Optimal Proportional-integral-derivative Controller Research Articles

Design a robust intelligent power controller for pressurized water reactor using particle swarm optimization algorithm

Abstract Proportional–Integral–Derivative (PID) controllers have been optimized and used to overcome many types of problems in nuclear reactor systems. The high performance of PID controllers depend on optimizing their gains. In this research, an optimized robust PID controller is proposed to control power perturbations in a pressurized water reactor (PWR). The optimization process of robust PID using particle swarm optimization (PSO) algorithm aims to adapt PID gains then after that, H-infinity controller is used. The results show a good performance when that suggested hybrid controller is applied to the nuclear power system since the suggested design makes the system robust due to applying H-infinity method, in addition to get the benefits of the optimized PID controller.

Multi-objective optimization of PI controller for BLDC motor speed control and energy saving in Electric Vehicles: A constrained swarm-based approach

Proportional Integral Derivative (PID) controllers are widely employed in industrial applications due to their effectiveness, simplicity, and versatility. Within the automotive sector, one notable application of the Proportional Integral (PI) controller is in the realm of electric motors, particularly the Brushless Direct Current (BLDC) motors powering Electric Vehicles (EVs). The precision of speed control over BLDC motors, renowned for their efficiency and reliability, is paramount for optimizing vehicle performance and ensuring energy efficiency. PIDs must be tuned each time they are used in an application to optimize performance. A well-known empirical hit and trial tuning strategy is the Ziegler–Nichols method, which results in sub-optimal performance in the presence of locally optimal solutions of large-dimensional search spaces. Existing Artificial Intelligence methods tailored for PID controller tuning often focus on singular optimization aspects, neglecting potential performance gains achievable through multi-objective considerations. Furthermore, prevalent swarm-based PID optimization methods typically initialize the population randomly without imposing any bounds on input parameters, thus rendering them susceptible to inconsistent, unreliable, sub-optimal solutions in unconstrained search environments. In our research endeavors, we mathematically model the multi-objective optimization of BLDC motor speed control, energy usage, and efficiency using constrained Differential Evolution and Particle Swarm Optimized PID controllers. The Ziegler–Nichols tuning method is used to ascertain the initial PI parameters and define bounds within the input space. Our methodology addresses a critical gap by integrating real-time road gradient data into the EV control system, enhancing precision and minimizing energy consumption, especially during challenging road conditions. The proposed approach significantly improves motor speed control and energy efficiency in EVs. With our proposed swam-based optimization over 30 iterations, MSE decreased by approximately 95.4% (from 3.8834 to 0.1809), while energy consumption reduced by about 3.1% (from 1.015 kWh to 0.984 kWh). These results highlight the effectiveness of our method in enhancing both speed control precision and energy efficiency. In addition, code related data is available at Github.

A fast relay feedback auto-tuning tilt-integral-derivative (TID) controller method with the fractional-order Ziegler–Nichols approach

The relay feedback auto-tuning method, which was an early commercialized approach, has maintained its popularity due to its simplicity and robustness. However, the classical proportional integral derivative (PID) controller auto-tuning method often results in unacceptable overshoot, especially for integrating and higher-order processes. By integrating the TID controller with the relay feedback technique, we significantly enhance dynamic control performance without relying on prior knowledge of the system. However, the direct application of the classical auto-tuning method to the TID controller encounters challenges due to the additional fractional-order transfer function s−1n. Therefore, we have developed a fractional-order Ziegler–Nichols (FOZ-N) approach, specifically designed to adjust the parameters of the TID controller. The proposed FOZ-N method is fast, simple, and capable of achieving the desired performance. In contrast to the previous Ziegler–Nichols tuning method, the TID controller parameters Kt and Ki are determined to shift the critical point (−1/Ku,j0) to the FOZ-N point (−0.5,−j0.7) on the Nyquist curve, ensuring system robustness and dynamic performance. The impact of the fractional order parameter s−1n and ratio r is explored through time-domain analysis, where these parameters are determined to ensure optimal dynamic performance. Additionally, we provide a detailed tuning procedure along with a helpful example. To demonstrate the advantages of the proposed auto-tuning TID controller over the Ziegler–Nichols PID controller, Optimal PID controller, simple internal model control (SIMC) PID controller, and Ziegler–Nichols FOPID controller, we present a simulation illustration involving multiple different systems. To validate the practical outcomes of this paper, we present experimental results on the temperature control of a Peltier cell.

Tuning the Proportional-Integral-Derivative Control Parameters of Unmanned Aerial Vehicles Using Artificial Neural Networks for Point-to-Point Trajectory Approach.

Nowadays, trajectory control is a significant issue for unmanned micro aerial vehicles (MAVs) due to large disturbances such as wind and storms. Trajectory control is typically implemented using a proportional-integral-derivative (PID) controller. In order to achieve high accuracy in trajectory tracking, it is essential to set the PID gain parameters to optimum values. For this reason, separate gain values are set for roll, pitch and yaw movements before autonomous flight in quadrotor systems. Traditionally, this adjustment is performed manually or automatically in autotune mode. Given the constraints of narrow orchard corridors, the use of manual or autotune mode is neither practical nor effective, as the quadrotor system has to fly in narrow apple orchard corridors covered with hail nets. These reasons require the development of an innovative solution specific to quadrotor vehicles designed for constrained areas such as apple orchards. This paper recognizes the need for effective trajectory control in quadrotors and proposes a novel neural network-based approach to tuning the optimal PID control parameters. This new approach not only improves trajectory control efficiency but also addresses the unique challenges posed by environments with constrained locational characteristics. Flight simulations using the proposed neural network models have demonstrated successful trajectory tracking performance and highlighted the superiority of the feed-forward back propagation network (FFBPN), especially in latitude tracking within 7.52745 × 10-5 RMSE trajectory error. Simulation results support the high performance of the proposed approach for the development of automatic flight capabilities in challenging environments.

Designing an optimal PID controller for a PV-connected Zeta converter using genetic algorithm

This paper suggests a way of fixing problems of voltage fluctuations and peak overshoot in a PV-connected Zeta converter system. The Zeta converter in the proposed approach is controlled using proportional integral derivative (PID) while a genetic algorithm (GA) calculates the PID coefficients based on the control mechanism. The performance of the designed system was analyzed in a MATLAB/Simulink environment. The analysis showed that the proposed system reduced the output voltage ripple and peak overshoot during transient conditions by providing feedback to the converter through the PID controller, this is a significant improvement when compared to the results found without a PID controller.

Comparative Analysis of Optimal Control Strategies: LQR, PID, and Sliding Mode Control for DC Motor Position Performance

This study applies these control methods to the DC motor system to examine the robustness and performance of four optimal control methods. Optimal controllers aim to control the system to minimize a selected performance index. These control methods offer advantages such as improving energy efficiency, reducing costs, and enhancing system security. The Linear Quadratic Regulator (LQR) based controller is the primary optimal control method. Two well-known traditional control techniques include the Proportional-Integral-Derivative (PID) and Integral Sliding Mode Controller (ISMC). However, they do not usually contain optimal properties. In this study, the optimal control algorithms, defined by obtaining controller parameters through the Riccati equation, are applied to achieve accurate position-tracking control in a DC motor system using Matlab/Simulink. The integral term-based algorithms seem to be robust and eliminate steady-state errors. The optimal PID controller could not provide the minimum performance index, unlike the other controllers in the study. LQR and optimal ISMC algorithms could allow the performance index to be a minimum. An illustrative comparison of the performances of all optimal control algorithms has been presented through graphical representation, along with corresponding interpretations.

Load frequency control in three-area single unit power system considering non-linearities effect

Load frequency control is always a crucial aspect in delivering quality power in integrated power system. This paper proposes an optimally tuned Proportional-Integral-Derivative (PID) controller to remove frequency errors caused by unexpected load fluctuations while ensuring tie-line power exchange. Moreover, the threearea power system with non-linearities such as Generation Rate Constraint and Governor Dead Band has been investigated. For tuning the parameters of PID controller Improved Grey Wolf Optimization (IGWO) has been used. The dynamic response of optimized PID controller have been compared with the result obtained from Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Sine Cosine Algorithm (SCA).

Fractional-order PID controller design via optimal selection strategy of frequency domain specifications

In this paper, a novel fractional-order Proportional-Integral Derivative (PID) controller design depending on optimal selection of frequency domain specifications is proposed for time delay systems. The frequency domain specification sets, namely, (i) phase margin and gain crossover frequency and (ii) phase margin and gain margin are determined so that the reference model is optimal according to three time domain performance indices, i.e. Integral Square Error (ISE), Integral Time Square Error (ITSE) and Integral Absolute Error (IAE). Here, the delayed Bode's ideal transfer function is employed in the reference model. Moreover, the stability region of the reference model is given via a theorem. In simulation studies, the proposed methodology is compared with other two different methods using the same frequency domain specifications. It is observed that the proposed optimal fractional-order PID controllers outperform according to the mentioned performance indices, and they also possess considerably acceptable performance in terms of other time domain specifications such as overshoot, settling time, etc.

Ant Colony Optimization of Fractional-Order PID Controller based on Virtual Inertia Control for an Isolated Microgrid

Background: Increasing the penetration of renewable energy sources has become necessary, especially in isolated microgrids. This increase leads to a decrease in the total inertia of the microgrids, which affects microgrid stability. Moreover, voltage and frequency control in lowinertia microgrids is more difficult and sensitive. Objective: Improve low inertia isolated microgrids' dynamic response and save the microgrid stability at different contingency and uncertainty conditions. Moreover, it allows for more penetration of renewable energy sources. Method: Proposing different control strategies based on virtual inertia control. The first is a proportional- integral-derivative (PID) controller, and then, to allow for more tuning flexibility, a fractional- order proportional-integral-derivative (FOPID) controller is used. MATLAB TM/Simulink is used to compare the response of the isolated microgrid without virtual inertia control, with conventional virtual inertia control, PID-based virtual inertia control, and FOPID-based virtual inertia control. The PID and FOPID controllers’ parameters are tuned using the ant colony optimization (ACO) technique. Results: The proposed control techniques save the isolated microgrids' stability at different penetration levels of renewable energy sources and operating conditions. At the same time, the isolated microgrid without virtual inertia control or conventional virtual inertia control can not save its stability in many operating conditions. Conclusion: The proposed fractional-order proportional-integral-derivative (FOPID)-based virtual inertia control has proven its effectiveness in saving the isolated microgrid stability and gives the best controller response. FOPID-based virtual inertia control minimizes the frequency deviation with different disturbances and operating conditions.

Comparison of Machine Learning Algorithms for DC Motor PID Control with Genetic Algorithm

Proportional-Integral-Derivative (PID) is a closed loop control system based on dynamic system feedback commonly employed in industrial control systems that require continuous modulated control. The purpose of this project was to improve the efficacy of PID control, a branch of classical control theory, to allow for the application of PID controllers in more complex and non-linear environments. The research compares the results of different machine learning algorithms with genetic algorithms to optimize PID control parameters to achieve more precise control of 12V DC motors. Genetic Algorithm (GA) is a metaheuristic algorithm used to solve search and optimization problems in machine learning. GAs are developed based on the process of natural selection and genetics, relying on biologically inspired operators. After a series of selections and crossovers, the genetic algorithm selected the fittest generation of PID constants that would result in the optimal PID controller which minimizes system error value and linearizes the system behavior. Optimizing PID parameters to enhance the efficacy of classical control theory could increase machining precision in industrial production and improve the robustness of integrated PID controllers in complex environments such as the human body, enabling PID controllers to be an adaptive, simple, and viable option to be implemented in implantable artificial organs and motorized prosthetics. The results of the study suggest that GA optimized PID parameters are effective in regulating the system behavior of DC motors and the enhanced PID control system could be implemented in a wide range of rapidly changing and non-linear applications.

Design of the PID temperature controller for an alkaline electrolysis system with time delays

Electrolysis systems use proportional–integral–derivative (PID) temperature controllers to maintain stack temperatures around set points. However, because of heat transfer delays in electrolysis systems, the manual tuning of PID temperature controllers is time-consuming, and temperature oscillations often occur. This paper focuses on the design of the PID temperature controller for an alkaline electrolysis system to achieve fast and stable temperature control. A thermal dynamic model of an electrolysis system is established in the frequency domain for controller designs. Based on this model, the temperature stability is analysed by the root distribution, and the PID parameters are optimized considering the temperature overshoot and the settling time. The performance of the optimal PID controllers is experimentally verified. Furthermore, the simulation results show that the before-stack temperature should be used as the feedback variable for small lab-scale systems to suppress stack temperature fluctuations, and the after-stack temperature should be used for larger systems to improve the economy. This study helps ensure the temperature stability and control of electrolysis systems.

Seismic structural control using magneto-rheological dampers: A decentralized interval type-2 fractional-order fuzzy PID controller optimized based on energy concepts

In this paper, a combination of the interval type-2 fuzzy logic controller (IT2FLC) with the fractional-order proportional–integral–derivative (FOPID) controller, namely optimal interval type-2 fractional-order fuzzy proportional–integral–derivative controller (OIT2FOFPIDC), is developed for enhancing the seismic performance and robustness in seismic structural control applications. Based on the energy concepts, a decentralized framework of the OIT2FOFPIDC is proposed for easy and simple implementation in structures during earthquakes. For this purpose, a coot optimization algorithm (COA), as a powerful optimization algorithm, is also applied to adjust the membership functions (MFs), scaling factors, and the main controller parameters. Three controllers, namely optimal type-1 fuzzy proportional–integral–derivative controller (OT1FPIDC), optimal interval type-2 fuzzy proportional–integral–derivative controller (OIT2FPIDC), and optimal proportional–integral–derivative controller (OPIDC), are also proposed for comparison purposes. The seismic performances of the suggested controllers are examined with the evaluation of nine seismic performance indices and different ground accelerations in a 6-story smart structure equipped with two dampers. The robustness of the four controllers in the presence of the stiffness uncertainties is also compared in this study. On average, a reduction of 25.0%, 18.8%, and 18.5% in peak displacement, inter-story drift, and acceleration of stories is obtained for the OIT2FOFPIDC over the OT1FPIDC, respectively. Similarly, these reductions in comparison with the OIT2FPIDC are 16.3%, 13.3%, and 12.0%. Also, these reductions, in comparison with the OPIDC, are 33.3%, 27.8%, and 25.8%. Furthermore, simulation results show that the OIT2FOFPIDC is more robust than the other proposed controllers against uncertainties due to structural stiffness.

Optimal fractional-order proportional–integral–derivative control enabling full actuation of decomposed rotary inverted pendulum system

Allowing for a “virtual” full actuation of a rotary inverted pendulum (RIP) system with only a single physical actuator has been a challenging problem. In this paper, a hybrid control scheme that involves a pole-placement feedback controller and an optimal proportional–integral–derivative (PID) or fractional-order PID (FOPID) controller is proposed to simultaneously enable the tracking control of the rotary arm and the stabilization of the pendulum arm in an input–output feedback linearized RIP system. The PID controller is optimized first with the particle swarm optimization (PSO) to obtain three optimal gains, and then the other two parameters of the FOPID controller are optimized with the PSO. Compared to the optimized PID controller, the optimized FOPID controller improves the tracking and stabilizing accuracy by 53% and 29%, respectively, and demonstrates better adaptability for tracking different reference signals. Moreover, the hybrid FOPID controller exhibits 74.8% and 53% higher tracking accuracy than previous optimized model reference adaptive control PID (MRAC-PID) and linear–quadratic regulator (LQR) controllers, respectively. The proposed hybrid controllers are also digitized with different rules and sampling times, showing a closer performance between the discrete-time and continuous-time hybrid controllers under smaller sampling times.

Design of Optimal PID Controller for Electric Vehicle Based on Particle Swarm and Multi-Verse Optimization algorithms

The automotive industry is moving toward more environmentally friendly automobiles with greater range and performance than traditional vehicles as the effects of global warming worsen. Because of the positive impact, electric vehicles can have on reducing harmful emissions from the transportation sector, scientists have grown increasingly interested in the possibility of analyzing and simulating electric vehicles. In this study, we develop a non-linear dynamic concept of an electric vehicle by fusing kinetic and electrical components. Then we create a proportional Integral derivative (PID) controller to help it stay on course. To obtain optimal parameters for this controller by minimizing the error between the desired and actual output, Particle Swarm Optimization (PSO), and Multi-Verse Optimization (MVO) algorithm are used. The proposed controllers tested with linear and nonlinear trajectories to represent the electric vehicle's speed. The computation findings show that the proposed controller works perfectly, keeping up with the electric vehicle's speed quickly and precisely. In particular, the MVO-based proportional-integral-derivative (PID) controller is superior to the proportional-integral-derivative (PID) -based PSO method in terms of no steady-state error and smallest overshoot (0.05% with MVO while 0.25% with PSO) prevention for electric vehicle (EV) speed despite the better results of settling time and rising time obtained in PSO(0.767 And 0.211 s) respectively while these values were (0.807 and 0.215 s), respectively, in MVO. All works are performed in MATLAB (R2020a) /Simulink environment.

A self-tuning PID controller based on analog-digital hybrid computing with a double-gate SnS2 memtransistor.

Most commercial drones utilize a traditional proportional-integral-derivative (PID) controller because of its design simplicity. However, the traditional PID controller has certain limitations in terms of optimality and robustness; it is difficult to actively adjust the PID gains under some disturbances. In this study, we demonstrated an analog-digital hybrid computing platform based on double-gate SnS2 memtransistors to implement a self-tuning/energy-efficient PID controller in drones. The customized analog circuit with memtransistors executes the PID control algorithm with low power consumption; we experimentally verified that the energy consumption of the proposed hybrid computing-based PID controller is only 63% of that of the traditional PID controller. In addition, the precise tunability of analog conductance states in the memtransistor proved to be capable of reconfiguring the performance of the PID controller, where the developed self-tuning algorithm can automatically find the optimal PID control performance.

Optimal Proportional Integral Derivative Controller for Two-Wheeled Self- Balanced Mobile Robots Based on Particle Swarm Algorithm

Optimal Proportional Integral Derivative Controller for Two-Wheeled Self- Balanced Mobile Robots Based on Particle Swarm Algorithm

Real-time implementation of an enhanced proportional-integral-derivative controller based on sparrow search algorithm for micro-robotics system

This paper presents a new approach to control the position of the microrobotics system with a proportional-integral-derivative (PID) controller. By using sparrow search algorithm (SSA), the optimal PID controller indicators were obtained by applying a new objective function namely, integral square time multiplied square error (ISTES). The effeciency of the proposed SSAbased controller was verified by comparisons made with grey wolf optimization (GWO) algorithm-based controllers in terms of time. Each control technique will be applied to the identified model using MATLAB Simulink and the experimental test facility was conducted using LabVIEW software. The simulation and experimental results show that the performance of SSA-PID controller based on ISTES cost function achieves the best performance among various techniques. Moreover, the SSA technique had the highest performance compared to GWO technique based on rising and setting time and many other performance measurements. Thus, it is recommended to apply SSA for tuning the parameters of PID as it can enhance its performance in micro-robotic systems. It was found that the amount of error is reduced by 50% using SSA than other former experiments.

LQ optimal robust multivariable PID control for dynamic positioning of ships with norm-bounded parametric uncertainties

The design of a suitable controller for dynamic positioning (DP) of ships is a challenging task keeping the hydrodynamic uncertainties in mind. The magnitude and rate constraints on the actuators make the problem more difficult. The present work employs a two-degree-of-freedom (2-DOF), multivariable, proportional–integral–derivative (PID) control for DP of a ship. To design the controller, first, the ship dynamics with hydrodynamic parameter uncertainties is represented in an uncertain state-space descriptor form. Then, the design of feedback gains of 2-DOF PID controller for the uncertain descriptor plant is converted into a state feedback design for an augmented uncertain descriptor plant. Next, a linear matrix inequality-based condition is obtained to solve this state feedback problem in order to ensure a desired linear quadratic (LQ) performance, even in presence of uncertainties. Finally, to further improve the tracking performance, the feedforward gain of the 2-DOF PID controller is designed using H∞ approach. The DP performance of the proposed controller is tested for the considered ship model along with uncertainties, actuator constraints, and environmental disturbances. A comparison with the existing PID controllers is also carried out to show superiority of the proposed controller.

Optimal PID Control of a Brushed DC Motor with an Embedded Low-Cost Magnetic Quadrature Encoder for Improved Step Overshoot and Undershoot Responses in a Mobile Robot Application.

The development of a proportional–integral–derivative (PID) control system is a simple, practical, highly effective method used to control the angular rotational velocity of electric motors. This paper describes the optimization of the PID control of a brushed DC motor (BDCM) with an embedded low-cost magnetic quadrature encoder. This paper demonstrates empirically that the feedback provided by low-cost magnetic encoders produces some inaccuracies and control artifacts that are not usually considered in simulations, proposing a practical optimization approach in order to improve the step overshoot and undershoot controller response. This optimization approach is responsible for the motion performances of a human-sized omnidirectional mobile robot using three motorized omnidirectional wheels.

A Comparison Among Random Search Algorithms for PID Controller Optimization

Random search algorithms have been widely applied in practice to solve optimization problems. In the field of automatic control, there has been much research applying random search algorithms to optimize the parameter of Proportional – Integral - Derivative (PID) controller. The content of this research mainly stops at comparing the performance of the PID controller using the traditional tuning method with the optimization algorithm-based tuning method. Therefore, there is a need for research to compare the performance among random search algorithms for finding optimal parameters of the PID controller. In this paper, authors simulate five well-known and modern stochastic search algorithms including Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Chemical Reaction Optimization (CRO), Teaching Learning Based Optimization (TLBO) to find optimal parameters of the PID controller for controlling the speed of the DC motor. The simulation results showed that the CRO algorithm is the most suitable to optimize PID controller parameters for the proposed problem.