Proportional-integral-derivative Parameters Research Articles

Design of Optimal Controllers for Automatic Voltage Regulation Using Archimedes Optimizer

Automatic voltage regulators (AVRs) in electrical grids preserve the voltage at its nominal value. Regulating the parameters of proportional–integral–derivative (PID) controllers used for AVRs is a nonlinear optimization issue. The objective function is designed to minimize the settling time, rise time, and overshoot of step response of resultant voltage with subjugation to constraints of PID controller parameters. In this study, we suggest using an Archimedes optimization algorithm (AOA) to tune the parameters of the PID controllers for AVRs. In addition, using an AOA to optimize the parameters of a fractional-order PID (FOPID) controller and a PID plus second-order derivative (PIDD2) controller for AVRs is also investigated to validate their effectiveness. The disturbance repudiation and robustness of the AOA-PID controllers are also examined and confirmed. To validate the results of the AOA-PID controllers, they are compared with those of other optimized controllers for convergence speed, the quality of the step response. The results indicate that the AOA functions perfectly and it has good potential for optimizing the PID controller parameters with better step response compared with the PID controller based on other approaches while preferring the results of the AOA–PIDD2 controller over other kinds of the AOA-PID controllers.

Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming

This paper deals with the design problem of multivariable Proportional-Integral-Derivative (PID) controllers for square and stable multivariable processes when a linear margin at the Nyquist plot is considered as robustness specification for each closed loop. A tuning method is developed based on the new concept of equivalent loop transfer function, which is proposed for centralized control and allows an independent design for each loop considering the interactions with the other loops through an iterative procedure. For the k-th loop, the PID parameters of the k-th column of the control matrix are calculated in each iteration by a linear programming optimization that maximizes the integral gains while fulfilling the robustness specification and achieving static decoupling. The method uses a frequency response array as representation of the process, which allows its applicability to systems with multiple time delays without requiring model reductions or approximations. The effectiveness of the method is illustrated by means of two simulation examples with dimensions <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3 \times 3$ </tex-math></inline-formula> . Comparisons with other centralized control methodologies show that the proposed approach achieves similar or greater performance and a remarkable better disturbance rejection response.

LQR-based MIMO PID control of a 2-DOF helicopter system with uncertain cross-coupled gain

This work deals with designing multi-input multi-output (MIMO) proportional-integral-derivative (PID) controllers to achieve linear quadratic (LQ) performance of a laboratory-based two degree-of-freedom (2-DOF) helicopter system with norm-bounded uncertainties in the cross-coupled gain. It is shown that, for such an uncertain system, the MIMO PID design problem can be recast as a full-state feedback control for an augmented uncertain system. Consequently, a simple linear matrix inequality problem is solved to determine the PID parameters in order to achieve robust LQ performance. The efficacy of the proposed controller is shown through extensive simulations and experiments.

Adaptive Fuzzy Neural Network PID Algorithm for BLDCM Speed Control System

Because of its simple structure, high efficiency, low noise, and high reliability, the brushless direct current motor (BLDCM) has an irreplaceable role compared with other types of motors in many aspects. The traditional proportional integral derivative (PID) control algorithm has been widely used in practical engineering because of its simple structure and convenient adjustment, but it has many shortcomings in control accuracy and other aspects. Therefore, in this paper, a fuzzy single neuron neural network (FSNNN) PID algorithm based on an automatic speed regulator (ASR) is designed and applied to a BLDCM control system. This paper introduces a BLDCM mathematical model and its control system and designs an FSNNN PID algorithm that takes speed deviation e at different sampling times as inputs of a neural network to adjust the PID parameters, and then it uses a fuzzy system to adjust gain K of the neural network. In addition, the frequency domain stability of a double closed loop PID control system is analyzed, and the control effect of traditional PID, fuzzy PID, and FSNNN PID algorithms are compared by setting different reference speeds, as well as the change rules of three-phase current, back electromotive force (EMF), electromagnetic torque, and rotor angle position. Finally, results show that a motor controlled by the FSNNN PID algorithm has certain superiority compared with traditional PID and fuzzy PID algorithms and also has better control effects.

Online self-adaptive proportional-integral-derivative control for brushless DC motor based on variable universe fuzzy inference system optimized by genetic algorithm

In this study, we propose a novel robust online self-adaptive Proportional-Integral-Derivative (PID) control design for Brushless DC Motor (BLDCM) speed system under different operating conditions. The online adaptive tuning for PID parameters is realized accurately by optimizing the control rules of variable universe fuzzy inference with a modified genetic algorithm (GA). Based on the variable fuzzy inference theory, the method of solving contraction–expansion factor in real-time through fuzzy inference is proposed. Furthermore, the process to optimize two inference rules by GA is improved to get optimal control rules for adjusting PID parameters. Finally, multiple sets of simulations and experiments are conducted to validate the proposed controller in different conditions by building Simulink models and setting up experiment platforms. The results of this study not only demonstrate the effectiveness of the proposed controller but also provide technical suggestions for the speed control of BLDCM.

Metaheuristic Optimization of PD and PID Controllers for Robotic Manipulators

In this paper, the Particle Swarm Optimization algorithm (PSO) is combined with Proportional-Derivative (PD) and Proportional-Integral-Derivative (PID) to design more efficient PD and PID controllers for robotic manipulators. PSO is used to optimize the controller parameters Kp (proportional gain), Ki (integral gain) and Kd (derivative gain) to achieve better performances. The proposed algorithm is performed in two steps: (1) First, PD and PID parameters are offline optimized by the PSO algorithm. (2) Second, the obtained optimal parameters are fed in the online control loop. Stability of the proposed scheme is established using Lyapunov stability theorem, where we guarantee the global stability of the resulting closed-loop system, in the sense that all signals involved are uniformly bounded. Computer simulations of a two-link robotic manipulator have been performed to study the efficiency of the proposed method. Simulations and comparisons with genetic algorithms show that the results are very encouraging and achieve good performances.

Optimal tuning of a PID controller using a wound healing algorithm based on the clonal selection principle

Control strategies for uncertainties or nonlinear effects need to be developed for control systems. Optimization algorithms developed with the rapid development of computer technology are frequently used to improve the steady-state response with the help of the ambiguous mathematical characteristics or nonlinearity of control systems. In this study, an optimum proportional–integral–derivative (PID) controller was designed using the wound healing algorithm based on the clonal selection principle. The proposed algorithm is applied in self-tuning a PID controller in the ball and hoop system which represents a system of complex industrial processes. In order to adjust the PID parameters with the aid of the developed algorithm, an integral absolute error (IAE) has been chosen as the objective function. Thus, the system reached the optimum solution quickly and time was saved. The advantages of the proposed algorithm have been proved by comparing the obtained results with other algorithms. To succeed this, a programme was written in the MATLAB GUI environment.

Freeway ramp metering based on PSO-PID control.

Ramp metering on freeway is one of the effective methods to alleviate traffic congestion. This paper advances the field of freeway ramp metering by introducing an application to the on-ramp, capitalizing on the macro traffic follow theory and improved the freeway traffic flow. The Particle Swarm Optimization (PSO) based on Proportional Integral Derivative (PID) controller is further developed to single ramp metering as well as to optimize the PID parameters. The approach is applied to a case study of the Changyi Freeway(G5513) in Hunan, China. The simulation is conducted by applying the actual profile traffic data to PID controller to adjust the entering traffic flow on the freeway on-ramp. The results show that the PSO-PID controller tends to converge in about 80 minutes, and the density tends to be stable after 240 iterations. The system has smaller oscillation, more accurate adjustment of ramp regulation rate, and more ideal expected traffic flow density. The traffic congestion on mainline is effectively slowed down, traffic efficiency is improved, and travel time and cost are reduced. The nonlinear processing ability of PSO-PID controller overcomes the defects of the traditional manual closing ramp, and can be successfully applied in the field of intelligent ramp metering.

Comparative of Ziegler Nichols, Fuzzy Logic and Extremum Seeking Based Proportional Integral Derivative Controller for Quadcopter Unmanned Aerial Vehicle Stability Control

Unmanned aerial vehicle is potentially recognized in autonomous sectors where intelligence gathering, surveillance, reconnaissance missions, power line inspection, aerial video, search and rescue monitoring devices are required. It is essential in modern era control and monitoring especially a rotary unit where quadcopter performed a crucial task. However, the flight behavior of a quadcopter is determined by the synchronous speed of each of the motors as the speed changes with load torque variations. The dynamics model equation of the system, external disturbances and its parameters variation of the motor makes it difficult for the manual tuning techniques employed into the system to perform its stability operation. The purpose of this work is to employ adaptive controllers to enhance the stability performance so as to prevent the risk of human lives and financial implication that may arise from improper monitoring of the system. Therefore, Ziegler Nichols, fuzzy logic and extremum seeking controllers were employed to auto-tuned the parameters of proportional integral derivative (PID) gains controller to optimize and give a satisfactory performance of motor speed control at different operating condition. The altitude, pitch, roll and yaw parameters of the quadcopter are simulated using the x-plane II flight simulator MATLAB tools. The simulation results presented in this work show better performance for extremum seeking-PID in terms of decrease in rise time, settling time and overshoot relative to Zigler-Nichols-PID and Fuzzy-PID controllers.

Real-time tuning of PID controller based on optimization algorithms for a quadrotor

PurposeThis study aims to develop a quadrotor with a robust control system against weight variations. A Proportional-Integral-Derivative (PID) controller based on Particle Swarm Optimization and Differential Evaluation to tune the parameters of PID has been implemented with real-time simulations of the quadrotor.Design/methodology/approachThe optimization algorithms are combined with the PID control mechanism of the quadrotor to increase the performance of the trajectory tracking for a quadrotor. The dynamical model of the quadrotor is derived by using Newton-Euler equations.FindingsIn this study, the most efficient control parameters of the quadrotor are selected using evolutionary optimization algorithms in real-time simulations. The control parameters of PID directly affect the controller’s performance that position error and stability improved by tuning the parameters. Therefore, the optimization algorithms can be used to improve the trajectory tracking performance of the quadrotor.Practical implicationsThe online optimization result showed that evolutionary algorithms improve the performance of the trajectory tracking of the quadrotor.Originality/valueThis study states the design of an optimized controller compared with manually tuned controller methods. Fitness functions are defined as a custom fitness function (overshoot, rise-time, settling-time and steady-state error), mean-square-error, root-mean-square-error and sum-square-error. In addition, all the simulations are performed based on a realistic simulation environment. Furthermore, the optimization process of the parameters is implemented in real-time that the proposed controller searches better parameters with real-time simulations and finds the optimal parameter online.

Design of an Optimized GMV Controller Based on Data-Driven Approach

This paper presents a data-driven scheme that can obtain the optimized Generalized Minimum Variance (GMV) control parameters by applying the Nelder—Mead (NM) method based on Proportional-Integral Derivative (PID) controller for linear system. An adjustable λ is included in the GMV-PID controller. In the existing GMV-PID controller, the PID parameters are calculated by simply changing λ manually. Therefore, it is hard to get desirable control performance. The NM method is introduced to improve the control performance. The application of NM method can optimize the calculation of λ. However, the objective function in NM method needs the output calculation. In other words, the model information is inevitably to obtain output. To achieve model-free design scheme, the estimation of closed-loop response method is introduced in database-driven approach. Using obtained closed-loop data can predict the output and then substitute it into the objective function without any model information of the process. The effectiveness is verified by experiment.

Experimental study on isolated operation of hydro-turbine governing system of Lunzua hydropower station in Zambia

This paper focused on the stable operation and control strategy of the hydro-turbine governing system (HTGS) in an isolated-grid operation mode. The stable operation of a hydropower station in isolated-grid operation mode is important for the safe operation of a power system. A regional power grid can be isolated from a main grid due to factors such as natural disasters, grid failures, and human errors. The Lunzua hydropower station in Zambia is often forced to operate as an isolated grid. To ensure its safe and stable operation, we conducted isolated-grid regulation tests in conjunction with field testing of HTGS and determined the parameters of the HTGS for stable operation of the isolated grid. In the field test, we first set the no-load and initial parameters for the isolated-grid mode through the no-load disturbance tests. Through simulated isolated-grid operation tests, we verified and further tuned the initial parameters. Meanwhile, we propose a control strategy for the transition between large-grid and isolated-grid modes. Through operational tests, we determined the parameters for stable operation in isolated-grid mode. During testing, we found that the water flow inertia time constant Tw was too large and the inertial time constant Ta of the impulsive generator was too small, which resulted in a narrow stability range of proportional–integral–derivative (PID) controller parameters for isolated-grid operation. The governing stability for isolated-grid operation was thus sensitive to the PID parameters. Since the isolated-grid field operation test of the HTGS of the Lunzua hydropower station was completed in August 2016, the generator units have maintained safe and stable operation in large-grid and isolated-grid modes, which validated the isolated-grid operation parameters and control strategy for the transition between large-grid and isolated-grid modes as determined by our test method. The methods of field test and control strategies used for isolated-grid operation have important practical value for the isolated grid operation of hydropower stations.

Analysis and design of auto-adaptive leveling hydraulic suspension for agricultural robot

The application of agricultural robot in hilly and mountain areas faces several problems, such as bad walking performance, easy tilt, and low safety. The auto-adaptive leveling hydraulic suspension for the agricultural robot can help to eliminate some sort of problems. The design of such system is the main aim of the article. The hydraulic system with load-sensing system and its controlling model were established and then the load-sensing system was modeled and simulated in Advanced Modeling Environment for SIMulation. The optimal proportional–integral–derivative parameters were determined by the optimized algorithm. The simulation results illustrated that the inlet and outlet pressure difference of throttle and the flow rate through throttle are 42 bar and 29.65 L/min, respectively, all the time when the load pressure varies from 0 bar to 100 bar. The load-sensing system has good power follow-up and high control accuracy. And then the experimental bench of auto-adaptive leveling hydraulic suspension was researched and developed to verify the leveling performance. The experimental results demonstrate that auto-adaptive leveling hydraulic suspension can keep frame leveling dynamically on upslope, downslope, side slope, and continuous undulating road surface. The maximum errors of the pitch angle and the tilt angle are −0.93° and 0.97°. The feasibility of the designed hydraulic suspension was verified. The research methods in this article can provide theoretical basis for the design of other auto-adaptive leveling systems in hilly and mountain areas.

Optimization of Neural Network-Based Self-Tuning PID Controllers for Second Order Mechanical Systems

The feasibility of a neural network method was discussed in terms of a self-tuning proportional–integral–derivative (PID) controller. The proposed method was configured with two neural networks to dramatically reduce the number of tuning attempts with a practically achievable small amount of data acquisition. The first network identified the target system from response data, previous PID parameters, and response characteristics. The second network recommended PID parameters based on the results of the first network. The results showed that it could recommend PID parameters within 2 s of observing responses. When the number of trained data was as low as 1000, the performance efficiency of these methods was 92.9%, and the tuning was completed in an average of 2.94 attempts. Additionally, the robustness of these methods was determined by considering a system with noise or a situation when the target position was modified. These methods are also applicable for traditional PID controllers, thus enabling conservative industries to continue using PID controllers.

Corrosion risk analysis of tube-and-shell heat exchangers and design of outlet temperature control system

This study deals with the high-risk shell-and-tube heat exchangers in the effluent system of hydrogenation reaction of the petrochemical industry. The process of hydroprocessing reactor effluent system is simulated in Aspen Plus to study the distribution of corrosive medium in the three phases of oil, gas and water. The least-squares method is utilized to calculate the ammonium salt crystallization temperature. Then, the heat exchanger with risk of ammonium salt crystal corrosion is identified. Dynamic mathematical modeling of the heat exchanger is established to determine the transfer function. A temperature control system with proportional integral derivative (PID) control of the heat exchanger outlet is designed, and fuzzy logic is used to implement self-tuning of PID parameters. After MATLAB simulation, the results show the control system can achieve rapid control of the heat exchanger outlet temperature.

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.

Control of Nonlinear Uncertain Systems by Extended PID

Since the classical proportional-integral-derivative (PID) controller is the most widely and successfully used ones in industrial processes, it is of vital importance to investigate theoretically the rationale of this ubiquitous controller in dealing with nonlinearity and uncertainty. Recently, we have investigated the capability of the classical PID control for second-order nonlinear uncertain systems, and provided some analytic design methods for the choices of PID parameters, where the system is assumed to be in the form of cascade integrators. In this article, we will consider the natural extension of the classical PID control for high-order affine-nonlinear uncertain systems. In contrast to most of the literature on controller design of nonlinear systems, we do not require such special system structures as normal or triangular forms, thanks to the strong robustness of the extend PID controller. To be specific, we will show that under some suitable conditions on nonlinearity, and uncertainty of the systems, the extended PID controller can semiglobally stabilize the nonlinear uncertain systems, and at the same time the regulation error converges to zero exponentially fast, as long as the control parameters are chosen from an open unbounded parameter manifold constructed in this article.

Mössbauer Spectrometer With Advanced Modulation of Gamma Ray Energy Utilizing Real-Time Industrial Computer

A new Mössbauer spectrometer based on a CompactRIO platform was developed. The CompactRIO is a modular industrial computer platform developed by the National Instruments. This device runs under “LabVIEW RT OS”-Linux-based real-time operating system, which has a support of the LabVIEW programming environment. The CompactRIO has an integrated field programmable gate array (FPGA), which was used for most critical functions of the developed spectrometer, such as scintillation detector signal acquisition and accumulation of Mössbauer spectra, and for driving a velocity transducer movement using a proportional-integral-derivative (PID) regulation. The velocity transducer modulates gamma rays' energy by movement using the Doppler effect. Precision of this movement is crucial, as it defines whole spectrometer accuracy. More sophisticated algorithms (i.e., PID parameters autotuning and additional Mössbauer spectra linearization methods) have been implemented on the real-time part of the CompactRIO. The developed spectrometer demonstrates the advantages of the real-time systems such as deterministic processing of large amounts of data allowing measurement in a very high velocity resolution.

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.

Application of an adaptive PID controller enhanced by a differential evolution algorithm for precise control of dissolved oxygen in recirculating aquaculture systems

In aquaculture, the dissolved oxygen (DO) content of a water body is important for the growth of aquatic products and thus needs to be precisely controlled. For this purpose, through an open-loop experiment of DO aeration under different airflow rates, empirical transfer function models that can fully describe the dynamic response relationship between aeration flow rate and DO content were established. Based on these models, this study proposed a differential evolution (DE) algorithm-optimised radial basis function (RBF) neural network proportional integral derivative (PID) controller (DE-RBF-PID). The proposed controller has two optimisation parts. The first part is devoted to finding the optimal initial parameters of PID using an improved DE algorithm. The second part utilises the powerful learning ability of the RBF neural network to adjust the PID parameters online, which can not only eliminate overshoots, but also improve the controller adaptability. The simulation results for a typical DO nonlinear control system demonstrated the superiority of the proposed DE-RBF-PID controller over conventional PID and RBF-PID controllers. Therefore, this controller can be applied for precise tracking control of DO in complex circulating aquaculture systems. • The transfer function models of the control process for DO were established. • An adaptive PID controller enhanced by DE algorithm was proposed. • This proposed controller was used for DO control in circulating aquaculture. • This work can provide theoretical basis and accumulate experience for practical application.