Proportional Integral Derivative Controller Research Articles

A model predictive control for a multi-chiller system in data center considering whole system energy conservation

To meet the thermal environment requirements for the continuous and stable operation of Information Technology (IT) equipment in data rooms, the cooling system needs to operate all day, which has become the second largest energy-consuming system in data centers. The absence of an effective operational control strategy in the data center cooling process results in high energy consumption and poor Power Usage Effectiveness (PUE) of the data center. This study proposes a model predictive control (MPC) strategy considering the constraint of whole system energy conservation for a multi-chiller system in a data center. This strategy aims to maintain the data center server room temperature stable in the IT equipment working environment, and at the same time, the energy consumption of the cooling system is significantly reduced, thus the PUE of the data center is lowered. The long and short-term memory (LSTM) neural network prediction models for data center cooling load and server room temperature were constructed using the mechanism-coupled data law method. The MPC algorithmic structure coupled with cooling load prediction model and server room temperature prediction model. It takes the balance between supply and demand of cooling capacity as a constraint. The cost function of multi-chiller system control considers the temperature-controlling error in the server room and the power consumption of the chilled-water system. A particle swarm optimization (PSO) algorithm is used to solve the optimal configuration strategy of the chilled water flow rate and the water supply temperature of each chiller, which realizes the dynamic control of the chilled-water system. A dynamic regulation model was developed for a data center in North China. TRNSYS was utilized for verification based on the actual measured data and relevant meteorological parameters of the case building. Compared with the operation results of the data center cooling system with Proportional Integral Derivative (PID) control and fuzzy control. The results show that under MPC strategy, the stability of the server room temperature has improved by 27.77% compared to PID control and by 18.08% compared to fuzzy control, demonstrating the superiority of MPC in temperature stability control in the server room. In terms of chilled-water system energy consumption, compared to the PID control and fuzzy control strategies, the MPC strategy has achieved energy savings of 11.81% and 7.58%, respectively, showing significant energy-saving effects.

Optimizing the position of photovoltaic solar tracker panels with artificial intelligence using MATLAB Simulink

This research aims to apply an artificial intelligence (AI) system to control the position of photovoltaic (PV) panels to maximize the use of solar energy using the solar tracker. The implementation of AI algorithms to achieve optimal panel orientation, considering factors such as sunlight intensity and sun position is also discussed. The simulation results using matrix laboratory (MATLAB) Simulink can be observed on the scope, displaying the position control graph of the solar panel from sunrise to sunset. By employing proportional integral derivative (PID) control, the error is likely to be minimal, ensuring that the panel will continue to follow the sun until it sets at the maximum point of 4:00 PM. After that, the panel can be adjusted back or reset to the initial position at 6:00 AM for the following day. In a full-day simulation, the solar panel will follow the sun's movement from sunset to sunrise. At the basic level, sunrise occurs in the first hour at position 1.0, which is 6:00 AM in the minimum point at the bottom left corner of the curve, and sunset occurs in the afternoon at position 5.25, which is 4:00 PM at the maximum point in the top right corner of the curve.

Low cost pulsed electric field generator using DC-DC boost converter and capacitor diode voltage multiplier

Traditional high-voltage pulse generators, like Marx generators often face challenges related to efficiency and complexity. In this paper, a solid-state multi-module high-voltage pulse generator that integrates capacitor-diode voltage multipliers (CDVM) with DC-DC boost converters and closed-loop voltage control is proposed to overcome these challenges. The system achieves high output voltage by coupling the pulsed output voltages of individual low-voltage DC sources in series across each module. The proposed design was modeled using MATLAB, and experimental testing was conducted on a single stage. Comparative analyses between timedomain parameters, proportional-integral (PI), and fractional order proportional integral derivative (FOPID) controllers were performed. Both MATLAB simulations and experimental validations demonstrate the effectiveness of this approach. The rise time, peak time, settling time, and steady-state error are all improved using an FOPID controller, decreasing from 0.32 to 0.31 seconds, 0.42 to 0.35 seconds, and 3.15 to 2.20 seconds, respectively. These findings indicate that a closed-loop FOPID controller enhances time-domain performance parameters more effectively than a PI controller for a two-stage DC-DC voltage multiplier.

PID control algorithm based on multistrategy enhanced dung beetle optimizer and back propagation neural network for DC motor control.

Traditional Proportional-Integral-Derivative (PID) control systems often encounter challenges related to nonlinearity and time-variability. Original dung beetle optimizer (DBO) offers fast convergence and strong local exploitation capabilities. However, they are limited by poor exploration capabilities, imbalance between exploration and exploitation phases, and insufficient precision in global search. This paper proposes a novel adaptive PID control algorithm based on enhanced dung beetle optimizer (EDBO) and back propagation neural network (BPNN). Firstly, the diversity of exploration is increased by incorporating a merit-oriented mechanism into the rolling behavior. Then, a sine learning factor is introduced to balance the global exploration and local exploitation capabilities. Additionally, a dynamic spiral search strategy and adaptive [Formula: see text]-distribution disturbance are presented to enhance search precision and global search capability. The BPNN is employed to fine-tune both PID and network parameters, leveraging its powerful generalization and learning ability to model nonlinear system dynamics. In the simplified motor experiments, the proposed controller achieved the lowest overshoot (0.5%) and the shortest response time (0.012s), with a settling time of 0.02s and a steady-state error of just 0.0010. In another set of experiments, the proposed controller recorded an overshoot and response time of 0.7% and 0.0010s, across five DC motor tests. These results demonstrate the proposed adaptive PID control algorithm has superior performance in optimizing control system parameters, as well as improving system robustness and stability.

Modelling, Simulation and Testing of Steer-by-Wire System with Variable Steering Ratio Control Strategy in 14-DOF Full Vehicle Model

This research explores the application of Proportional-Integral-Derivative (PID) controllers and Variable Steering Ratio (VSR) control strategies within a Steer-by-Wire (SbW) system, utilizing a comprehensive 14 Degrees of Freedom (DOF) full vehicle dynamic model. The study aims to advance vehicle dynamics and control through SbW technology. This research addresses the challenge of optimizing steering control by integrating an SbW system with PID and VSR strategies to overcome the limitations of traditional steering mechanisms and enhance vehicle responsiveness and stability. The SbW system, using a PID-based controller, was rigorously tested and validated using MATLAB Simulink and Hardware-in-the-Loop System (HiLS) method. The performance of the system was assessed through four distinct signal tests: step, sine, square, and sawtooth inputs. These tests confirmed the precision of the PID controller in position tracking. To improve the practical applicability of the SbW system, a 14-DOF vehicle dynamic model was developed and validated before integration with the SbW system. The integrated system accurately replicated conventional steering behavior, as validated by Step Steer Input (SSI) and Double Lane Change (DLC) tests, demonstrating less than 11% RMS percentage error - well within the acceptable threshold of less than 15%. Additionally, the study proposed and validated VSR control strategies through the DLC test. Results indicate that the PID controller effectively tracked desired signals, while the VSR strategy reduced driver workload and improved steering stability. This research offers valuable insights into enhancing SbW system performance and lays a foundation for future advancements in vehicle control systems.

Error governor for active fault tolerance in PID control of MIMO systems

Input saturation and actuator faults are common issues in control system engineering. This paper proposes an Error Governor (EG) policy that dynamically manages the feedback error to enhance the tracking error in Multiple Input-Multiple Output (MIMO) closed-loop system controlled by Proportional-Integral-Derivative (PID) regulators. By integrating an Adaptive Kalman Filter (AKF) for optimal fault estimation with the EG scheme, the solution enables fault-tolerant control without requiring modifications to the baseline controller, which can be impractical or unsuitable in certain applications. Furthermore, the proposed control scheme completely avoids windup, thereby replacing conventional Anti-Windup (AW) schemes for PIDs, and is computationally cheap and easy to implement, needing only the same inputs as conventional AW algorithms and the actuator fault estimation. Simulation results on the MIMO model of the Zagi flying-wing aerial vehicle show that the EG reduces the tracking error in presence of actuator faults by − 49.92 % in terms of Integral Absolute Error (IAE), outperforming conventional AW methods.

Speed controller design for turboshaft engine using a high-fidelity AeroThermal model

Abstract One of the main objectives of this research is to construct a high-fidelity aerothermal model for controlling the turboshaft engine power turbine rotational speed. Firstly, a high-fidelity aerothermal model of General Electric T700 is formed. The turboshaft engine aerothermal model is simulated and compared to engine design point data on MATLAB/Simulink environment. Thermodynamic equations and some algebraic equations are used. In predicting compressor mass flow rate, the adaptive neuro-fuzzy inference system method is preferred. A propeller model is also added to the turbo shaft engine aerothermal model and to keep the power turbine rotational speed at a constant value, a Proportional Integral Derivative controller is designed and applied. Open-loop and closed-loop simulations are conducted and successful outcomes are achieved. Results indicate that the differences between simulation and actual engine data are within acceptable limits. The suggested model can be readily updated and expanded to control additional parameters of the engine. PACS 2010 Classification: Control theory in mathematical physics, 02.30. Yy, Computer modeling and simulation, 07.05.Tp, 05.70.Ce Thermodynamic functions and equations of state.

The Application of PID Control in DC Motor Control Systems

Abstract. The application of Proportional-Integral-Derivative (PID) control in direct current (DC) motor control systems is essential for achieving high levels of precision and reliability in both industrial and robotic applications. As DC motors are widely utilized in environments requiring accurate speed and torque control, this study seeks to address common challenges such as overshoot, instability, and sluggish response times that can compromise performance. The research is centered on the development and implementation of a PID-based control strategy using MATLAB/Simulink as the primary tool for simulation and testing. The study involves detailed simulation models and experimental validation, using data collected from controlled lab environments to evaluate the effectiveness of various tuning methods. These methods include adjusting the proportional, integral, and derivative gains to optimize motor responsiveness and system stability. The results indicate that with appropriate tuning, PID controllers can significantly enhance DC motor performance, leading to reduced overshoot, faster response times, and greater overall system reliability. The research concludes that adaptive PID control strategies, which dynamically adjust parameters in response to changing operating conditions, provide a robust solution for improving DC motor control in complex, dynamic, and nonlinear environments. This study lays the groundwork for future innovations in automation and precision-driven industries, offering insights that could be applied across a wide range of applications.

FUZZY-PROPORTIONAL INTEGRAL DERIVATIVE CONTROLLER WITH INTERACTIVE DECISION TREE

The STATCOM is extensively used in the power system to address the power quality issues by actively compensating the reactive power requirements of the load. However, the STATCOM performance depends on the underlying controller operation to handle sudden load changes and disturbances optimally with faster response. To solve this issue, this paper presents the intelligent algorithm-optimized fuzzy rule-based Proportional Integral Derivative (PID) controller to enhance the performance of the STATCOM. The proposed controller consists of a fuzzy-PID controller capable of handling non-linear dynamics and sudden changes in the load. The interactive decision tree (IDT) technique detects weaker metrics and improves their influence in control scenarios. The Biogeography-based optimization (BBO) algorithm minimizes the controller's integral absolute error to tune the fuzzy-PID controller parameters. The algorithm terminates once all the metrics are tuned to satisfaction with the operator’s consent. The proposed IDT-based fuzzy PID controller is tested on a power system containing a nonlinear load, and its performance is compared with the existing controller and simulated using the MATLAB/Simulink tool. The proposed controller provides fast control action, reduces the reactive power from the source by 42.5%, and improves the power factor by 1.5%.

Enhanced Frequency/Voltage Control in Multi-Source Power System Using CES and SSA-Optimized Cascade TID-FOPTID Controller

The stability and reliability of modern power systems, especially those with several renewable energy sources, strongly rely on load frequency control (LFC) and automatic voltage regulation (AVR) for frequency and voltage control under inconstant load demands. In this study, a new cascade tilt integral derivative-fractional order proportional tilt integral derivative (TID-FOPTID) controller is presented that is polished through the salp swarm algorithm (SSA) for LFC of a multi-area power system with AVR in all control areas. The system integrates capacitive energy storage (CES) and deals with governor dead-band and generation rate constraint nonlinear effects in a thermal-hydro-gas three-area multi-source power system (TAMSPS). The analysis of results, due to the SSA-based TID-FOPTID controller compared to TID-FOTID and TID-FOTID + 1 shows a positive outcome. Integrating CES brings additional improvement in the system performance, the overshoot/undershoot, and settling time are minimized. Finally, the sensitivity analysis reveals that the suggested controller will be effective and reliable for enhancing the frequency stability of the complex power system with a high RES integration level.

A Novel Enhanced Fire Hawks Optimization Approach for Improving the Efficiency of Converter‐Based Controllers in Switched Reluctance Motors

ABSTRACTSwitched reluctance motors (SRMs) have gained popularity in various industrial applications due to their advantages, including structural simplicity, high reliability, low cost, and operational stability over a wide speed range without relying on rare‐earth permanent magnet materials. However, these motors exhibit drawbacks such as weak torque density, low efficiency, and significant torque ripple, particularly in high‐speed operation. An efficient converter‐based control approach is proposed to manage speed and torque variations in SRM motors, addressing these issues. A multilevel converter (MC) is introduced as a fundamental component. The novel multilevel converter (NMC) accommodates SRMs with varying numbers of phases and exhibits quick demagnetization and excitation behaviors, enabling independent operation of each phase even during conduction overlaps. Subsequently, an effective controller is developed for the SRM motor, combining proportional integral derivative (PID) control with enhanced fire hawks optimization (EFHO). The EFHO optimizes the PID gain values to enhance controller performance. The converter operation minimizes torque ripple and facilitates speed management. The EFHO technique is a fusion of fire hawks optimization (FHO) and the sine cosine algorithm (SCA). This amalgamation improves the updating process of FHO by incorporating SCA. The proposed methodology is implemented in MATLAB and evaluated through various metrics, including SRM motor current, voltage, speed, and torque, under electric vehicle (EV) load conditions. Performance comparisons are conducted with traditional optimization algorithms such as the whale optimization algorithm (WOA) and ant colony optimization (ACO). The results validate the effectiveness of the proposed methodology in achieving improved SRM motor control and performance.

A Computational Study on Effects of PID Temperature Target and RF Frequency for PID-Controlled Nonablative RF Cosmetic Systems.

Commonly adopted in cosmetic dermatology, nonablative radiofrequency (RF) devices convert high-frequency electromagnetic energy into thermal energy to induce a wound-healing response in skin tissue. However, differences in the electrical properties of different skin layers raise questions about the impact of different RF frequencies and target temperatures on treatment effectiveness. This paper presents a finite element analysis (FEA)-based computational study aimed at simulating and optimizing the effects of a proportional integral derivative (PID)-controlled RF cosmetic devices under different combinations of these two parameters during treatment. A 3D physical model for the application of a nonablative RF device was constructed using COMSOL, which included the human tissue and RF electrodes, electromagnetic and thermal boundary conditions, as well as the PID controller. FEA was performed for each of the twelve models with parameter combinations of three RF frequencies (0.1, 0.5, and 1 MHz) and three PID-controlled target temperatures (60°C, 65°C, and 70°C) plus one group without PID control. Treatment effectiveness was quantitatively assessed using the integration of tissue thermal damage fraction, i.e., thermal damage volume. In the earlier stage of heating (0-10 s), higher RF frequency resulted in a larger thermal damage volume. At 10 s, among models with a temperature target of 70°C, there is a 6.04% difference between the thermal damage volume at RF frequencies of 1.0 and 0.1 MHz. In the later stage of heating(11-80 s), the impact of RF frequency decreases. The difference in thermal damage volume caused by higher temperature targets is more significant, at 80 s, among models with an RF frequency of 1.0 MHz, the 70°C model produces 1.15 and 1.36 times more tissue thermal damage than the 65°C and 60°C models. PID controller has ensured treatment safety and uniformity, in exchange for some efficiency. Among 12 parameter combinations, the one with a temperature of 70°C and RF frequency of 1.0 MHz achieved the highest thermal damage volume, which could potentially result in the best esthetic effect. Considering users' different susceptibility to heat, engineers or physicians can select better temperature targets and RF frequencies to bring the desired cosmetic results based on thermal damage volume curves from this study.

Observer‐based PID control for fuzzy dynamic systems with memory triggering protocol

AbstractThis paper addresses the issue of observer‐based proportional–integral–derivative control for Takagi–Sugeno fuzzy dynamic systems using a memory triggering protocol. To tackle the challenges of managing nonlinear systems, the Takagi–Sugeno fuzzy approach is employed to approximate these systems with a series of local linear models. A novel memory event‐triggering mechanism is introduced, utilizing a computer's storage unit to store historical data and adjust the triggering threshold based on this data, thereby reducing unnecessary network resource usage. Given that the system state can be affected by external disturbances and become unpredictable, an observer‐based proportional–integral–derivative controller is designed to manage these uncertainties. Finally, a car‐damper‐spring model is presented to validate the proposed methodology.

Optimization of chemical engineering control for large-scale alkaline electrolysis systems based on renewable energy sources

In the context of renewable energy, dynamic control is crucial for large-scale alkaline water electrolysis systems. Under traditional Proportional-Integral-Derivative (PID) control, the system's temperature and impurity levels may exceed safe limits during sudden load changes, compromising system safety. Therefore, this study proposes a control strategy based on mathematical models of system temperature and impurities, including Model Predictive Control (MPC) for temperature and Optimal Curve Tracking (OCT) for impurities. The MPC controller offsets the disturbances in temperature caused by current fluctuations through state prediction, while the OCT controller ensures that impurity levels remain within safe limits. Real-time application of these control strategies is achieved through MATLAB-PLC communication, validating controller performance. Experimental results show that the MPC controller exhibits excellent dynamic response and stability in controlling the stack temperature, with a maximum temperature peak deviation of only 2.9 K and a temperature fluctuation range of 5.9 K. This represents a reduction of 1.6 K in peak deviation compared to traditional PID controllers and significantly decreases the temperature fluctuation range. The OCT controller also demonstrates good safety and stability in controlling hydrogen to oxygen (HTO) impurity levels, consistently maintaining the HTO content at the set upper limit of 1.5%, thereby expanding the safe operational range of the system and reducing the need for frequent adjustments to the system setpoints.

Trajectory Tracking Control of a Morphing UAV using Radial Basis Function Artificial Neural Network Based Fast Terminal Sliding Mode: Theory and Experimental

Lately, Morphing Aerial Systems (MASs) have seen a surge in demand due to their exceptional maneuverability, flexibility, and agility in navigating complex environments. Unlike conventional drones, MASs boast the ability to adapt and alter their morphology during flight. However, managing the control and stability of these innovative and unconventional vehicles poses a significant challenge, particularly during the aerial transformation phases. To solve this problem, this manuscript proposes a Radial Basis Function Artificial Neural Network-Based Fast Terminal Sliding Mode Control (RBFANN-FTSMC) method. This approach is designed to effectively manage morphology changes, ensure precise trajectory tracking, and mitigate the impact of external disturbances and parameter uncertainties. Accordingly, the RBFANN-FTSMC will be evaluated against Proportional Integral Derivative (PID), Sliding Mode (SM), and Fast Terminal Sliding Mode (FTSM) controllers through two flight simulation scenarios to validate its effectiveness. Additionally, the control parameters will be optimized using a recent metaheuristic algorithm known as the Whale Optimization Algorithm (WOA). A novel hardware control diagram is explained. Finally, the ability to alter morphologies and the results of experimental tests are discussed to highlight the performance and limitations of the mechanical structure and the implemented RBFANN-FTSMC.

Tracking performance optimization of balancing machine turntable servo system based on deep deterministic policy gradient fractional order proportional integral derivative control strategy

Tracking performance optimization of balancing machine turntable servo system based on deep deterministic policy gradient fractional order proportional integral derivative control strategy

PIDNODEs: Neural ordinary differential equations inspired by a proportional–integral–derivative controller

Neural Ordinary Differential Equations (NODEs) are a novel family of infinite-depth neural-net models through solving ODEs and their adjoint equations. In this paper, we present a strategy to enhance the training and inference of NODEs by integrating a Proportional–Integral–Derivative (PID) controller into the framework of Heavy Ball NODE, resulting in the proposed PIDNODEs and its generalized version, GPIDNODEs. By leveraging the advantages of control, PIDNODEs and GPIDNODEs can address the stiff ODE challenges by adjusting the parameters (i.e., Kp, Ki and Kd) in the PID module. The experiments confirm the superiority of PIDNODEs/GPIDNODEs over other NODE baselines on different computer vision and pattern recognition tasks, including image classification, point cloud separation and learning long-term dependencies from irregular time-series data for a physical dynamic system. These experiments demonstrate that the proposed models have higher accuracy and fewer function evaluations while alleviating the dilemma of exploding and vanishing gradients, particularly when learning long-term dependencies from a large amount of data.

Development of a PID-Controlled Refrigeration System for Reduced Power Consumption

Refrigerator systems are used for food preservation as well as other applications. However, the cost of running the system is high due to rising fuel and electricity prices. Traditionally, these systems are controlled by On/Off controllers. This study proposes the use of a proportional-integral-derivative (PID) controller algorithm to reduce costs for domestic and industrial refrigeration without negatively affecting the system performance. To accomplish this, a physical model was developed, comprising a domestic refrigerator, microcontroller, and MATLAB computer software for analysis. A mathematical model of second-order lead and second-order lag transfer function was also developed for a typical refrigerator system. The physical model was connected, and open-loop temperature-time response data was collected for system modeling. In addition, Data were collected from industries namely Fan Milk Industry and Benue State University Teaching Hospital Mortuary for a robust system analysis. All data sets were imported into MATLAB's system identification toolbox to estimate model parameters. The ultimate gains, frequency, and period were determined for each feedback closed-loop model, allowing the application of Ziegler-Nichols and Tyreus-Luyben PID tuning settings. The closed-loop models were then simulated in MATLAB to evaluate system performance. Simulation results showed that the Tyreus-Luyben model performed better, and offered better temperature response, less undershoot, and faster settling time than the Zeigler-Nichols method. Both PID models outperformed the traditional On/Off controller, with energy consumption reduced to less than one-third of the conventional method. The study concludes that PID controllers are a better alternative to On/Off systems when properly tuned.

PID-based control strategies for enhancing stability and precision in electro-hydraulic actuation systems

Electro-hydraulic actuation systems are essential in industrial applications but often face challenges related to nonlinearity, leading to instability and reduced precision. This paper explores the application of Proportional-Integral-Derivative (PID) control strategies to enhance the stability and precision of these systems. A detailed system model is developed, and the PID controller is designed and tuned using optimization techniques. Simulation results demonstrate improvements in performance metrics, such as reduced overshoot, settling time, and steady-state error. The proposed control strategy is validated experimentally on a physical setup, confirming its effectiveness in real-world applications. The findings show that PID-based control significantly enhances both stability and precision in electro-hydraulic actuation systems, offering a practical solution for industrial control challenges.

Active Disturbance Rejection Control for Flux Weakening in Interior Permanent Magnet Synchronous Motor Based on Full Speed Range

To address the impact of load disturbances on the full-speed-range control of an interior permanent magnet synchronous motor (PMSM), an active disturbance rejection control (ADRC) method is proposed. The speed loop employs phased field-weakening control (FW) based on ADRC, while the current loop utilizes proportional-integral-derivative (PID) control. Starting from the motor parameters, the Lagrange multiplier method was used to derive the critical speeds for the maximum torque per ampere (MTPA) and maximum torque per voltage (MTPV) ratios, and the timing for the field-weakening control was analyzed. A full-speed-range control model of the motor was established, and an ADRC-based speed loop controller was designed to achieve smooth transitions between high speeds and anti-disturbance solid capabilities. Based on the proposed control strategy, a 21 kW PMSM was used as the research object, and a full-speed-range control simulation model was developed in MATLAB/SIMULINK to verify the strategy. Compared to the traditional PID control, the simulation results demonstrate that the proposed strategy effectively observes and compensates for load disturbances, significantly reducing initial torque oscillations under three different operating conditions. After a sudden load increase, torque oscillations were reduced by 16%, with the stator current reaching steady state 0.03 s faster, response speed improving by 0.02 s, smooth transitions between speed ranges, and enhanced anti-disturbance performance.