulation, a partial attraction adaptive firefly algorithm (PAAFA) is proposed in this paper. Specifically, a partial attraction strategy is designed to speed up the convergence of the PAAFA and reduce the oscillation problem at the late stage of the algorithm. In addition, an adaptive inertia weight operator is proposed to balance the global search capability and local search capability of PAAFA and avoid the algorithm from trapping in the local optimum. Subsequently, to test the performance of PAAFA, the algorithm is subjected to a series of simulation experiments and bench tests with the latest methods, i.e., genetic algorithm (GA), Adaptive genetic algorithm (AGA), and firefly algorithm (FA) applied to PID parameter optimization problems. The simulation results demonstrate that the regulation times of the response curve of PAAFA-based PID control are reduced by 22.75%,10.10%and 20.61%, respectively, compared with GA, AGA, and FA. The bench test results show that the PAAFA-based PID control has the smallest relative error, and best control accuracy compared to GA, AGA, and FA, with an average relative error reduction of 3.99, 2.42, and 3.50 percentage points respectively.

Proportional-integral-derivative controller optimization by particle swarm optimization and back propagation neural network for a parallel stabilized platform in marine operations

The parallel stabilized platform is an important equipment to ensure the stability of marine operations, which can effectively mitigate collisions of lifted goods. The 3UPU_UP parallel stabilized platform system is proposed, and the kinematics and dynamics of the 3UPU_UP parallel stabilized platform are researched, where U denotes universal joint; P denotes prismatic joint. The platform motion can be realized by controlling the actuators to realize compensation ship motion. While conventional control algorithms are difficult to cope with complex nonlinear systems, the optimization control method has been proposed. Based on the back propagation (BP) neural network proportional-integral-derivative (PID) controller, the particle swarm optimization (PSO) is combined with the BP neural network, and the combined PSO-BP PID controller optimization algorithm is introduced into the servo control system. Compared with classic PID and BP PID, the overshoot of PSO-BP PID to the response of step signal is reduced by 10.2% and 11.48%, respectively, and 0.36s and 0.17s reduce the time required to reach stable states. By comparing the reduction of the error under various sea conditions, the upper platform tracking error curve is flatter under a PID controller based on PSO-BP, the tracking motion is closer to the theoretical value and the control accuracy is improved. The maximum tracking error of the upper platform is smaller, the overall motion vibration of the platform is reduced, and the anti-interference ability is enhanced. The PSO-BP PID controller for wave compensated platform servo system control is more reasonable, more adaptable to the complex and changing environment.

Design and Optimization of Fractional Order PID Controller to Enhance Energy Storage System Contribution for Damping Low-Frequency Oscillation in Power Systems Integrated with High Penetration of Renewable Sources

This paper proposes adding a controller to the energy storage system (ESS) to enhance their contribution for damping low-frequency oscillation (LFO) in power systems integrated with high penetration of different types of renewable energy sources (RES). For instance, wind turbines and photovoltaic (PV) solar systems. This work proposes superconducting magnetic energy storage (SMES) as an ESS. The proportional–integral–derivative (PID) and fractional-order PID (FOPID) are suggested as supporter controllers with SMES. The PID and FOPID controller’s optimal values will be obtained using particle swarm optimization (PSO) is used as the optimization method. Both local area and inter-area oscillation is considered in this work as a LFO. To investigate the impact of adding the SMES with the proposed controller, a multimachine power system with different integration scenarios and cases is carried out with a PV system and wind turbine. The system responses are presented and discussed to show the superiority of the proposed controller both in the time domain and by eigenvalues analysis.

Load frequency control based on an improved Chimp optimization algorithm using adaptive weight strategy

PurposeThis study aims to implement an improved version of the Chimp algorithm (IChimp) for load frequency control (LFC) of power system.Design/methodology/approachThis work was adopted by IChimp to optimize proportional integral derivative (PID) controller parameters used for the LFC of a two area interconnected thermal system.FindingsThe supremacy of proposed IChimp tuned PID controller over Chimp optimization, direct synthesis-based PID controller, internal model controller tuned PID controller and recent algorithm based PID controller was demonstrated.Originality/valueIChimp has good convergence and better search ability. The IChimp optimized PID controller is the proposed controlling method, which ensured better performance in terms of converging behaviour, optimizing controller gains and steady-state response.

A Comparison on PSO Optimized PID Controller for Inter-Area Oscillation Control in an Interconnected Power System

This paper emphasizes on the development of control strategy for inter area oscillation suppression for a unified two-area hydro-thermal deregulated power system. A particle swarm optimization (PSO) optimized Proportional Integral Derivative (PID) controller is proposed for automatic generation control (AGC). Further comparison between different variants of PSO are carried out, where 6 different variants have been explored, which are success rate based PSO, evolution speed and aggregation degree factors based PSO, global-local best inertia weight based PSO, distance from global best based PSO, fixed inertia weight based PSO and varying acceleration coefficients based PSO. A comprehensive analysis of these optimization techniques are presented on the basis of major dynamic performance parameters, i.e. settling time and peak overshoot. Successive rate based PSO variant found best among these six variants.

Frequency Regulation of Interconnected Power System Using Black Widow Optimization

A frequency regulation of interconnected power system comprising thermal reheat system and photovoltaic panel systems is disclosed in this research article with Proportional Integral Derivative (PID) controller optimized using Black Widow Optimization Algorithm (BWOA) based on distinct feature of cannibalism of black widow spiders. With rising demand for perfectly optimized power systems, a best optimal solution for controller gains besides merit of faster convergence and avoidance of trapping in local minimal are becoming key requirements for system engineers. In tune with these requirements, we have developed an optimized solution based on BWOA in the power system realm to minimize the fitness function which is Integral Time Absolute Error composing of frequency and tie-line power variations. Superiority of BWOA optimized controller in power system realm is established by comparing and analyzing its simulation results with some other known tuned controllers which uses different optimization algorithms namely firefly algorithm, genetic algorithm, whale optimization algorithm and modified whale optimization algorithm. Results in this paper lays out that BWOA optimized PID controller outperforms other reported controllers in terms of fitness function value, settling time, undershoot/overshoot of the incremental variations in frequency and tie-line power of the interconnected power system. Further, the potency and robustness of the proposed tuned controller are also proven by considering large variation in load demand, real-time constraints namely generation rate constraint and governor dead band in the system. Additionally, the sensitivity analysis of the optimized controlled system is performed to conclude that the proposed BWOA optimized PID controller optimized controller is insensitive to changes in system parameters and eliminates the necessity of resetting of controller parameters. The performance of the proposed control technique is also tested on two-area non-reheat thermal power system with non-linear constraints namely time delay, generation rate constraint and governor deadband.

Real Time Implementation for Tuning PID Controller Based on Advanced Optimization Techniques for Micro Robotics System

The process of tuning the PID controller’s parameters is considered to be a difficult task. Several approaches were developed in the past known as conventional methods. One of these methods is the Ziegler and Nichols that relies on accurate mathematical model of the linear system, but if the system is complex the former method fails to compute the parameters of PID controller. To overcome this problem, recently there exist several techniques based on artificial intelligence such as optimization techniques. The optimization techniques does not require any mathematical model and they are considered to be easy to implement on any system even if it complex, can reach optimal solutions on the parameters. In this study, a new approach to control the position of the micro-robotics system proportional - integral - derivative (PID) controller is designed and a recently developed algorithm based on optimization is known as the sparrow search algorithm (SSA). By using the sparrow search algorithm (SSA), the optimal PID controller parameters were obtained by minimizing a new objective function, which consists of the integral square Time multiplied square Error (ISTES) performance index. The effectiveness of the proposed SSA-based controller was verified by comparisons made with the Sine Cosine algorithm (SCA), and Flower pollination algorithm (FPA) controllers in terms of time and frequency response. Each control technique will be applied to the identified model (simulation results) using MATLAB Simulink and the laboratory setup (experimental results) using LABVIEW software. Finally, the SSA showed the highest performance in time and frequency responses.

Implementing optimization of PID controller for DC motor speed control

The point of this paper presents an optimization technique which is flexible and quick tuning by using a genetic algorithm (GA) to obtain the optimum proportional-integral-derivative (PID) parameters for speed control of aseparately excited DC motor as a benchmark for performance analysis. The optimization method is used for searching for the proper value of PID parameters. The speed controller of DC motor using PID tuning method sincludes three types: MATALB PID tunner app., modified Ziegler-Nicholsmethod and genetic algorithm (GA). PID controller parameters (Kp, Ki and Kd) will be obtained by GA to produce optimal performance for the DC motor control system. Simulation results indicate that the tuning method of PID by using a genetic algorithm is shown to create the finest result in system performance such as settling time, rise time, percentage of overshoot and steady state error. The MATLAB/Simulink software is used to model and simulate the proposed DC motor controller system.

Optimization of PID Controller to Stabilize Quadcopter Movements Using Meta-Heuristic Search Algorithms

Quadrotor UAVs are one of the most preferred types of small unmanned aerial vehicles, due to their modest mechanical structure and propulsion precept. However, the complex non-linear dynamic behavior of the Proportional Integral Derivative (PID) controller in these vehicles requires advanced stabilizing control of their movement. Additionally, locating the appropriate gain for a model-based controller is relatively complex and demands a significant amount of time, as it relies on external perturbations and the dynamic modeling of plants. Therefore, developing a method for the tuning of quadcopter PID parameters may save effort and time, and better control performance can be realized. Traditional methods, such as Ziegler–Nichols (ZN), for tuning quadcopter PID do not provide optimal control and might leave the system with potential instability and cause significant damage. One possible approach that alleviates the tough task of nonlinear control design is the use of meta-heuristics that permit appropriate control actions. This study presents PID controller tuning using meta-heuristic algorithms, such as Genetic Algorithms (GAs), the Crow Search Algorithm (CSA) and Particle Swarm Optimization (PSO) to stabilize quadcopter movements. These meta-heuristics were used to control the position and orientation of a PID controller based on a fitness function proposed to reduce overshooting by predicting future paths. The obtained results confirmed the efficacy of the proposed controller in felicitously and reliably controlling the flight of a quadcopter based on GA, CSA and PSO. Finally, the simulation results related to quadcopter movement control using PSO presented impressive control results, compared to GA and CSA.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Steam Turbine Governor (STG) Controller Design Based on Particle Swarm Optimization (PSO)

A reheat and non-reheat steam turbines governor is a component of the turbine control system that regulates rotational speed in response to changing load conditions. The governor output signal manipulates the position of a steam inlet valve or nozzles which in turn regulates the steam flow to the turbine. The application of PID (proportional integral derivative (controller has been widely used from small industry to high technology industry. Tuning the parameters of a PID controller is very important in PID control, Ziegler-Nichols method also used to tune the coefficients of a PID controller. The compensation has been proposed to be 4%, 6%, 8%, 10% and 15% of the actual load.This paper evaluates the feasibility of using the Particle Swarm Optimization (PSO) method for determining the optimal PID controller parameters for steam turbine speed control. The PSO optimization technique is compared with Ziegler-Nichols method and (PID) controllers. It is validated that PSO based controller is more efficient in reducing the steady-states error, settling time, rising time, and overshooting limit in speed control of the steam turbine control. In which the maximum peak overshoot has been reduced from 44.8% in case of the original system without any controller to 3.45% for the case of PSO based controller and that for 15% load change.

Intelligent Trajectory Tracking Behavior of a Multi-Joint Robotic Arm via Genetic-Swarm Optimization for the Inverse Kinematic Solution.

It is necessary to control the movement of a complex multi-joint structure such as a robotic arm in order to reach a target position accurately in various applications. In this paper, a hybrid optimal Genetic–Swarm solution for the Inverse Kinematic (IK) solution of a robotic arm is presented. Each joint is controlled by Proportional–Integral–Derivative (PID) controller optimized with the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), called Genetic–Swarm Optimization (GSO). GSO solves the IK of each joint while the dynamic model is determined by the Lagrangian. The tuning of the PID is defined as an optimization problem and is solved by PSO for the simulated model in a virtual environment. A Graphical User Interface has been developed as a front-end application. Based on the combination of hybrid optimal GSO and PID control, it is ascertained that the system works efficiently. Finally, we compare the hybrid optimal GSO with conventional optimization methods by statistic analysis.

Robust optimal proportional–integral–derivative controller design for a class of uncertain second-order delay-free and time-delay systems

The second-order systems can capture the dynamics of a vast majority of industrial processes. However, the existence of uncertainty in second-order approximation of such processes is inevitable because the approximation may not be accurate or the operating condition changes, resulting in performance degradation or even instability. This article aims at designing a novel robust proportional–integral–derivative controller for the uncertain second-order delay-free and time-delay systems in an optimal manner. The method is simple, effective, and can efficiently improve the performance of the uncertain systems. The approach is based on the linear quadratic theory, in which by adding a new matrix in the quadratic cost function regarding the uncertainties, the stability of the perturbed system is guaranteed and proven for both time-delay and delay-free second-order cases. The comparison with the recent works in the literature supports the effectiveness of the proposed methodology.

Proportional Integral Derivative Control in Spark Plasma Sintering Simulations.

The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS.

Design of controllers for automatic frequency control of different interconnection structures composing of hybrid generator units using the chaotic optimization approach

This paper deals with the determination of the proportional–integral–derivative (PID) parameters of automatic generation control (AGC) based on the chaotic optimization approach (COA). Unlike the literature approaches that are based on the usage of the classic objective function, in this paper, novel objective functions for determination of the optimal PID parameters are proposed and tested. The proposed algorithm was tested on different interconnection structures of two thermal generator units, a thermal generator unit and a photovoltaic system, and a multi generator system consisting of three generator units: thermal, hydro, and gas. Further, to prove the superiority of the proposed algorithm over many algorithms used in the literature, the transient performance of the AGC system was investigated. Various transient parameters, such as the settling time of the observed variables, the value of the objective function, and the overshoot, were considered in the analysis. Different robustness analysis tests were performed to validate the effectiveness of the proposed controller optimized through the COA against parametric variations, noise, and unstable mode of operation with negative damping. It was shown that the optimized PID controller outperformed other controllers proposed in the literature in terms of the analyzed criteria.

Determination of optimal PID control parameters by response surface methodology

Proportional–Integral–Derivative (PID) controllers are the most widely used systems in industrial applications and in academic research regarding control engineering. In this study, the optimal PID control parameters of a liquid level control system were determined with Response Surface Methodology. Dynamic analysis was carried out on the liquid level control system to prepare the reaction curve. Accordingly, dead time, time constant and process gain values were determined as 16s, 261s and 0.842, respectively. Based on the dynamic analysis, PID parameters were calculated in accordance with the Cohen-Coon, Ziegler-Nichols, Yuwana-Seborg methods, which are the commonly used tuning methods. The Kp, τI, τD parameters were calculated as 30.77, 29.15 and 5.4 with the Cohen-Coon method, as 0.453, 30.0 and 7.5 with the Ziegler-Nichols method and as 1.63, 686.3 and 117.7 with the Yuwana-Seborg method, respectively. The PID control parameters applied for the 40cm, 50cm and 60cm set points and ISE and IAE control performance values after experiments were calculated. The Kp, τI and τD values were selected as the independent parameters, while the ISE and IAE values were chosen as the dependent variables. The numerical values of the responses for the runs in the design matrices were determined with a closed-loop PID controller with the liquid level system block diagram that was designed in MATLAB/Simulink. The simulations proposed by the trial version of Design Expert 7.0 program were performed in order and the IAE and ISE values were calculated after the simulations were processed. In this study, minimum ISE and IAE values were selected to determine the best PID parameters of a liquid level control system. The optimal PID control parameters of the liquid level system required to obtain the lowest ISE and IAE values were determined as 23.14, 28.31 and 11.50 for Kp, τI and τD, respectively.

Dynamic Modeling of Multiple Microgrid Clusters Using Regional Demand Response Programs

Preserving the frequency stability of multiple microgrid clusters is a serious challenge. This work presents a dynamic model of multiple microgrid clusters with different types of distributed energy resources (DERs) and energy storage systems (ESSs) that was used to examine the load frequency control (LFC) of microgrids. The classical proportional integral derivative (PID) controllers were designed to tune the frequency of microgrids. Furthermore, an imperialist competitive algorithm (ICA) was proposed to investigate the frequency deviations of microgrids by considering renewable energy resources (RERs) and their load uncertainties. The simulation results confirmed the performance of the optimized PID controllers under different disturbances. Furthermore, the frequency control of the microgrids was evaluated by applying regional demand response programs (RDRPs). The simulation results showed that applying the RDRPs caused the damping of frequency fluctuations.

Load Frequency Control of Two-area Interconnected Power System Using Optimal Controller, PID Controller and Fuzzy Logic Controller

In this paper, decentralized control scheme for Load Frequency Control (LFC) problem in a two-area interconnected power system with Fuzzy Logic Controller (FLC) is presented and its performance is compared with that of Optimal Controller (OC) and Proportional-Integral-Derivative (PID) Controller used in the same power system. This control scheme is simulated in MATLAB-Simulink for a two-area interconnected power system consisting of two generating units with non-reheat turbines to highlight the performance in terms ofrobustness and optimality. The step response of these control schemes against step load change is analysed and compared.