Proportional-integral-derivative Controller Design Research Articles

Design and optimal tuning of fractional order PID controller for paper machine headbox using jellyfish search optimizer algorithm

This manuscript proposes the Jellyfish Search Optimization (JSO) algorithm-based Fractional Order Proportional-Integral-Derivative (FOPID) controller tuning for a paper machine headbox. The novelty of this method lies in integrating the JSO technique for optimizing the parameters of the FOPID controller to monitor and control headbox pressure and stock level efficiently and effectively. The JSO algorithm ensures optimal tuning of controller parameters by minimizing error indices such as Integral of Squared Error (ISE), Integral of Time Absolute Error (ITAE), and Integral of Absolute Error (IAE). Simulations conducted on the MATLAB/Simulink platform demonstrate that the FOPID controller tuned using JSO achieves superior performance compared to conventional PI (Proportional-Integral) and PID (Proportional-Integral-Derivative) controllers. Specifically, the JSO-tuned FOPID controller exhibited a 25% reduction in rise time, a 30% improvement in settling time, and a 20% decrease in overshoot when compared to the PID controller. Furthermore, comparative analyses with other optimization techniques, including Moth Flame Optimization (MFO), Ant Lion Optimization (ALO), and Elephant Herding Optimization (EHO), reveal that the JSO algorithm provides higher accuracy and stability in diverse operating conditions. This study underscores the efficacy of the JSO-tuned FOPID controller as a robust solution for complex industrial applications, such as paper machine headbox systems, and highlights its potential to enhance process efficiency and control precision.

Adaptive Neural Network-Based PID Controller Design for Velocity Control of an Internal Combustion Engine Using Back Propagation Technique

Precise velocity control in internal combustion engines (ICEs) is essential for optimizing performance, improving fuel efficiency, and minimizing emissions. However, the nonlinear dynamics and inherent uncertainties within ICE systems present substantial challenges for traditional control methods. In this paper, we propose an adaptive control strategy that integrates a Proportional-Integral-Derivative (PID) controller with Back Propagation Neural Networks (BPNNs) to effectively address these complexities. The proposed controller architecture consists of two key components: a BPNN to estimate modelling uncertainties, such as unknown friction and external disturbances affecting the ICE, and a primary PID controller responsible for velocity regulation. The BPNN functions as a dynamic estimator, continuously learning and adapting to changes in system dynamics, thereby enhancing the robustness and adaptability of the control system. By accurately capturing the nonlinearities and uncertainties inherent in ICEs, the BPNN contributes to improved control performance and system stability. To validate the effectiveness of the proposed approach, extensive numerical simulations are performed using MATLAB Simulink. These simulations encompass a range of operating conditions and scenarios to thoroughly evaluate the controller's performance. Additionally, the proposed method is compared to conventional PID control techniques found in the literature, with a focus on robustness, tracking accuracy, and disturbance rejection. The results indicate that the adaptive PID controller, incorporating BPNNs, outperforms traditional PID methods, delivering superior velocity regulation and disturbance rejection. Furthermore, the proposed approach demonstrates significant potential for real-world applications in ICE systems, providing enhanced control performance and efficiency. This study advances the field of control engineering by introducing an innovative adaptive control strategy tailored specifically for velocity control in internal combustion engines. Leveraging the capabilities of BPNNs to address uncertainties, this approach contributes to improved system performance and offers a promising direction for future advancements in engine control technologies.

Performance analysis of DC-DC Buck converter with innovative multi-stage PIDn(1+PD) controller using GEO algorithm

Power electronic converters are widely used in various fields of electrical equipment. Due to their fast dynamics and non-linear nature, controlling them requires dealing with various complexities. Therefore, having a well-designed, high-speed, and robust controller is critical to ensure the effective operation of these devices. In a DC-DC converter, steady-state performance with minimum error and fast dynamic response relies on controller design. This paper presents the design of a multi-stage PID controller with an N-filter combined with a one plus proportional derivative (1+PD) controller. This controller illustrates fast tracking reference voltage; additionally, it shows incredible results when the DC-DC converter operates in different modes. The parameters of the proposed controller are effectively determined using the golden eagle optimization (GEO) algorithm. Furthermore, a comprehensive comparison between the proposed controller, proportional–integral–derivative (PID), and fractional order PID (FOPID) controllers, as well as different metaheuristic optimization methods in various conditions, has been conducted to demonstrate the effectiveness of the proposed controller. The behavior of the closed-loop system under different conditions has been thoroughly investigated. The superior time and frequency domain characteristics of the closed-loop system with the PIDn(1+PD) controller highlight its superiority over other controllers. The demonstrated enhancements in settling time, voltage regulation accuracy, and transient response emphasize the potential applicability of the proposed control strategy in real-world power electronics systems, particularly in scenarios requiring high efficiency, stability, and dynamic performance.

FOPDT model and CHR method based control of flywheel energy storage integrated microgrid

The main causes of frequency instability or oscillations in islanded microgrids are unstable load and varying power output from distributed generating units (DGUs). An important challenge for islanded microgrid systems powered by renewable energy is maintaining frequency stability. To address this issue, a proportional integral derivative (PID) controller is designed in this article. Firstly, islanded microgrid model is constructed by incorporating various DGUs and flywheel energy storage system (FESS). Further, considering first order transfer function of FESS and DGUs, a linearized transfer function is obtained. This transfer function is further approximated into first order plus time delay (FOPTD) form to design PID control strategy, which is efficient and easy to analyze. PID parameters are evaluated using the Chien-Hrones-Reswick (CHR) method for set point tracking and load disturbance rejection for 0% and 20% overshoot. The CHR method for load disturbance rejection for 20% overshoot emerges as the preferred choice over other discussed tuning methods. The effectiveness of the discussed method is demonstrated through frequency analysis and transient responses and also validated through real time simulations. Moreover, tabulated data presenting tuning parameters, time domain specifications and comparative frequency plots, support the validity of the proposed tuning method for PID control design of the presented islanded model.

Robust PID controller design for positioning systems with hysteresis and time-varying delay

This paper presents Linear Matrix Inequalities (LMIs) conditions for designing Proportional-Integral-Derivative (PID) controllers that guarantee asymptotic stability with exponential convergence rate for positioning systems affected by hysteresis nonlinearity and time-varying delay. The hysteresis is modelled using the Prandtl-Ishlinskii operator, and the effects of both the time-varying delay and hysteresis are encapsulated into a bounded uncertain parameter confined within a known convex polytope. Numerical results support the theoretical developments, confirming that the controller effectively mitigates the effects of disturbances while suppressing both the hysteresis and time-varying delay influences.

Intelligent Proportional Integral Derivative Control Design for Sampled and Delayed Output Measurements Systems

This paper considers the problem of control systems with sampled and delayed output measurements. Moreover, the considered system is Continuous Time Linear systems (CTLS) which is X-Y robot. The proposed control system design to solve this problem is called Intelligent Proportional Integral Derivative controller (IPID) which has a simple structure. Furthermore, the intelligent technique which is Genetic Algorithm is used to optimize parameters of the proposed controller. In order to restate the continuous state with non-time delay the piecewise estimator observer is utilized. Moreover, an example on MATLAB Simulink is presented to validate the proposed control approach with comparisons of the conventional Proportional Integral Derivative controller and the simulation results are provided to demonstrate its effectiveness.

Design of Mixed-Mode Analog PID Controller with CFOAs.

The design of a mixed-mode proportional-integral-derivative (PID) controller circuit using current-feedback operational amplifiers (CFOAs) as active components is proposed. With the same circuit topology, the proposed configuration of three CFOAs, four resistors, and two capacitors is capable of performing the PID controller in each of the following four modes: voltage mode, trans-admittance mode, current mode, and trans-impedance mode. Numerous mathematical analyses are conducted to determine the controller's performance under both ideal and non-ideal conditions. Additionally, the mixed-mode second-order lowpass filter is suggested and also used to examine the workability of the proposed mixed-mode PID controller in a feedback control structure. The proposed PID controller is implemented with the commercially available IC-type CFOA AD844, and the simulation results are presented to illustrate the functionality of the controller and its closed-loop control system. According to the findings, the total power consumption of the proposed PID controller is 0.348 W, with symmetrical supply voltages of ±9 V. It also has a temperature variation of less than 0.2% over the AD844's usable range. Monte Carlo statistical analysis results revealed that the gain responses of the controller exhibited a deviation of no more than 7.72% from the theoretical value. The controlled filter in a closed-loop control system has a 43% faster rise time and peak time than the uncontrolled filter in all four modes of operation. It also has a steady-state error less than 0.2 mV for voltage responses and 0.72 µA for current responses.

A Cascade PID Controller Design with Cuckoo Optimization Algorithm (COA) and Input Shaping (IS)

From past to present, Proportional-Integral-Derivative (PID) controllers stand out as the most widely used types of controllers. Due to the high-performance requirements, experimentally determined controller coefficients necessitate the application of modern optimization techniques. In this study, Ziegler-Nichols, Chien-Hrones-Reswick, and Cohen-Coon methods, which allow parameter calculation through the open-loop system's step response method, were compared with the Cuckoo Optimization Algorithm for PID controllers designed for a brush-commutated DC motor with unknown parameters in the Matlab environment. The comparison was based on Integral of Absolute Error (IAE), Integral of Square Error (ISE), Integral of Time-weighted Absolute Error criterion. Similarly, the performance of the Cuckoo Algorithm was discussed in terms of stability margins and stability peaks. In this comparison, it was observed that the PID controller optimized with the Cuckoo Algorithm operated with high proportional and integral coefficients to minimize the cost function, resulting in overshoot in the system response. Input shaping, a commonly used method in open-loop control of both brushed and brushless DC motor systems, was integrated into the system to mitigate this overshoot. The hybrid controller achieved the best performance in terms of IAE, ISE and ITAE in the system response, with less overshoot compared to the other mentioned methods.

Elitism-crossover barnacle mating optimization and its application to PID controller design for a buck converter

This paper presents an elitism-crossover barnacle mating optimization (ECBMO). It is an improvement of barnacle mating optimization (BMO). The original BMO suffers from local optima problem leading to a low accurate solution. A new method of offspring generation is adopted into the original BMO structure. Some features of the best-so-far solution are incorporated into the generated offspring. The accuracy performance of the proposed algorithm is tested on several IEEE functions. A statistical analysis is conducted to compare its performance over the original BMO. It is also applied to optimize proportional integral derivative (PID) parameters for controlling output voltage of a buck converter. Result of benchmark functions test shows the proposed algorithm has attained higher accuracy for all functions compared to BMO algorithm. Application on the real problem shows both algorithms control the converter voltage satisfactorily. However, the ECBMO has achieved more optimal PID parameters and leading to a better output voltage response.

Analytically derived disturbance rejection‐based PID controller tuning for second‐order plus dead time plants

AbstractThis letter proposes a proportional‐integral‐derivative (PID) design method for second‐order plus dead time models based on a desired closed‐loop transfer function for load disturbance changes. Also, tuning rules for single integrating first‐order plus dead time models are provided. Using a two‐degree‐of‐freedom control scheme, the design problem considers load disturbance rejection, robustness to model uncertainties, and setpoint tracking. Three examples are used to assess the performance of the proposed method. Finally, the results are compared to two popular PID control design methodologies, skogestad internal model control or skogestad IMC (SIMC) and improved SIMC (iSIMC).

Reaction Curve-Assisted Rule-Based PID Control Design for Islanded Microgrid

In a renewable energy-based islanded microgrid system, frequency control is one of the major challenges. In general, frequency oscillations occur in islanded microgrids due to the stochastic nature of load and variable output power of distributed generating units (DGUs). In the presented research proposal, frequency oscillations are suppressed by implementing the proportional integral derivative (PID) controller-based control design strategy for an islanded microgrid. The modeling of the islanded microgrid is firstly presented in the form of a linearized transfer function. Further, the derived transfer function is approximated into its equivalent first-order plus dead time (FOPDT) form. The approximated FOPDT transfer function is obtained by employing the reaction curve method to calculate the parameters of the FOPDT transfer function. Furthermore, the desired frequency regulation is achieved for the manifested FOPDT transfer function by incorporating PID control design. For PID controller tuning, different rule-based methods are implemented. Additionally, comparative analysis is also performed to ensure the applicability of the comparatively better rule-based tuning method. The Wang–Chan–Juang (WCJ) method is found effective over other rule-based tuning methods. The efficacy of the WCJ method is proved in terms of transient response and frequency deviation. The tabulated data of tuning parameters, time domain specifications, and error indices along with responses are provided in support of the presented control strategy.

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

Optimal Fuzzy Logic Proportional Integral Derivative Controller Design by Bee Algorithm for Hydro-Thermal System

This paper proposes a robustness and an optimum of the fuzzy logic-proportional integral derivative (FLPID) controllers for automatic generation control (AGC) of a two area interconnected hydro-thermal system and an application of bee algorithm (BA) in order to design FLPID controllers. Traditionally, membership functions (MF) and control rules (CR) of the fuzzy logic controller (FLC) were achieved by trial and error methods of designers. To solve this problem, BA was proposed to concurrently tune PID gains, MF and CR of the FLPID controllers to minimize frequency deviations and tie-line power deviations of power system. Simulation results clearly showed that the performance and the robustness of the optimal FLPID controllers were superior to the conventional PID and the FLPID controllers in terms of settling time and overshoot.

Modeling and Tuning of Electronic Throttle Control System in Formula Student Car

The Lookprabida formula student team uses an electronic throttle control (ETC) system in the racecar. Unfortunately, the ETC system cannot regulate the throttle valve to closely pursue angular setpoints. Thus, this paper endeavors to improve the response of the ETC system in racing cars. The ETC system is first examined using frequency response analysis. Parameter identification is carried out to obtain a mathematical model for the electronic throttle body. The Ziegler-Nichols’ second method is then applied to preliminarily select the proportional integral derivative (PID) gains using MATLAB/Simulink®. Then, the ETC system fine-tuning on the experimental set is carried out. The final PID controller design results in a reduction in the settling time from 0.35 to 0.20 s, overshoot from 29.6 to 19.33%, and steady-state error from 2.00 to 0.22%. The racecar with the finally designed PID gains is tested on a training track; the root mean square error (RMSE) shows that the throttle valve approaches much closer to angular setpoints.

Frequency-based multivariable control design with stability margin constraints: A linear matrix inequality approach

In this paper, a proportional–integral–derivative controller design problem for stable multivariable process is considered. A frequency-based control technique is formulated as a convex optimization problem with linear matrix inequality constraint. The multivariable proportional–integral–derivative controller is designed so that H∞ norm of the difference between the designed loop gain function and a desired one is minimized. Linear matrix inequality constraints on the stability margin guarantees designed loop stability. Process frequency domain data is used to solve the proposed optimization problem. Knowledge of the process parametric model is not necessary. The desired loop gain transfer function is defined from the reference complementary sensitivity function. Simulation results show the comparison between the proposed technique and technique from the literature. In these examples, the proposed technique resulted in stable closed-loops different from the others and in a reduction of the performance indices.

Complex-order PID controller design for enhanced blood-glucose regulation in Type-I diabetes patients

Type-I Diabetes (TID) is a chronic autoimmune disease that elevates the glucose levels in the patient’s bloodstream. This paper formulates a fractional complex-order Proportional-Integral-Derivative (PID) control strategy for robust Blood Glucose (BG) regulation in TID patients. The glucose-insulin dynamics in blood plasma are modeled via the Bergman-Minimal-Model. The proposed control procedure employs the ubiquitous fractional order PID controller as the baseline BG regulator. The design flexibility of the baseline regulator to effectively normalize the BG levels is enhanced by assigning complex orders to the integral and differential operators instead. The resulting Complex Order PID (CO-PID) regulator strengthens the controller’s robustness against abrupt variations in the patient’s BG levels caused by meal disturbances or sensor noise. The controller parameters are numerically optimized offline. The aforesaid propositions are justified by performing credible simulations in which the proposed controller is tasked to effectively track a set point value of 80 mg/dL from an initial state of hyperglycemia under various disturbance factors. As compared to the FO-PID controller, the CO-PID controller improves the reference tracking-error, transient recovery-time, and control expenditure by 13.1%, 33.4%, and 28.1%, respectively. The simulation results validate the superior reference-tracking accuracy of the proposed CO-PID controller for BG regulation.

Ters Sarkaç Sisteminde Referans Model Kullanarak Kesir Dereceli PID Denetleyici Tasarımı

The proportional Integral Derivative (PID) controller has three basic parameters: Proportional gain (Kp), Integral gain (Ki) and Derivative gain (Kd). In a conventional PID controller, integral and derivative operators are integer order. The researchers proposed a fractional order PID (PIλDµ) controller by using the fractional integral and derivative operators instead of the integer order integral and derivative operators in the traditional PID controller because it improves the control performance. The PIλDµ controller has an additional fractional integrator degree (λ) and fractional derivative degree (µ). In this study, the focus is on the design of a fractional-order PID controller according to a reference model in the time domain. Bode's ideal transfer function was used as the reference model. It is aimed to obtain PIλDµ parameters by minimizing the error between the time domain response of Bode's ideal transfer function model and the output of the system to be controlled by using the optimization method. Genetic Algorithm (GA) optimization was used as the optimization method. The study was carried out as a simulation study on an inverted pendulum system with a single-input multiple-output (SIMO) structure.

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.

Design of Sliding Mode Control Strategy for DC Motor

Abstract: This research paper presents a comparative study ofsliding mode control (SMC) strategies and proportional- integralderivative (PID) control for DC motor applications. The project involves the design and implementation of PID and SMC controllers, as well as the evaluation of their respective response characteristics. Furthermore, the SMCcontroller is designed using three different sliding surfaces to analyze their impact on the control system's performance. A model is developed and simulated usingMATLAB/SIMULINK. Overall, the simulation results show that sliding mode controller is superior than PID for speed control of dc motor.

VDIBA-Based Current-Mode PID Controller Design

This paper aims to bring a voltage differencing inverting buffered amplifier (VDIBA)-based current-mode (CM) proportional integral derivative (PID) controller circuit. This CM PID controller is designed with a single VDIBA, three resistors, and two grounded capacitors. The proposed circuit is easy to design, and the control parameters can be tuned without changing the design configuration. A sensitivity analysis of the control parameters to electronic components has been conducted. The Simulation Program with Integrated Circuit Emphasis (SPICE) simulation has been performed using Taiwan Semiconductor Manufacturing Company (TSMC) [Formula: see text]m complementary metal-oxide semiconductor (CMOS) technology parameters. An application circuit example is given to demonstrate the reliability of the proposed PID design. A comparison table of the PID controllers previously reported in the literature is also presented.