PI-PD Controller Research Articles

Enhancing Active Disturbance Rejection Control for a Vehicle Active Stabiliser Bar with an Improved Chicken Flock Optimisation Algorithm

An active stabiliser bar significantly enhances the anti-roll capabilities of vehicles. The control strategy is a crucial factor in enabling the active stabiliser bar to function effectively. This paper investigates an active disturbance rejection control (ADRC) strategy. Given the numerous parameters of the ADRC and their significant mutual influence, optimising these parameters is challenging. To address this, an improved chicken flock optimisation algorithm is proposed to optimise the ADRC parameters and enhance its performance. First, a three-degree-of-freedom dynamic model of the vehicle is established, and an active disturbance rejection control-based optimisation model utilising a chicken flock optimisation algorithm is constructed. To tackle the issues of getting stuck in local optima and low precision when dealing with complex problems in the traditional chicken flock optimisation (CFO) algorithm, several strategies, including improved Lévy flight, have been adopted. Subsequently, the twelve parameters of the ADRC are optimised using the improved chicken flock optimisation algorithm. Comprehensive testing on multiple benchmark functions demonstrates that the improved chicken flock optimisation (ICFO) algorithm is distinctly superior to other advanced algorithms in terms of solution quality and robustness. Simulation results show that the ICFO-ADRC controller is significantly superior. In four different complex road condition tests, the ICFO-ADRC controller shows an average performance improvement of 8% compared to the fuzzy PI-PD controller, an average improvement of 82% compared to the non-optimised ADRC controller, and an average improvement of 18% compared to the CFO-ADRC controller. Our findings confirm that this paper was able to provide new solutions for vehicle stability control whilst opening up new possibilities for the application of metaheuristic algorithms.

Robust PI-PD Controller Design: Industrial Simulation Case Studies and a Real-Time Application

PI-PD controllers have superior performance compared to traditional PID controllers, especially for controlling unstable and integrating industrial processes with time delays. However, computing the four tuning parameters of this type of controller is not an easy task. Recently, there has been significant interest in determining the tuning rules for PI-PD controllers that utilize the stability region. Currently, most tuning rules for the PI-PD controller are presented graphically, which can be time-consuming and act as a barrier to their industrial application. There is a lack of analytical tuning guidelines in the literature to address this shortfall. However, the existing analytical tuning guidelines do not consider a rigorous design approach. This work proposes new robust analytical tuning criteria based on predefined gain and phase margin bounds, as well as the centroid of the stability region. The proposed method has been tested using various simulation studies related to a DC–DC buck converter, a DC motor, and a heat exchanger. The results indicate that the proposed tuning rules exhibit strong performance against parameter uncertainty with minimal overshoots. Furthermore, the suggested technique for simultaneous control of yaw and pitch angles has been tested in a real-time application using the twin rotor multi-input multi-output system (TRMS). Real-time results indicate that, compared to other methods under investigation, the suggested approach provides nearly minimal overshoots.

Load frequency control in interconnected microgrids using Hybrid PSO–GWO based PI–PD controller

Load frequency control in interconnected microgrids using Hybrid PSO–GWO based PI–PD controller

Relay feedback identification and PI-PD control of asymmetrical heating and cooling processes

A common type of nonlinear system in the field of process industry is asymmetrical heating and cooling processes. These systems have two operating modes, heating and cooling, each with a particular dynamic feature. This study deals with identifying and controlling such processes. The relay feedback identification method based on the state-space approach, which results in exact estimates, is used in the identification procedure to achieve two first-order plus dead time (FOPDT) process models. Following process identification, two sets of PI-PD controller parameters are acquired in line with the user-defined gain and phase margin specifications, and the system is controlled using a gain-scheduled PI-PD control method. Some simulation examples are provided to demonstrate the use and profitability of the suggested identification and control approaches. Comparisons with a similar study are provided for both identification and control approaches to clearly demonstrate the benefits of the suggested procedures.

A comparative study on PI-PD controller design using stability region centroid methods for unstable, integrating and resonant systems with time delay

In this paper, controller tuning methods based on stability region centroid methods reported in the literature are used to design PI-PD controllers for unstable, integrating and resonant systems with time delay. By analyzing the stability boundary locus (SBL) for the PD controller, which is utilized in the inner loop of this structure, the controller parameters are obtained using three methods which are the Weighted Geometric Center (WGC), Centroid of Convex Stability Region (CCSR), and Stability Triangle Approach (STA). These techniques were applied analytically, step by step. For the closed loop transfer function obtained in the inner loop of the controlled system, these three methods were utilized to design the PI controller in the outer loop, individually. Unit step responses of the controlled system, using PI-PD gains determined by each method, have been obtained. Furthermore, a disturbance of a certain time and amplitude was added to the systems to test the disturbance rejection behavior and the robustness performance of the methods. Perturbed responses were obtained through changing the model parameters at a certain rate. Time domain performance metrics were analyzed to compare the responses. The simulations were evaluated using settling time, rise time, and percentage overshoot as the assessment criteria. As a result of this study, the effectiveness of three methods, namely WGC, CCSR, and STA, in controller design for unstable, integrating, and resonant time-delay systems has been demonstrated. In addition, a comparison of time domain performance metrics is presented for the nominal and perturbed systems. Based on these comparisons, it is concluded that the methods outperform each other only in some time response performance measures. The presented results showed the advantages of these methods over each other in terms of some performance criteria. The contribution of this study to the literature is the comparative analysis of these three analytical methods.

Coot optimization algorithm-tuned neural network-enhanced PID controllers for robust trajectory tracking of three-link rigid robot manipulator

Robotic manipulators are nonlinear systems, multi-input multi-output, highly coupled and complicated whose performance is negatively impacted by external disturbances and parameter un-certainties. Therefore, the controllers designed for such systems must be capable of managing their complexity. The main aim of this study is to tackle the trajectory tracking issue of the three-Link Rigid Robot Manipulator (3-LRRM) based on designing three control structures using a combi-nation Neural Network (NN) with Proportional, Integral and Derivative (PID) actions named Neural Controller Like PIPD (NN-PIPD) controller, Neural Network plus PID (NN + PID) controller NN + PID controller and Elman Neural Network Like PID (ELNN-PID) controller. The parameters of the proposed controllers are adjusted utilizing the Coot Optimization Algorithm (COOA) in order to reduce the Integral Time Square Error (ITSE). A novel objective function for tuning process to produce a controller with minimum value of the chattering in the control signal is proposed. The performance of the proposed controllers is evaluated in terms of disturbance rejection, model uncertainty, fluctuating initial conditions and reference trajectory tracking. According to the simulation results proved that the suggested NN-PIPD controller outperforms all other proposed controller structures for tracking performance, stability, and robustness. As a result of the com-parison analysis the optimal controller was considered to be an NN-PIPD controller for tracking trajectory, rejecting disturbances, and parameter variation with minimizing ITSE of 0.001777.

Design and Development of Complex-Order PI-PD Controllers: Case Studies on Pressure and Flow Process Control

This article examines the performance of the proposed complex-order, conventional and fractional-order controllers for process automation and control in process plants. The controllers are compared regarding disturbance rejection and set-point tracking, considering variables such as response time, robustness to uncertainty, and steady-state error. The study shows that a complex PI-PD controller has better accuracy, faster response time, and better noise rejection. Still, implementation is challenging due to increased complexity and processing requirements. In contrast, a standard PI-PD controller is a known solution but may have problems with accuracy and robustness. Fractional-order controllers based on fractional computations have the potential to improve control accuracy and robustness of non-linear and time-varying systems. Experimental insights and real-world case studies are used to highlight the strengths and weaknesses of each controller. The findings provide valuable insights into the strengths and weaknesses of complex-order and fractional-order controllers and help to select the appropriate controller for specific process plant requirements. Future perspectives on controller design and performance optimization are detailed, identifying the potential benefits of using complex and fractional-order controllers in process plants.

Optimized PI-PD Control for Varying Time Delay Systems Based on Modified Smith Predictor

Optimized PI-PD Control for Varying Time Delay Systems Based on Modified Smith Predictor

PI-PD Controller Design Based on Weighted Geometric Center Method for Time Delay Active Suspension Systems

In this study, a PI-PD controller was designed via weighted geometric center method (WGC) for a quarter vehicle model to suppress the vertical vibrations. The proposed design is based on finding the weighted geometric center of the area formed by the control parameters that make the system stable. The WGC method has two main stages. First, an area formed by the parameters of the PD controller (kf, kd) in the inner loop is obtained and the weighted geometric center of this area is calculated. Then, using these obtained parameters, the inner loop is reduced to a single block, and the parameters of the PI controller in the external loop (kp, ki) are calculated using the stability boundary curve as in the first step, and the weighted geometric center is calculated. The simulation results show that the PI-PD controller designed with the weighted geometric center method offers successful responses for the time delay quarter vehicle system.

Grid Secondary Frequency Control by Fuzzy PI–PD Controller

This paper develops a new approach for controlling the frequency in a two-area power system using a fuzzy PI PD controller. Frequency stabilization is one of the important factors for any power system to operate efficiently and reliably. The fluctuating characteristics of RES, like solar PV and wind energy, due to changing atmospheric conditions, require additional reserves to compensate for fluctuations in generated power. With growing application of EVs and their charging requirement, charting huge loads may add to the power grid and lead to stability problems if not properly regulated. This paper coordinates EV charging into the secondary frequency regulation, aided by an enhanced fuzzy controller designed for dealing with fluctuating imbalances between electricity demand and generation. In this context, a control technique is suggested that incorporates the flexibility of fuzzy logic with the accurate PI and PD methods for control. The controller continuously monitors changes in frequency at each node in the power system network. The fuzzy logic works on uncertain input data in terms of prescribed linguistic variables and rules that allow it to achieve a reasoned output. The difference between the desired and actual frequencies alters the control variable through the PI component of the controller, while the PD component considers the rate of change of this error to make the system's response time better. The effectiveness of the fuzzy PI PD controller is proven through detailed simulation experiments under different operational conditions and disturbances. It can be rundown that the controller efficiently reduces these frequency deviations, which guarantees smooth and reliable operation of the two-area power system network. In addition, it can be seen that the controller has robust performance but is rather reactive to dynamical changes in system parameters. Case studies are included in the research to test the performance of the proposed control approach in reducing frequency deviations; simulation findings always prove its efficacy. This paper therefore presents a complex method of frequency regulation in power systems using fuzzy logic and combined PI PD control to deal with problems caused by RES integration and EV charging. The proposed technique enhances the frequency stability in order to enhance both the reliability and efficiency of power grid operations due to the ever-changing energy demands and conditions.

Optimal Load Frequency Control for Interconnected Power Systems using Optimized PI-PD Controller with TCSC and HVDC Integration

Optimal Load Frequency Control for Interconnected Power Systems using Optimized PI-PD Controller with TCSC and HVDC Integration

Regulation of Load Frequency for a Hybrid Wind-Ocean Wave Energy-Based Microgrid via Advanced Fuzzy Logic-Based Control Approach

In this article, a model of wind and ocean wave power generation-based microgrid (MG) system with diesel engine generator and battery storage system is developed. To replicate the more practical scenarios, various system non-linearities, as well as measurement time delay, are also incorporated in the designing of the considered MG system. The stochastic nature of wind and ocean, and load demands create an imbalance among sources and loads, which may lead to severe frequency fluctuation. To mitigate the effect of frequency fluctuations, an advanced fuzzy logic (FL)-based control method is proposed for load frequency regulation (LFR). The various variants of FL-based control schemes, such as fuzzy P, fuzzy P + I, fuzzy PI, cascaded fuzzy PI-PD, and fuzzy PID controllers, are designed and implemented for the LFR of the considered hybrid MG system (HMGS). A comparative analysis of HMGS with all designed and implemented controllers is performed for the identification of the suitable controller to alleviate the effect of frequency fluctuations. The obtained results show the effectiveness of the cascaded fuzzy PI-PD controller over the other designed controllers. Finally, the stability analysis of HMGS with proposed cascaded fuzzy PI-PD control approach is also performed.

Efficient power management and control of DC microgrid with supercapacitor-battery storage systems

This paper introduces a novel power management strategy (PMS) that aims to facilitate power-sharing between battery and supercapacitor (SC) energy storage systems. The proposed technique is employed to resolve the discrepancy between power demand and generation, as well as to regulate the voltage of the dc bus. The implementation of a hybrid adaptive fuzzy integrated fractional order PD-PI controller (HAFI FPD-PI controller), in the hybrid energy storage system (HESS) results in enhanced regulation of the dc bus, while simultaneously minimising the levels of stress imposed on the battery. Moreover, the proposed PMS improves the lifespan of batteries by redirecting unwaged battery currents to SCs for rapid compensations. In addition, the stability study of dc microgrid is performed. The efficacy of the proposed PMS is evaluated by the utilisation of varying solar irradiation, wind speed, and load. The effectiveness of the proposed PMS was examined by simulations, which involved a comparison of peak deviations in the dc bus voltage with conventional PMS techniques used in literature. The real-time verification of the results has been conducted using OPAL-RT real-time simulator.

Smith-Predictor-Based Design of Analytical PI-PD Control for Series Cascade Processes with Time Delay

For series cascade processes with a time delay, such as the first-order with time-delay (FOTD) process, the integral with time-delay (ITD) process, second-order integral with time-delay (SOITD) process, and unstable first-order with time-delay (UFOTD) process, this paper proposes a Smith-predictor-based design of analytical PI-PD control for these series cascade processes with a time delay. Firstly, targeting the common FOTD model in the secondary loop, a controller with a PID structure is designed using the direct synthesis method. Additionally, a Smith-predictor-based PI-PD control structure is adopted for the prevalent process model in the primary loop. Then, expressions representing the relationship between the corresponding controller parameters and the maximum sensitivity (Ms) index are established to facilitate the analytical design of the controllers. Finally, based on simulation experiments, the effectiveness and superiority are validated by using the proposed method.

MPPT of PEM Fuel Cell Using PI-PD Controller Based on Golden Jackal Optimization Algorithm.

Subversive environmental impacts and limited amounts of conventional forms of energy necessitate the utilization of renewable energies (REs). Unfortunately, REs such as solar and wind energies are intermittent, so they should be stored in other forms to be used during their absence. One of the finest storage techniques for REs is based on hydrogen generation via an electrolyzer during abundance, then electricity generation by fuel cell (FC) during their absence. With reference to the advantages of the proton exchange membrane fuel cell (PEM-FC), this is preferred over other kinds of FCs. The output power of the PEM-FC is not constant, since it depends on hydrogen pressure, cell temperature, and electric load. Therefore, a maximum power point tracking (MPPT) system should be utilized with PEM-FC. The techniques previously utilized have some disadvantages, such as slowness of response and largeness of each oscillation, overshoot and undershoot, so this article addresses an innovative MPPT for PEM-FC using a consecutive controller made up of proportional-integral (PI) and proportional-derivative (PD) controllers whose gains are tuned via the golden jackal optimization algorithm (GJOA). Simulation results when applying the GJOA-PI-PD controller for MPPT of PEM-FC reveal its advantages over other approaches according to quickness of response, smallness of oscillations, and tininess of overshoot and undershoot. The overshoot resulting using the GJOA-PI-PD controller for MPPT of PEM-FC is smaller than that of perturb and observe, GJOA-PID, and GJOA-FOPID controllers by 98.26%, 86.30%, and 89.07%, respectively. Additionally, the fitness function resulting when using the GJOA-PI-PD controller for MPPT of PEM-FC is smaller than that of the aforementioned approaches by 93.95%, 87.17%, and 87.97%, respectively.

Optimized cascaded controller for frequency stabilization of marine microgrid system

The trend towards reducing greenhouse gas emissions by dipping the use of traditional sources of energy in marine power grids, as well as the rapid expansion of renewable energy sources (RESs), were the driving forces behind the incorporation of RESs in maritime microgrid systems and enquiry of the ensuing prevalent control mechanism. The frequency stability of a Marine Microgrid System (MMGS) is a critical aspect that directly affects its reliable and efficient operation. This study describes a method for frequency stabilization in independent maritime microgrids consists of diverse renewable energy resources including wind turbine generators, sea wave energy/tidal power generation, solar generation, bio-diesel generator and energy storage systems. This paper aims to develop a new optimal cascaded order proportional integral based proportional derivative for marine load frequency control. Due to the fact that the performance of the controller is highly dependent on the parameters of the controller, optimizing these coefficients can have a significant impact on the output performance of the LFC control. In light of this, this paper presents the sewing training-based optimization (STBO), a new human-based metaheuristic algorithm to optimize the coefficient of the suggested controller. The essential stimulation of STBO is the teaching procedure of sewing to beginner tailors. By utilizing a population of candidate solutions, the algorithm iteratively refines the control parameters to find the optimal set that minimizes frequency deviations and enhances system stability. The responses of the cascaded PI-PD controller are linked to those of the PID and PI controllers in order to demonstrate its superiority. To evaluate the efficiency of STBO, it is compared to well-established recent techniques such as fitness dependent optimization, grey wolf optimization and Jellyfish search optimization. From the results, it is observed that our proposed approach improved the settling time by 25.35%, 45.89%, and 29.35%, reduced peak overshoot by 78.34%, 67.71%, and 78.23%, and similarly reduced undershoot by 81.56%, 56.22% and 76.56% as compared to FDO, GWO and JSO techniques respectively. Finally, the sensitivity analysis is performed under ±50% load variation and ± 40% power system parameters to prove the robustness of the proposed controller.

Novel Fractional-Order Proportional-Integral Controller for Hybrid Power System with Solar Grid and Reheated Thermal Generator

This paper presents a new fractional-order proportional-integral, (PI)λ (FO[PI]) type structure to investigate the load frequency control (LFC) problem. In the literature, some controllers’ extensive tuning options may slow or complicate the optimization process. Due to the intricacy of the tuning, even if there are fewer tuning parameters, a robust structure can be obtained. The (PI)λ structure deviates from the standard FOPI, integer PID, or PI-PD controllers with the same or fewer tuning parameters. The efficacy of a tri-parametric fractional-order controller is examined on a two-area interconnected hybrid power system comprising a photovoltaic (PV) grid and a Reheated Thermal Generator (RTG). In order to obtain optimal performance with lower control efforts, a novel dual-performance index is developed for the LFC problem. Various analyses are also proven to perform better than other optimized controllers from the recent literature. The presented scheme is significantly robust to disturbance interruptions, non-linearities, and parameter perturbations. It is also observed that there are no stability issues due to communication time delays. It is highlighted that the improvement can be obtained without adding complex structure or controller parameters.

Time delay effect reduction on the wireless networked control system using an optimized FOPI-FOPD controller

Wireless Networked Control System (WNCS) is made up of an actuator, sensor, and controller that communicates through a wireless network rather than typical point-to-point cable connections. Lower maintenance costs, greater flexibility, and increased safety are the main WNCS advantages, so as a result, it has attracted a lot of researchers. Nevertheless, time delays and packet losses in wireless data transmission are classified as complicated problems, which impair WNCS output accuracy and may influence the overall system stability. Integer-Order PI-PD (PI-PD) and Fractional-Order PI-PD (FOPI-FOPD) controllers are proposed to reduce the impact of the control signal transmission's time delay and improve system performance. Matlab Simulink and True-time simulator are used to simulate the WNCS, and ZigBee protocol is used in transceiving the control signal between the controller and the system. Rotary Inverted Pendulum (RIP) acted as the controller's objective. The Grey Wolf Optimization (GWO) technique is utilized to evaluate the best controller parameters. Xbee S2 modules are used to implement the signal transmission process over ZigBee protocol. The FOPI-FOPD controller outperforms the PI-PD controller in the simulation and experimental results in decreasing the influence of time delay on system stability

Comparison Performances between MABSA-PI Controller and MABSA-PD Controller for DC Motor Position System

The goal of this project is to create two different types of controllers for regulating DC motor position systems which are the MABSA-PI controller and the MABSA-PD controller. The MATLAB controllers are developed using the Simulink toolbox, while the transfer function of a DC motor is obtained from its circuit. Modified adaptive bats sonar algorithm (MABSA) will be implemented in the PI controller and PD controller as the main algorithm. MABSA is one of the swarm intelligences and is usually for an optimization problem. Next, the tuning method for the PI controller and PD controller will be the trial-and-error method. The combination graph of each controller will be shown in Simulink scope as the project is tested for various positions. The controller's ability to regulate the position of a DC motor was studied. The comparision among the system's transient response parameters, including percentage overshoot, rising time (Tr), and settling time (Ts), would be discused. Various toolbox functions available in Simulink software can be employed to repossess these parameter outcomes.

A Novel PI-PD Controller Tuning Method based on Neutrosophic Similarity Measure for Unstable and Integrating Processes with Time Delay

Integrating systems and unstable systems are two types of systems that are widely used in various industries, including control engineering and electrical engineering. However, controlling these systems can be a daunting task due to their inherent complexity. To address this challenge, the PI-PD controller structure has been widely adopted in the industry, as it has proven to be very successful in controlling integrating and unstable systems. In this paper, a new design method is proposed to determine the optimal controller parameters in the control of integrating and unstable systems with time delay. The design method utilizes a Genetic Algorithm-based optimization technique, which incorporates a new objective function that is based on the neutrosophic similarity measure. Two different types of plants have been chosen as examples in this study. The first plant is a time-delayed integrating system. The second plant is an unstable system, which means that the output signal is very sensitive to any changes or disturbances in the input signal. This study examines the parameter uncertainties of systems by comparing them with some design methods from the literature. The results are presented comparatively in figures and tables to show the superiority of the proposed method.