Proportional Integral Derivative Controller Tuning Research Articles

Investigating PID Controller Effectiveness: An Extensive Analysis and Wide-ranging Uses

This study offers an in-depth investigation of the performance of proportional-integral-derivative (PID) controllers, providing an extensive evaluation and analyzing a wide range of applications. PID controllers, essential feedback mechanisms in various domains, are recognized as foundational instruments in control systems. This study evaluates PID controllers in in scenarios such as DC motor speed regulation, power system stability, Automatic Voltage Regulator (AVR) performance optimization, time delay processes, load frequency management, DC drive control, systematic process stability, and their developments in industrial control. The purpose of the study is to highlight the adaptability and effectiveness of PID controllers in contemporary control systems, including how artificial intelligence (AI) can be integrated into PID controller tuning.

PID controller tuning based on PSO and dominant pole placement

This paper proposed a new approach for proportional integral derivative (PID) controller tuning. particle swarm optimization (PSO) algorithm and dominant pole placement were used for PID controller tuning. Minimizing the estimation criterion with integral of absolute error (IAE) and overshoot by PSO algorithm, we determined the dominant pole and crossover frequency satisfying the maximum sensitivity and phase margin. This dominant pole and crossover frequency were used in order to design the PID controller. It satisfied robust stability and improves the control effect of the system to balance the trade-off between overshoot and settling time. We simulated this approach for SOPDT model. A simulation results were given to demonstrate the effectiveness of this approach.

Deep reinforcement learning for PID parameter tuning in greenhouse HVAC system energy Optimization: A TRNSYS-Python cosimulation approach

The control of indoor temperature in greenhouses is crucial as it directly impacts the crop's thermal comfort and the performance of heating, ventilation, and air-conditioning (HVAC) systems. Conventional feedback controllers, like on/off, can sometimes make HVAC system work at full capacity when only half that capacity is needed. In contrast, the proportional-integral-derivative (PID) controller, provides precise control based on its P, I, and D parameters. However, it lacks a formal design procedure for optimizing a specified objective function. Previous studies have utilized conventional PID tuning approaches to track room setpoint temperature for residential buildings, data centers, and office buildings, with limited research in greenhouse applications. To address this gap, this study proposes a flexible PID controller that employs a deep reinforcement learning (DRL) algorithm to optimize its parameters, by tracking the setpoints and energy consumption of a greenhouse planted with tomatoes. This approach is different from the typical method of using the trained RL agent directly in HVAC controls. Through a self-made TRNSYS-Python cosimulation framework, the DRL agent interacts directly and in real time with the greenhouse and its plants. Consequently, optimized PID parameters were established and tested in the simulated environment. The resulting performance, in terms of both energy consumption and its ability to maintain the crop’s comfort temperature, was compared with the simulated on/off and manually tuned PID controllers. Compared to the on/off baseline control, the proposed PID optimized parameters reduce energy use by 8.81% to 12.99% and the manually tuned PID parameters with the Ziegler-Nichols tuning method reduce energy use by 7.17 %. Additionally, the proposed method had a deviation of 2.07% to 3.13%, while the manually tuned PID controller and the on/off controller had deviations of 7.27% and 3.27%, respectively, from the minimum comfortable temperature. This study serves as a framework for improving the energy efficiency of greenhouse HVAC system operations.

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).

Improving precision and robustness in level control of coupled tank systems: A tree seed optimization and [formula omitted]-analysis approach

Background:Efficient control of liquid levels in interconnected tank systems is a fundamental challenge in various industries, including chemical processes, wastewater treatment, and manufacturing. The traditional approach to achieving precise control has relied on Proportional–Integral–Derivative (PID) controllers, whose performance largely depends on tuned parameters. However, tuning PID controllers for complex and nonlinear systems like coupled tanks remains a challenging task. In recent years, nature-inspired optimization algorithms have gained prominence in control system design. The tree seed optimization (TSO), inspired by the dispersion of tree seeds in search of optimal growth conditions, has shown promise in solving complex optimization problems. This study seeks to explore the application of TSO in tuning PID controllers for coupled tank systems. Methodology:This research employs the TSO to optimize PID controller parameters for enhanced liquid-level control in coupled tank systems. The optimization process involves integrating performance metrics and closed-loop gain constraints to achieve optimal control of coupled tank systems. The imposed constraints aim to ensure robustness and system stability in the face of uncertainties and disturbances. Besides, μ analysis quantifies the robustness of the system by assessing its ability to tolerate uncertainties. Findings:Simulation studies conducted in this research verify the efficacy of the proposed TSO-based approach for tuning PID controllers in coupled tank systems. Compared with various methods, the TSO consistently yields better control performance, reduces settling time, and minimizes overshoot. The robustness of the optimized controllers is also evaluated, showing the ability to handle varying operating conditions effectively.

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.

Artificial bee colony with predator effect algorithm for proportional integral derivative controller tuning

This paper proposes a novel artificial bee colony with predation effect (ABCPE) algorithm for tuning a proportional integral derivative (PID) controller. The mathematical model of ABCPE algorithm to introduce predator effect in the foraging behavior of artificial bees colony algorithm has been formulated. The proposed algorithm has been tested on tuning problems of different process models. The simulation results reveal that the closed-loop responses are relatively fast and non-oscillatory as compared to the frequency response analysis method for reference tracking. Further, the results obtained using ABCPE are also compared with other evolutionary algorithms. The exhaustive analysis shows that the ABCPE-based solution approach leads to a set of tuning parameters having smaller overshoot, less setting time, and rise time compared to other solution approaches. The stability analysis using Nichols plot reveals that the phase margin of proposed algorithm is higher as compared to other tuning methods. Finally, the convergence behavior and robustness analysis reveals the effectiveness of the proposed approach to solve engineering design problems.

Blockchain-Based Decentralized Frequency Control of Microgrids Using Federated Learning Fractional-Order Recurrent Neural Network

This paper presents a blockchain-based decentralized frequency control of an islanded microgrid (MG) using a novel federated learning fractional order recurrent neural network (FL-FORNN). A self-adaptive proportional-integral-derivative (PID) controller is proposed using FL-FORNN to handle the uncertainties of power generation by the prosumers while participating in the trading of the islanded MG. In this work, the frequency oscillations during peer-to-peer (P2P) energy trading are regulated through the appropriate design of an adaptive controller and the implementation of a smart contract participation matrix (SCPM) for balancing the generation and consumer demand. A Proof-of-Authority (PoA) private blockchain-based SCPM has been developed to secure the contract among peers. The SCPM provides the power demand information from a consumer to a prosumer who participates in the P2P energy market. It also provides power reference to the prosumer distributed generation as a supplementary control, in addition to the secondary frequency control of the system. To study this, an islanded MG comprising four source nodes (prosumers) and three demand nodes (consumers) are tested with the implementation of the PoA-based blockchain framework. With its SCPM calculation running in the blockchain framework, the decentralized control of prosumers is implemented by interfacing the OPAL-RT with Raspberry Pi devices. The robustness of the proposed FL-FORNN controller has been verified with the FORNN tuned PID controller. Furthermore, a comparative analysis is made with the centralized scheme and traditional decentralized frequency control technique.

Application of Deep Reinforcement Learning for Proportional–Integral–Derivative Controller Tuning on Air Handling Unit System in Existing Commercial Building

An effective control of air handling unit (AHU) systems is crucial not only for managing the energy consumption of buildings but ensuring indoor thermal comfort for occupants. Although the initial control schema of AHU is appropriate at installation and testing, it is frequently necessary to adjust the control variables due to the changing thermal response of the building envelope and space usage. This paper presents a novel optimization process for the control parameters of old AHU systems in existing commercial buildings without system downtime and massive operational data. First, calibrating the building and system simulator with limited system operation data and unknown building parameters can provide identical responses to the system operation with the Hooke–Jeeves algorithm during the cooling season. The deep deterministic policy gradient algorithm is employed to determine the optimal control parameters for the valve opening position of the cooling coil within less than three hours of training based on the calibrated simulator. By using actual implementations with the developed optimal control variables for an old AHU in a real building, the proposed auto-tuned PID control in the simulator and with machine learning improves thermal environments with a steady room temperature (23.5 ± 0.5 °C) by 97% in occupied periods. It is also proved that this can reduce cooling energy consumption by up to 13.71% on a daily average. The successful AHU controller can improve not only the stability of AHU systems but the efficiency of a building’s energy use and indoor thermal comfort.

Performance analysis of voltage profile improvement in AVR system using zebra optimization algorithms based on PID controller

Many problems are associated with dynamic changes in the power system, mainly because the number of switching loads has increased. These loads induce ineffective system behaviour, reduce the system voltage profile, and lead to improper voltage regulation. The proposed Automatic Voltage Regulator (AVR) system is intended to eliminate the above problem and preserve the system voltage at the generator terminal within the allowable range. In this work, Proportional-Integral-Derivative (PID) controllers are applied to enhance the dynamic behaviour of the AVR system. The Zebra Optimization Algorithm (ZOA) and Osprey Optimization Algorithm (OOA) algorithms are implemented to optimize the system's transient response by modifying the gain of PID controller parameters, which include proportional, integral, and derivative parameters, to preserve a stable voltage profile. To achieve an optimal solution, the mathematical model of the proposed system is realized in the Internet of Things (IoT). The connected loads in the system can operate at the nominal voltage level through PID controller tuning using ZOA and OOA. The proposed system's performance is evaluated and verified with MATLAB R2023a. ZOA showed an improvement of 18.5 % with a peak overshoot of 0.01 % during the system-transient condition. Compared to conventional optimization algorithms implemented in AVR systems, ZOA provides faster responsiveness and enhanced system stability.

An intelligent PID controller tuning for speed control of BLDC motor using driving training-based optimization

Tuning of proportional-integral-derivative (PID) controller remains a matter of great concern for the control engineers as it plays a major role to obtain optimal performance of any system Due to their simplicity and excellent efficiency, metaheuristic algorithms have recently become extremely popular among researchers for handling a wide range of real-world optimization challenges. In order to optimize a PID controller for managing the speed of a BLDC motor, this work proposes a novel application of the driving training-based optimization (DTBO) algorithm, one of the latest and most recent human-based metaheuristic algorithms. The purpose of this present study is to optimize a PID controller for a BLDC motor speed control by DTBO method and evaluate its performance with a similar controller tuned by grey wolf optimization (GWO) method. Additionally, the suggested DTBO-PID controller's robustness analysis is being carried out with BLDC motor parameter modifications as well as a comparison to the GWO-PID controller. The comparison is carried out in MATLAB/Simulink, and the results are based on common step response metrics such rise time, settling time, and maximum overshoot. For easier comprehension, the results are presented in tabular and graphical form. The chosen BLDC motor drive system's selected DTBO-PID controller performs better and is more reliable than the GWO-PID controller, according to the final simulation findings.

Modern Optimization Techniques Based PID Controller Tuning for the Speed Control of a DC Motor

In this paper, the optimal configuration of the Proportional Integral Derivative (PID) controller for the speed control of a DC motor are determined and compared using five optimization algorithms. The five optimization algorithms are respectively Ant Lion Optimization (ALO), Grey Wolf Optimizer (GWO), Moth-Flame Optimization (MFO), Multi-Verse Optimization (MVO) and Salp Swarm Optimization (SSO). The objective function uses The Integral of Time multiplied by Absolute Error (ITAE) as the performance index. A comparison of all these methods is done using the following step response parameters - steady-state error, settling time, maximum overshoot and rise time. ALO performed best among all the optimization algorithms.

Optimal tuning proportional integral derivative controller on direct current motor using reptile search algorithm

<span lang="EN-US">This paper presents the reptile search algorithm (RSA) method to optimize the proportional integral derivative (PID) parameters on direct current (DC) motors. RSA was adopted from crocodile hunting behavior. Crocodile behavior is modeled in two important steps: surrounding and attacking prey. The RSA method was applied using twenty-three classical test functions. The search method of the proposed RSA method with other existing algorithms such as particle swarm optimization (PSO), and differential evolution (DE). Integral multiplied by absolute error (ITAE) and integral of time multiplied squared error (ITSE) were used as comparisons in measuring the performance of the RSA method. The results show that the proposed method, namely RSA, has better efficiency. Optimization of PID parameters with RSA on DC motor control shows superior performance. From the experiment, the ITSE average value of the RSA method is 4.17% better than the conventional PID method.</span>

Optimal tuning of PID controllers with derivative filter for stable processes using three points from the step response

This paper proposes a novel approach for tuning Proportional Integral Derivative (PID) controllers, utilizing experimental data obtained from an open-loop step input. We propose to use the measurements of the times taken to reach 5%, 35.3% and 85.3% of the final output, as well as the process static gain, to tune the controller. The tuning equations are applicable for a wide range of stable and over damped systems. Starting from an approximate model with three real poles and time delay (obtained from the measurements), the tuning equations approximate the controller that minimizes the Integral of Absolute Error (IAE) of the disturbance response. The designer can freely decide the Sensitivity Margin (Ms) to fix a desired robustness, as a difference with respect to other known methods where the user chooses among few predefined robustness values. The user can also select freely the derivative filter parameter, N, to find the required compromise between speed response and measurement noise amplification. For N=0 a PI controller is chosen. As N increases, a faster PID controller is selected, with higher noise amplification. We have also developed a web-based application and an Android application, downloadable for free, that implement the tuning equations as well as the whole required procedure.

Multi-Phase Focused PID Adaptive Tuning with Reinforcement Learning

The Proportional-Integral-Derivative (PID) controller, a fundamental element in industrial control systems, plays a pivotal role in regulating an extensive array of controlled objects. Accurate and rapid adaptive tuning of PID controllers holds significant practical value in fields such as mechatronics, robotics, and automatic control. The three parameters of the PID controller exert a substantial influence on control performance, rendering the tuning of these parameters an area of significant interest within related research fields. Numerous tuning techniques are widely employed to optimize its functionality. Nonetheless, their adaptability and control stability may be constrained in situations where prior knowledge is inadequate. In this paper, a multi-phase focused PID adaptive tuning method is introduced, leveraging the deep deterministic policy gradient (DDPG) algorithm to automatically establish reference values for PID tuning. This method constrains agent actions in multiple phases based on the reward thresholds, allowing the output PID parameters to focus within the stable region, which provides enhanced adaptability and maintains the stability of the PID controller even with limited prior knowledge. To counteract the potential issue of a vanishing gradient following action constraints, a residual structure is incorporated into the actor network. The results of experiments conducted on both first-order and second-order systems demonstrate that the proposed method can reduce the tracking error of a PID controller by 16–30% compared with the baseline methods without a loss in stability.

Power quality enhancement by using Z-DVR based series voltage compensation with black widow optimization technique

In distribution system, voltage quality issues are the most concerning disturbances influencing the power quality (PQ). As a result, to alleviate this PQ concerns such as sag, swell, fluctuation, interruption, and harmonics on the sensitive load, the series voltage compensator dynamic voltage restorer (DVR) is utilized. Furthermore, a Z-source inverter (ZSI) based DVR is proposed in this paper to improve the power system's voltage restoration properties. To compensate the voltage concerns which is occurs in passive and transmission components, the 3-φ Z-DVR inverter with proportional integral derivative (PID) controller tuned by black widow optimization (BWO). By short circuiting the legs of inverter in the ZSI, prepare the possibility of buck and boost in voltage and utilize the LC impedance grid which incorporated power source to inverter circuit. In addition, to obtain the injecting voltage, PID control scheme for ZSI based DVR is proposed in this paper. The proposed modelling and simulation of DVR is implemented in MATLAB/Simulink tool and the outcomes are analyzed. Furthermore, reduction in voltage concerns, and total harmonics distribution (THD) with BWO tuned PID controller is superior which is 1.01% when compared with existing methods such as Harris Hawks optimization (HHO) based PID, genetic algorithm (GA) based PID controller.

An Improved Tuning of PID Controller for PV Battery-Powered Brushless DC Motor Speed Regulation Using Hybrid Horse Herd Particle Swarm Optimization

In this study, speed control of PV battery-powered brushless DC motor (BLDC) is controlled by novel hybrid horse herd particle swarm optimization- (HHHPSO-) tuned proportional integral derivative (PID) controller. The optimal gain parameter of the PID controller is tuned by hybrid horse herd optimization algorithm. The purpose of the newly developed HHHPSO algorithm is to enhance the performance of the classic horse herd algorithm (HHA), specifically in two different ways. In the first place, it bolsters HHA’s aptitude for exploratory learning related to the ageing issue. By doing so, it is possible to circumvent the phenomenon of the local minimum stagnation. Second, it permits HHA to have a superior capability of exploitation with the assistance of hybridization through the utilisation of particle swarm optimization. This hybrid technique helps improve the rate convergences of the HHA method. The time domain-based performance indices were considered as an objective function such as addition of integral of squared speed error, integral of squared current error, and integral of squared electromagnetic torque error for finding the optimal gain values for the PID controller using HHHPSO. The proposed HHHPSO-tuned PID controller for PV battery-powered BLDC motor is tested for various working conditions such as constant speed conditions, varying speed conditions, and varying load conditions and also compared with state-of-the-art method. The proposed method has quick rise time around 20-21 msec, quick settling time around 35-39 msec, zero steady-state error, and zero overshoot than state-of-the-art optimization method. The proposed control techniques were also tested in hardware to confirm the suitability for real-time applications.

Tuning of PID controllers for unstable first-order plus dead time systems

Abstract In this paper, proportional-integral-derivative (PID) controllers are tuned for unstable first-order plus dead time (UFOPDT) systems. Genetic algorithm (GA) is used to find the parameters of the PID controller for UFOPDT systems under the constraint of robustness measure. By curve fitting, the controller parameters are expressed as the functions of the UFOPDT model parameters. Two tuning formulas which consider robustness and the tradeoff between disturbance rejection and robustness of the closed-loop system are proposed. The proposed tuning formulas extend the application range of the existing methods and simulation results show that the tuned PID controllers can achieve good performance for UFOPDT systems.

Indirect response-based tuning of PID controller with adjustable robustness

The response-based design approach is a straightforward method for proportional–integral–derivative (PID) controller tuning. In this method, an open-loop process response is used to tune the PID controller for fixed robustness. In this article, new response-based PID tuning rules are proposed with adjustable robustness and response. Instead of three PID variables, the proposed PID tuning method allows the user to adjust the process response with a single variable [Formula: see text]. The range of constant [Formula: see text] is provided for ensuring the stability of the process. Three MATLAB/SIMULINK examples and one temperature controller experiment are used to validate the proposed controller performance. The simulation result is also compared with three well-known response-based PID tuning rules Z-N, Cohen-Coon, Astrom et al., and with a model-based PID tuning proposed by Wang et al. Moreover, the proposed tuning provides lesser IAE, ITAE, ISE, and ITSE values than the existing methods.

An inherently fault tolerant control of sodium cooled fast reactors and its stability analysis using particle swarm optimization

In this study we propose a simple, yet inherently fault-tolerant and robust controller utilizing a combination of both feedforward and feedback control schemes. Feedback controllers are known to be robust, but feedforward controllers can be reliable in the context of safety as they can be less dependent on measurements. Though, many combined feedforward and feedback controllers have been proposed in the literature, to the best of our knowledge a controller tolerant to the failure of power feedback signal is nowhere demonstrated. In this scheme, major corrections are effected by a model predictive forward control unit, while bounded uncertain part is corrected by a feedback control unit. The feedforward control is implemented using the inverse equations of the nuclear reactor point kinetics model. The bounded error control is effected by a simpler limited Proportional–Integral–Derivative (PID) feedback controller. Stability analysis of the controller is carried out numerically by Lyapunov’s direct method with the help of Particle Swarm Optimization (PSO) technique. The proposed controller (referred to as Inverse Dynamics Corrected Control (IDCC)), is studied for reactor power control with model error plus uncertainty and a principal feedback signal failure case ( i.e. power sensor failure). It is shown that the IDCC has excellent load tracking performance for a challenging demand profile with model error, in comparison to Sliding Mode Controller (SMC) and a manually tuned PID controller. For the loss of principal feedback signal case, there is a trade off between the tracking performance of IDCC and safety aspects. While both PID and SMC drive the reactor power to unsafe levels, IDCC maintains the reactor power within a safer bound.