Optimal FOPID Controllers for LFC Including Renewables by Bald Eagle Optimizer

In this study,a bald eagle optimizer(BEO)is used to get optimal parameters of the fractional-order proportional-integral-derivative(FOPID)controller for load frequency control(LFC).SinceBEOtakes only a very short time in finding the optimal solution,it is selected for designing the FOPID controller that improves the system stability and maintains the frequency within a satisfactory range at different loads.Simulations and demonstrations are carried out using MATLAB-R2020b.The performance of the BEOFOPID controller is evaluated using a two-zone interlinked power system at different loads and under uncertainty of wind and solar energies.The robustness of the BEO-FOPID controller is examined by testing its performance under varying system time constants.The results obtained by the BEOFOPID controller are compared with those obtained by BEO-PID and PID controllers based on recent metaheuristics optimization algorithms,namely the sine-cosine approach,Jaya approach,grey wolf optimizer,genetic algorithm,bacteria foraging optimizer,and equilibrium optimization algorithm.The results confirm that the BEO-FOPID controller obtains the finest result,with the lowest frequency deviation.The results also confirm that the BEOFOPID controller is stable and robust at different loads,under varying system time constants,and under uncertainty of wind and solar energies.

Optimal Tuning of Plant-Friendly PID Controllers

A plant-friendly proportional-integral-derivative （PID） controller optimization framework is proposed to make tradeoffs among set-point response,controller output variations and robustness.The objective function is chosen as the weighted sum of the integral of squared time-weighted error and the integral of squared timeweighted derivative of the control variable with respect to set-point response,while the robustness of the system is guaranteed by constraints on gain and phase margins.Due to the complex structure of the constraints,the problem is solved by genetic algorithms.Simulation analysis show the proposed method could efficiently reduce the controller output variations while maintaining a short settling time.Based on the simulation results,iterative tuning rules for the weighting factor in the objective function are obtained,which allows efficient simple proportional-integral（PI） tuning formulae to be derived.

Implementation on FPGA of Neuro-Genetic PID Controllers Auto-Tuning

The present paper studies the use of genetic algorithm to optimize the tuning of the Proportional, Integral and Derivative (PID) controller. Two control criteria were considered, the integral of the time multiplied by the absolute error (ITAE), and the integral of the time multiplied by the absolute output (ITAY). The time variant plant tested is a first-order plant with time delay. We aim at a real time implementation inside a digital board, so, the previous continuous approach was discretized and tested;the corresponding control algorithm is presented in this paper. The genetic algorithms and the PID controller are executed using the soft processor NIOS II in the Field Programmable Gate Array (FPGA). The computational results show the robustness and versatility of this technology.

Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative(PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative(PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.

Measurement-based control approach for tuning PID controllers:application to induction machines

This paper presents an approach to design proportional-integral-derivative controllers for inductionmachines usingmeasurements.Most controlmethods developed for induc-tion machines are generally based on mathematical models.Due to complex dynamics of induction machines,identified models are often unable to perfectly describe their behaviour.Thus,the system performance will be limited by the quality of the identified model.Hence,developing control methods that do not require the availability of system model is advantageous.Here,we propose an approach that uses the frequency response data to directly design controllers.The main idea here is to find controller parameters so that the closed-loop frequency response fits a desired frequency response.Its main advantage is that errors associated with the modelling process are avoided.Moreover,the control design process does not depend on the order and complexity of the plant.A practical application to induction machines illustrates the efficacy of the proposed approach.

Conical tank level control using fractional order PID controllers： a simulated and experimental study

In this paper, simulated and experimental results on the conical tank level control are presented. PI/PID controllers of integer order （IO） as well as of fractional order （FO） are studied and compared. The tuning parameters are obtained first by using root locus （RL） and Ziegler and Nichols methods, for comparison purposes. Next, particle swarm optimization （PSO） is employed to determine the optimal controllers＇ parameters using as fitness function the integral of the absolute value of tracking error （IAE）. From the experimental results it is concluded that PI/FOPI are the controllers presenting the lowest IAE indexes, whereas PID/FOPID controllers present the lowest energy consumption by the control signal.

Near Optimal PID Controllers for the Biped Robot While Walking on Uneven Terrains

The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation （PID） controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization （MCIWO） and particle swarm optimization （PSO） algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.

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.

A PID Tuning Approach for Inertial Systems Performance Optimization

In the practice of control the industrial processes, proportional-integral-derivative controller remains pivotal due to its simple structure and system performance-oriented tuning process. In this paper are presented two approaches for synthesis the proportional-integral-derivative controller to the models of objects with inertia, that offer the procedure of system performance optimization based on maximum stability degree criterion. The proposed algorithms of system performance optimization were elaborated for model of objects with inertia second and third order and offer simple analytical expressions for tuning the PID controller. Validation and verification are conducted through computer simulations using MATLAB, demonstrating successful performance optimization and showcasing the effectiveness PID controllers’ tuning. The proposed approaches contribute insights to the field of control, offering a pathway for optimizing the performance of second and third-order inertial systems through robust controller synthesis.

Unified Control Theory from PID to ACPID

To address the challenge of achieving unified control across diverse nonlinear systems, a comprehensive control theory spanning from PID (Proportional-Integral-Derivative) to ACPID (Auto-Coupling PID) has been proposed. The primary concept is to unify all intricate factors, including internal dynamics and external bounded disturbance, into a single total disturbance. This enables the mapping of various nonlinear systems onto a linear disturbance system. Based on the theory of PID control and the characteristic equation of a critically damping system, Zeng’s stabilization rules (ZSR) and an ACPID control force based on a single speed factor have been designed. ACPID control theory is both simple and practical, with significant scientific significance and application value in the field of control engineering.

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

Optimal PD/PID control of smart base isolated buildings equipped with piezoelectric friction dampers

Long-period pulses in near-field earthquakes lead to large displacements in the base of isolated structures.To dissipate energy in isolated structures using semi-active control,piezoelectric friction dampers（PFD） can be employed.The performance of a PFD is highly dependent on the strategy applied to adjust its contact force.In this paper,the seismic control of a benchmark isolated building equipped with PFD using PD/PID controllers is developed.Using genetic algorithms,these controllers are optimized to create a balance between the performance and robustness of the closed-loop structural system.One advantage of this technique is that the controller forces can easily be estimated.In addition,the structure is equipped with only a single sensor at the base floor to measure the base displacement.Considering seven pairs of earthquakes and nine performance indices,the performance of the closed-loop system is evaluated.Then,the results are compared with those given by two well-known methods：the maximum possive operation of piezoelectric friction dampers and LQG controllers.The simulation results show that the proposed controllers perform better than the others in terms of simultaneous reduction of floor acceleration and maximum displacement of the isolator.Moreover,they are able to reduce the displacement of the isolator systems for different earthquakes without losing the advantages of isolation.

Adaptive Nonlinear PID Control and Rule-Based Compensation for Systems with Backlash

The control of dynamic nonlinear systems with unknown backlash was considered. By using an efficient approach to estimate the unknown backlash parameters, a rule? based backlash compensator was presented for canceling the effect of backlash. Adaptive nonlinear PID controller together with rule? based backlash compensator was developed and a satisfactory tracking performance was achieved. Simulation results demonstrated the effectiveness of the proposed method.

Experimental Comparison Between PID Control and Friction Compensation Control for a Class of Nonlinear System with Friction

A point to? point positioning control of systems with highly nonlinear frictions is studied. In view of variable frictions caused by the changes of load torque, an experimental comparison was made between the valve? controlled hydraulic motor servo system with PID control and that with friction compensation control. Experimental results show that the gross steady errors are caused by frictions when the system is controlled by the conventional proportional control algorithm. Although the errors can be reduced by introducing the integral control, the limit cycle oscillation and the long setting time are caused. The positioning error for a constant load torque can be eliminated by using fixed friction compensation, but poor positioning accuracy is caused by the same fixed friction compensation when the load torques varies greatly. The dynamic friction compensation based on the error and change in error measurements can significantly improve the position precision in a broad range of the changes of load torque.

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.

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 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.

Fuzzy self-tuning PID control of the operation temperatures in a two-staged membrane separation process

A two-staged membrane separation process for hydrogen recovery from refinery gases is introduced. The principle of the gas membrane separation process and the influence of the operation temperatures are analyzed. As the conventional PID controller is difficult to make the operation temperatures steady, a fuzzy self-tuning PID control algorithm is proposed. The application shows that the algorithm is effective, the operation temperatures of both stages can be controlled steadily, and the operation flexibility and adaptability of the hydrogen recovery unit are enhanced with safety. This study lays a foundation to optimize the control of the membrane separation process and thus ensure the membrane performance.

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.

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.