Proportional Integral Derivative Controller Research Articles

Implementation of an Active Ankle-Foot Orthosis Prototype with a Cam-Driven Actuator

The high prevalence of conditions leading to foot drop highlights the need for devices that restore functionality, enabling patients to regain a natural gait pattern. There is a demand for a portable, lightweight, low-cost, and efficient active ankle-foot orthosis. In this work, we present the prototype of a new design that was simulated in a previous contribution, with a test bench evaluation of the low-level control. The dynamical behavior of a cam suspension interaction with a proportional–integral–derivative controller system for transmission is evaluated. The proposed active orthosis includes a novel cam-based actuator, designed to intervene at the dorsiflexion stage of gait, without influencing the plantar flexion. This design is aimed at specific lower limb ailments that cause a need for assistance only in raising the foot, and it leverages a commercial servomotor to achieve ankle angle tracking. System identification was performed using a test bench, with three degrees of freedom to emulate tibial motion during gait. Response evaluations of the device showed low values for the integral time squared error, peak overshoot, and settling time for step inputs, with and without additional periodic perturbations. The root mean squared error of the device while tracking an ankle angle signal varied from 0.1 to 6.5 degrees, depending on the speed of the changes.

Design and Real-Time Control of an Electric Furnace with Three-Dimensional Heating

Currently, heating in electric ovens is generally achieved using heaters placed on the top and bottom surfaces. In some advanced ovens, heaters are installed on the back surface, allowing 3D heating. However, in these ovens, temperature measurements are obtained from a single point, making the temperature control unreliable. Additionally, this type of oven cannot provide homogeneous heating since it lacks heaters on the left, right, or front surfaces. In this study, a unique electric oven equipped with heaters and temperature sensors was designed and produced on all six surfaces. To model its performance, the heating behavior of the oven was derived using the Ziegler–Nichols tangent method, and the gain factors for the proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers were determined. Subsequently, real-time digital control of the oven was performed using on-off, P, PI, and PID controllers, which ensured a comprehensive evaluation of the oven’s control performance. The experimental results showed that homogeneous heating could only be achieved when all panels were energized. Additionally, the PI and PID controllers stabilized the system with a maximum steady-state error of 1.3 °C in all cases, demonstrating the accuracy of the derived system model and adequacy of the implemented control system.

Artificial Neural Network (ANN) based Proportional Integral Derivative (PID) for Arm Rehabilitation Device

The current work was developed under the title of Artificial Neural Network (ANN) Proportional Integral Derivative (PID) for the arm rehabilitation device and included building and designing the simulation model and simulation results for the arm rehabilitation device. A set of tests were proposed to include firstly testing a system that represents the state of the open arm rehabilitation device and secondly It represents the closed arm rehabilitation device, third represents the closed-loop arm rehabilitation device with PID control device, fourth represents the arm rehabilitation device using ANN, and finally the closed-loop arm rehabilitation device can be used with a comparison between PIDC and ANN. To conduct all the proposed test cases, a program can be used MATLAB, which can help simulate a device that represents an attempt to regain movement in the arm, which is called rehabilitation. It can be noted that the target group is some people who suffer from stroke. By representing the system in the proposed simulation model, its effectiveness can be verified. It is possible to conduct tests aimed at improving performance by working on developing the model by adopting the appropriate design for the characteristics that match the required operational behavior of the system with all conditions that suit different situations. The test cases demonstrated through the simulation results the possibility of identifying the system behavior for the proposed cases. The difference between the system behavior for all these cases was also identified. In addition to the possibility of improving the performance of the movement recovery device to rehabilitate the injured arm through the system’s performance in the presence of an expert neural network controller, it is better than the traditional controller.

Low-order MIMO controller for turbomachinery supported by active magnetic bearings

In industry, the operation of turbomachinery supported by active magnetic bearings (AMBs) requires a robust and simple controller to meet increased performance requirements and stringent regulations. This study proposes an innovative low-order Multiple-Input Multiple-Output (MIMO) controller. Its structure is derived from the decentralized augmented Proportional-Integral-Derivative (PID) controller, enhanced with fixed terms in the skew-diagonals of the controller matrix. The resulting controller couples the information acquired by the AMB sensors on the same control axis to enhance the overall performance. The parameters of the new MIMO structure are tuned using a model-based procedure that exploits a non-smooth optimization algorithm, with the rotor model adjusted on experimental measurements to represent the real dynamics of the system. The novel controller performance is evaluated through two case studies: first, an expander-compressor system; second, a centrifugal turbo compressor designed for oil and gas applications, facing challenges associated with the observability and controllability of the second bending mode. The performance is then compared with that obtained using a decentralized augmented PID controller whose parameters have been tuned with the same non-smooth optimization algorithm. The new controller demonstrates a significant reduction in vibration caused by rotor bending modes. For example, in the analyzed case studies, unbalance responses were reduced by up to a factor of 10. Moreover, the proposed controller increases robustness compared to the decentralized case, as demonstrated by the second case study where controllability and observability issues are addressed.

Optimizing TRMS stability: a multi-objective genetic algorithm approach to PID controller design

PurposeThis paper aims to enhance the stability and control of twin rotor multi-input multi-output system (TRMS) helicopters by introducing a novel approach that utilizes a multi-objective genetic algorithm (MOGA) for optimizing proportional, integral, derivative (PID) controllers in simultaneous pitch and yaw motions.Design/methodology/approachThe TRMS, a common prototype for helicopter motion studies, is introduced, and a PID controller is designed for pitch and yaw stabilization. The gains of the PID controller are optimized using a MOGA, a technique not previously proposed for TRMS in the literature.FindingsWhile various controllers have been explored in literature for TRMS stabilization, a MOGA-optimized PID controller for TRMS has not been proposed before. Simultaneous optimization of both pitch and yaw motions using two PID controllers is expected to yield improved robustness.Research limitations/implicationsThe study focuses on simulations, and experimental validation is not conducted. The MOGA is introduced as an optimization technique, and future studies may explore its application in experimental settings.Originality/valueThis study introduces a novel approach by utilizing a MOGA to optimize PID controller gains for TRMS. Simultaneous optimization of pitch and yaw motions aims to enhance robustness, providing a unique contribution to the field of helicopter control.

Data analysis and visualization of electric vehicle engineering

We have visualized data using Excel to understand the relationship between battery chemistries and capacity. Examined Python code for tuning a Proportional – Integral – Derivative (PID) controller to understand its role in improving control accuracy. The challenges and benefits of PID tuning are discussed, highlighting the importance of precise tuning for optimal performance, efficiency, and safety. Analysing the impact of various battery form factors, including cylindrical, pouch, and prismatic options, on system cost, safety, and durability. Furthermore, the paper explores design trade-offs in electric vehicle development, emphasizing the need for balancing competing parameters such as performance, durability, and cost-effectiveness. The characteristics of various battery form factors (cylindrical, pouch, and prismatic) and Light Detection and Ranging (LiDAR) sensors (mechanical, solid-state, and hybrid) are compared, providing insights into their suitability for different applications. Overall, this article offers a comprehensive overview of the intricate relationships between battery chemistries, PID controllers, and design trade-offs in the development of efficient and sustainable electric vehicles. Conducted a comprehensive cost-benefit analysis for different LiDAR sensor models, comparing mechanical scanning, solid-state, and hybrid LiDAR sensors, with a focus on durability, scanning speed, and cost implications. Beside the aforementioned, we have also presented technical findings in a concise format using tables, aiding the engineering division in making informed decisions for various projects.

Probability Density Evolution and Fractional PID Control of Magnetic Bearing-Rigid Rotor System Influenced by Multisource Stochastic Factors

Magnetic bearings are widely used in engineering for their remarkable advantages of low friction, no wear and high speed. In this paper, the dynamics and control of the magnetic bearing-rigid rotor system under the influence of multisource stochastic factors are studied. Firstly, a model of magnetic bearing-rigid rotor system driven by multiplicative noise and additive noise is established. Secondly, the stationary response probability density function (PDF) of the proposed magnetic bearing system is obtained by using the amplitude envelope stochastic average method. Then we analyze the influence of different system parameters and noise intensity on the magnetic bearing-rigid rotor system, and find that internal stochastic factors are the main factors affecting the stability of the bearing system. Finally, the fractional Proportional Integral Derivative (PID) control of the system is studied. Based on the numerical analysis, we verify the effectiveness of the control strategy and draw the conclusion that adjusting appropriately the parameters of fractional PID controller can make the magnetic bearing system control better.

Greenhouse environmental monitoring and control system based on improved fuzzy PID and neural network algorithms

Abstract Compared with traditional agriculture, greenhouse planting can more accurately control the growth environment, thereby improving the yield and agricultural product quality. However, traditional greenhouse environments (GhEs) present a number of challenges, including inflexibility in monitoring and wiring, difficulty in management, and high labor costs. To improve the limitations of traditional GhEs and enhance the accuracy of GhE monitoring and control systems, a sensor-based GhE monitoring and control system is designed. In addition, a prediction model for GhE monitoring is constructed using a backpropagation neural network to better predict nonlinear factors such as humidity, temperature, and light intensity in the GhE. Simultaneously, an improved fuzzy proportional integral derivative (PID) controller is utilized to address issues such as fuzziness and uncertainty in GhEs. The results show that the temperature error of the greenhouse environment monitoring and control system based on improved fuzzy PID and neural network algorithms is 0.35–5.04%, the humidity error is −1.3 to 1.65%, and the lighting error is −3.5 to −0.79%. Comprehensive data show that the greenhouse environmental monitoring and control (GEMC) system based on improved fuzzy PID and neural network algorithms effectively improves the accuracy of environmental monitoring and control. The GEMC system, which is based on improved fuzzy PID and neural network algorithms, has facilitated the advancement of agricultural technology in China. It has also provided support and a reference point for GhE monitoring and agricultural production.

Research on the Coordinated Control of Mining Multi-PMSM Systems Based on an Improved Active Disturbance Rejection Controller

This study focuses on the problems of poor control performance, synchronization performance and stability in multi-motor permanent magnet drive systems in mining belt conveyors when a Proportional Integral Derivative (PID) controller is used to control the multi-motor. In this paper, a system model for three-motor synchronous control of a mine belt conveyor is established. On this basis, an Enhanced first-order Active Disturbance Rejection Controller (Efal_ADRC) is designed based on an optimized nonlinear function. Additionally, a weighted arithmetic mean is used to enhance the compensator of the ring coupling control structure. Finally, the system model is evaluated and simulated using various algorithms. Results show that synchronous control of a multi-Permanent Magnet Synchronous Motor (multi-PMSM) drive system based on the Efal_ADRC ring coupling control structure has better anti-interference ability, control accuracy and synchronization, which is conducive to the stable and efficient safe operation of the belt conveyor.

CO2 Concentration Control in Cleanrooms Using an Improved Crested Porcupine Algorithm

Cleanrooms are widely used in various industries, where the precise control of parameters such as CO2 concentration is crucial for optimal production. Most cleanrooms utilize variable air volume (VAV) air conditioning systems, but existing proportional–integral–derivative (PID) controllers in VAV systems often suffer from long response delays, excessive overshoot, and difficulties in handling dynamic changes in occupant conditions. This study introduces an Improved Crested Porcupine Optimizer (ICPO) to optimize PID controller parameters, aiming to enhance the control of VAV air supply. Additionally, a CO2 concentration control system for cleanrooms was designed based on an STM32 microcontroller. The results demonstrate that the Improved Crested Porcupine Optimizer PID (ICPO-PID) controller outperforms traditional PID, Fuzzy-PID, and Crested Porcupine Optimizer PID (CPO-PID) controllers in control accuracy, response speed, and robustness. In simulation, ICPO-PID achieves a settling time of just 59 s and an overshoot of only 5.14%. In real-world performance evaluations, ICPO-PID outperforms other controllers in terms of the Integral Absolute Error (IAE) and Integral Squared Error (ISE). Furthermore, ICPO-PID reduces energy consumption by approximately 40% during air volume adjustment compared to traditional PID. These results indicate that ICPO-PID is an efficient and reliable solution for maintaining cleanroom environments with precise CO2 concentration control.

Research on Energy-Saving Optimization Method and Intelligent Control of Refrigeration Station Equipment Based on Fuzzy Neural Network

Under the background of dual carbon, the retrofitting of the equipment operation system of a refrigeration station and the optimization combination of its control system are significant for its efficient operation and energy saving. The single-direction variable flow technology is often used in the chilled water system in refrigeration stations nowadays. However, the single-direction variable flow technology cannot achieve both thermal balance and flow balance for the chiller system, which is unfavorable for improving energy efficiency and reliability. To improve the reliability and energy efficiency of the refrigeration station equipment, the bidirectional variable flow technology of primary and secondary chilled water pumps was presented. Meanwhile, the feasibility of fuzzy neural networks in bidirectional variable flow systems and their energy-saving effect were studied. Before the energy saving retrofit, the refrigeration station used traditional PID (proportional-integral-derivative) controllers, and the chilled water system used single-direction variable flow technology; After the energy-saving retrofit, the refrigeration station adopted a fuzzy neural network control algorithm to optimize the PID controller parameters, and at the same time, the chilled water system used bidirectional variable flow technology. Through a large number of trial calculations of the established neural network model, it was found that 2 hidden layers and 25 hidden layer nodes can achieve higher accuracy. Specifically, the controller of the central refrigeration station consists of a training neural network and a predictive neural network working in parallel. The task of training neural networks is to learn the relationship between different input parameters and the whole energy consumption. Then it serves as the excitation function of the prediction network. The function of the predictive neural network is to find the control parameters that minimize energy consumption. The application results showed that before and after the retrofit annual power consumption and energy-saving effects were very Significant. After the energy-saving retrofit of the refrigeration station, the energy saving is 422,775 KWh every year, the energy-saving rate is 11.67%, and the annual saving cost is about 0.3382 million yuan. The results demonstrated that bidirectional variable flow technology and its control methods were feasible, reasonable, and worthy of promotion.

Linear Matrix Inequality‐based design of distributed proportional‐integral‐derivative for the output consensus tracking in heterogeneous high‐order multi‐agent systems

AbstractThis article addresses the cooperative output consensus tracking problem for high‐order heterogeneous multi‐agent systems via a distributed proportional‐integral‐derivative (PID)‐like control strategy and proposes two novel control methodologies for the tuning of the control gains, which do not require any assumption and/or limitation on agent system modeling. By extending the static output feedback (SOF) paradigm to distributed domain, the asymptotic stability problem for the overall MAS composed of agents is revisited into decoupled stabilization problems to be solved. Then, by exploiting the Lyapunov and matrix theory, the typical SOF bilinear matrix inequality (BMI)‐based stability conditions are recast into feasible linear matrix inequality (LMI)‐based ones, whose solutions allow finding the proper values of the PID control gains ensuring the achievement of the cooperative task. In doing so, the proposed procedures reduce the computational effort required for the control design, hence providing a greater attraction for a wider range of practical engineering applications. The scalability and the adaptability of the proposed control methodology in solving an alternative cooperative control problem in the presence of multiple leaders, that is, the output containment task, are also analytically investigated. Numerical simulations confirm the effectiveness of the theoretical derivations.

High-Order Engineering Fastest Controller and Its Application in Thermal Power Units

In the domain of industrial process control, the ubiquitous proportional–integral–derivative (PID) control paradigm, while foundational, is deemed insufficient amidst evolving complexities. In alignment with China’s strategic “dual-carbon” targets, extant thermal power installations are mandated to facilitate profound peak load navigation and expedited frequency modulation services. The incumbent PID control schema is found wanting in this regard, precipitating the imperative for an innovative process control technology to supplant the conventional PID regimen. Power system engineers have consequently devised the engineering fastest controller (EFC), which has adeptly succeeded PID control in nascent applications, thereby meeting the stringent control exigencies for deep peak regulation and agile frequency modulation. Employing rigorous theoretical analysis and sophisticated simulation experiments, this investigation meticulously compares the performance attributes of high-order controllers (HOCs) with the EFC. The empirical findings underscore the EFC’s pronounced superiority over PI, PID, and SOC in regulatory performance enhancements by 122.2%, 88.0%, and 77.3%, respectively, and in mitigating disturbances by 140.0%, 80.9%, and 54.5%, respectively. This study culminates in the assertion that the EFC represents a paradigmatic advancement in industrial control technology, not only manifesting pronounced performance benefits but also furnishing a robust theoretical scaffolding that transcends the performance zeniths of traditional PID and HOC technologies.

Control of a Mobile Line-Following Robot Using Neural Networks

This work aims to develop and compare the performance of a line-following robot using both neural networks and classical controllers such as Proportional–Integral–Derivative (PID). Initially, the robot’s infrared sensors were employed to follow a line using a PID controller. The data from this method were then used to train a Long Short-Term Memory (LSTM) network, which successfully replicated the behavior of the PID controller. In a subsequent experiment, the robot’s camera was used for line-following with neural networks. Images of the track were captured, categorized, and used to train a convolutional neural network (CNN), which then controlled the robot in real time. The results showed that neural networks are effective but require more processing and calibration. On the other hand, PID controllers proved to be simpler and more efficient for the tested tracks. Although neural networks are very promising for advanced applications, they are also capable of handling simpler tasks effectively.

Research on Underground Track Tracking of a New Type Shaft Boring Machine

A trajectory tracking control scheme is proposed in this paper to achieve unmanned underground construction of a new type of shaft boring machine. The body motion model is constructed, and the control relationship between the driving system and the body motion is deduced. MATLAB and Simulink simulate the joint of the track tracking process in the new shaft boring machine. The actual effect of the track tracking control scheme is validated by the track tracking field test of the new shaft boring machine. The results show that the new shaft boring machine can complete various complex track tracking tasks, with the maximum position error being less than 0.005 m. The running track and excavation areas of the boring machine are observed along with the track tracking field test of the new shaft boring machine, demonstrating that the track tracking control scheme makes the new shaft boring machine realize unmanned construction and verifies the co-simulation accuracy. The PID (proportional–integral–derivative control) algorithm can complete complex trajectory tracking tasks and promote the development of unmanned construction technology.

Optimal nonlinear PID TSK3DCMAC controller based on balancing composite motion optimization for ballbot with external forces.

This paper proposes an innovative approach to address the challenges of dynamic balance and external disturbances in ballbot systems, overcoming the limitations of conventional Proportional Integral Derivative (PID) controllers and their variants in handling highly nonlinear dynamics and external forces. Traditional PID controllers and their variants often have difficulty adapting to complex, real-time dynamic systems, leading to performance degradation under varying conditions. A nonlinear PID controller-based Takagi-Sugeno-Kang 3D Cerebellar Model Articulation Controller (TSK3DCMAC) is introduced to overcome these shortcomings. The proposed controller is developed utilizing a combination of nonlinear PID control, TSK3DCMAC, and the Balancing Composite Motion Optimization (BCMO) algorithm. The TSK3DCMAC is iteratively trained during the ballbot's motion to ensure the system balance in a very steady and seamless manner. Furthermore, the BCMO algorithm is utilized to obtain the optimal gains for precisely modeling the system. The stability of NPID-TSK3DCMAC law is analyzed using the Lyapunov technique. The simulation and experimental results highlight the effectiveness of the NPID-TSK3DCMAC controller. Without external force, it reduces the mean squared error (MSE) by 45.84 % and 99.87 % and the mean absolute error (MAE) by 25.68 % and 63.91 % compared to the PID and NPID controllers, respectively. With external force, it further surpasses the NPID controller by 64.94 % in MSE and 17.67 % in MAE, demonstrating its robustness and precision under varying conditions. Simulation and experiment results reveal that the proposed approach has robustness and effectively regulates the motion of the ballbot system despite external disturbances. This indicates a promising solution for applications requiring precise/agile motion control and stability under varying external conditions.

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.

PID and Fuzzy Logic Optimization of the Pitch Control of Wind Turbines

In the future, wind turbines may become an important source of energy generation because of their scalability and ability to be constructed in most places on Earth. To meet net-zero greenhouse gas emissions by 2050, emissions need to be reduced globally. This can be achieved in part by making renewable energy cheaper than fossil fuels. The energy production of wind turbines may be increased by integrating a smart controller that can optimize the pitch angles of the turbine. A smart controller would also reduce maintenance and servicing costs while increasing the turbine’s functional lifespan. By integrating proportional-integral-derivative (PID) and fuzzy logic controllers, which are used in many industrial control systems, the pitch control of a wind turbine could be optimized to generate the most electricity while avoiding overshoot. We hypothesized that the fuzzy-PID controller, which uses both fuzzy and PID controller algorithms, would be the most optimal for electricity generation by having the shortest settling and rise time with very little overshoot and settling error. We modeled a proportional-integral (PI) controller, a proportional-derivative (PD) controller, a PID controller, 7 and 9 membership function fuzzy controllers, and a fuzzy-PID controller in Simulink. In general, we observed that fuzzy logic-based controllers rose and settled slower than PID-based controllers with less overshoot and steady-state error. Overall, the PID controller had a fast rise time with little overshoot and appeared to be the most optimal for electricity generation, but the PI controller provided the best life span for the wind turbine by having zero overshoot with a slightly slower rise time.

Tuning PID Controller for Inverted Pendulum Using Whale Optimization Algorithm

Manual tuning of Proportional-Integral-Derivative (PID) controller is time consuming, tedious and generally lead to poor performance. PID controller is a simple and intuitive feedback-based control mechanism being useful to track set points and to reject disturbances. This paper presents a computational Intelligence (CI) technique of Whale Optimization Algorithm (WOA) for tuning the PID controller parameters for inverted pendulum. The inverted pendulum is a benchmark problem in control system design because of its high level of instability and non-linearity. It can mimic the behaviour of open-loop unstable systems such as robot manipulator and missile launcher. The metaheuristic algorithm achieved rise time (0.0913), settling time (1.57), maximum overshot (7.9%) and steady-state error (0.0294). Simulation results demonstrated that the WOA-optimized PID controller can provide an improved closed-loop performance over the Ziegler- Nichols tuned PID controller Parameters. The computational intelligence approach also has superior features, such as easy implementation, stable convergence characteristic and good computational efficiency over the conventional methods of Ziegler- Nichols.

Enhancing ride comfort of semi-active suspension through collaboration control using dung beetle optimizer optimized Fuzzy PID controller

The enhancement of automobile quality is a significant area of modern research and development, with a focus on improving ride comfort and driving experience. This is achieved not only through structural improvements but also through the optimization of suspension control strategies. To enhance the ability of online real-time adjustment and overcome the limitations of fuzzy control, this study combines dung beetle optimizer (DBO), Fuzzy control, and Proportional-Integral-Derivative (PID) control to propose a reduced optimization complexity control method to improve MR damper control. The control parameters generated by fuzzy control are utilized as the initial values for DBO iteration to obtain the optimal solution, which is subsequently fed into the PID controller to regulate changes in the actuator’s magnetic field. Use MATLAB/Simulink to build a quarter semi-active suspension model with magnetorheological (MR) dampers for simulation analysis. Under sinusoidal and random disturbances, compared with the passive suspension, the vehicle acceleration of the Fuzzy-DBO-PID controller is reduced by 51%, 50.82%, 47.56% and 11.42%. Compared with Fuzzy-PID, the vehicle acceleration of Fuzzy-DBO-PID is reduced by 25.98%, 32.86%, 29.41%, and 7.19% on sinusoidal and random disturbances, which improves the ride comfort and verifies the effectiveness of the proposed control strategy.