Proportional Integral Differential Controller Research Articles

Backstepping control of three‐degree‐of‐freedom hybrid magnetic bearing based on non‐linear disturbance observer

AbstractA backstepping controller based on a non‐linear disturbance observer (NDOB) was created to enhance the dynamic performance and reliability of three‐degree‐of‐freedom hybrid magnetic bearings. After the structure of three‐degree‐of‐freedom hybrid magnetic bearings is introduced, the mathematical model is established, and the equation of the state is derived by the equivalent magnetic circuit technique. Based on the mathematical model, non‐linear disturbance observer (NDOB) is designed and is used to predict the system disturbance, and the backstepping control algorithm is compensated. To verify the effectiveness of the proposed controller, the backstepping controller, proportion integration differentiation controller, and backstepping controller based on a NDOB were compared by simulation and experiment. Results show that the backstepping controller based on a NDOB has better dynamic performance and robustness.

Human–Machine Redundant Braking System for Aftermarket Low-Speed Electric Vehicle: Design and Validation

This paper presents the design and experimental validation of a novel human–machine redundant braking system (HMRBS) for aftermarket low-speed electric vehicles (LSEVs) to realise the backup redundancy ability and improve active safety. First, the HMRBS is designed by connecting the electro-hydraulic braking (EHB) unit oil pipelines in parallel with the manual braking (MB) unit through two three-way shuttle valves. Then, the mathematical model of the EHB subsystem is built, and a master cylinder pressure controller with adaptive fuzzy proportion integration differentiation (PID) and a servo motor speed controller with double-closed-loop proportion integration (PI) are proposed to improve the system response performance. Following this, the co-simulation model of the proposed closed-loop system is established based on AMESim and MATLAB/Simulink to validate the feasibility of the proposed control strategy. Finally, the effectiveness of the HMRBS is also validated by test rig and vehicle experiments. The results imply that the modified LSEV with the HMRBS meets the requirements of vehicle active braking ability and manual braking redundancy. Furthermore, the proposed controller can significantly enhance pressure control accuracy compared to the classical PID controller. The deceleration fluctuation and braking distance in the active braking mode are smaller than those in the manual braking mode, indicating that the proposed system makes the braking effect more stable and safer.

Velocity Control of a Multi-Motion Mode Spherical Probe Robot Based on Reinforcement Learning

As deep space exploration tasks become increasingly complex, the mobility and adaptability of traditional wheeled or tracked probe robots with high functional density are constrained in harsh, dangerous, or unknown environments. A practical solution to these challenges is designing a probe robot for preliminary exploration in unknown areas, which is characterized by robust adaptability, simple structure, light weight, and minimal volume. Compared to the traditional deep space probe robot, the spherical robot with a geometric, symmetrical structure shows better adaptability to the complex ground environment. Considering the uncertain detection environment, the spherical robot should brake rapidly after jumping to avoid reentering obstacles. Moreover, since it is equipped with optical modules for deep space exploration missions, the spherical robot must maintain motion stability during the rolling process to ensure the quality of photos and videos captured. However, due to the nonlinear coupling and parameter uncertainty of the spherical robot, it is tedious to adjust controller parameters. Moreover, the adaptability of controllers with fixed parameters is limited. This paper proposes an adaptive proportion–integration–differentiation (PID) control method based on reinforcement learning for the multi-motion mode spherical probe robot (MMSPR) with rolling and jumping. This method uses the soft actor–critic (SAC) algorithm to adjust the parameters of the PID controller and introduces a switching control strategy to reduce static error. As the simulation results show, this method can facilitate the MMSPR’s convergence within 0.02 s regarding motion stability. In addition, in terms of braking, it enables an MMSPR with random initial speed brake within a convergence time of 0.045 s and a displacement of 0.0013 m. Compared with the PID method with fixed parameters, the braking displacement of the MMSPR is reduced by about 38%, and the convergence time is reduced by about 20%, showing better universality and adaptability.

Research and Implementation of Intelligent Control System for Grassland Grazing Robotic Vehicle

In response to the complex animal husbandry environment, wide livestock range, and labor shortage in Inner Mongolia grasslands, this study designed an intelligent control system for robotic vehicles used in natural grazing grassland environments. The control system consists of software and hardware components and motion control algorithms. Based on the application characteristics of different mechanisms of the robotic vehicle, the motion control of the robotic vehicle is decomposed into longitudinal speed control and lateral steering control. The longitudinal speed control adopts the traditional Proportional-Integral-Differential (PID) control method. Since the hardware composition and internal angle calculation method of the steering system are complex and prone to deviations caused by external terrain, a lateral adaptive fuzzy PID controller was constructed with lateral deviation and deviation change rate as input variables and parameters Kp, Ki, and Kd as outputs. The field test results show that when the longitudinal speed was set to 0.5 m/s, the adjustment time was 1.95 s, and the steady-state error was about 0. When the longitudinal speed was the same, the lateral adaptive fuzzy PID controller reduced the rise time by 0.77 s compared to traditional control methods, reduced overshoot and steady-state error by 2%, and quickly recovered to a steady state after being disturbed. The following test results show that the designed intelligent control system can achieve real-time tracking of targets and that the motion controllers can effectively control speed and steering angle. Therefore, the intelligent control system designed in this paper can effectively achieve stable and real-time control of the robotic vehicle.

Frequency Domain Analysis of Load Frequency Control Using PIDTune Model Standard

The load frequency control system aims to regulate the frequency in the electric power system at a normal value with a predetermined tolerance limit. In practice, the load frequency control system does not always operate optimally, therefore a controller is needed to be added to the load frequency control system. The controller designed is a variation of the combination of Proportional-Integral-Differential (PID) controllers with the standard model PIDTune method consisting of proportional (P) controller, proportional integral (PI) controller, proportional differential (PD) controller, Proportional Integral Differential (PID) controller, Proportional Differential controller with first-order filter on differential section (PDF), and Proportional Integral Differential controller with first-order filter on differential section (PIDF). This study is aiming to carry out simulation and analysis in the frequency domain and then analyze the robustness of the reheat type power frequency control system and then design a PID controller for the reheat type power frequency control system in basic configuration, filter configuration, feedback configuration, feedforward configuration, and cascade configuration using PIDtune Model Standard on Matlab software. From the results of simulation and analysis, the controller that complies the design criteria and can make the reheat type of load frequency control system work optimally based on frequency domain analysis and robustness analysis is a proportional-integral (PI) controller in a feedback configuration with gain margin (Kg) equals to 38.11 dB, phase margin equals to 59.6°, infinity bandwidth, peak resonance value (Mr) equals to 1.19, maximum sensitivity peak value (MS) equals to 1.24, and complementary maximum sensitivity peak value (MT) equals to 1,17.

Numerical study on the interfacial heat and mass transfer characteristics of bubble direct contact condensation with the effect of non-condensable gas

Bubble condensation is one of the fundamental issues in the direct contact condensation, which is also affected significantly by the existence of non-condensable gas. In this study, a further investigation is carried out on air-steam bubble condensation with the Proportion Integration Differentiation (PID) control model which adjusts the mass transfer coefficient of Lee model in each time step by comparing the parameters obtained in the simulation with the ones calculated based on the empirical correlations originated from the experiments. Furthermore, species transport equations are employed to obtain the local mass fractions of steam and air. The proposed simulation schema is verified by the existing experimental data.Results show that the air-steam bubble condensation can be divided into initial and stable stages. The mass transfer coefficient used in Lee model can be regarded as linear growth over time at each stage, but with different slopes. The non-condensable gas can weaken the heat and mass transfer of condensation, but stabilize the bubble deformation. The present study also reveals the influences of subcooling and initial bubble diameter on the air-steam bubble condensation, which is expected to be instructive for better understanding the effect of non-condensable gas on the interfacial characteristics of bubble condensation in subcooled water.

Degradation index construction and learning-based prognostics for stochastically deteriorating feedback control systems

Degradation-based prognostics is crucial for the health management of technological systems. In this work, we are interested in the degradation index construction and remaining useful life prognostics for stochastically deteriorating feedback control systems. The main challenges reside in the lack of knowledge about the system structure and the latent internal damage, as well as in the fault tolerance nature of feedback control systems. Our solution is to consider the whole system as a black-box, and use its easy-to-observe reference input/time response output to estimate the system transfer function. The associated H∞ norm, also called maximum energy gain, is defined as a system degradation index. Since the system fault tolerance does not allow to efficiently model the index evolution by common stochastic processes, traditional prognostics based on degradation processes are no longer applicable. To remedy, we propose to fit the system remaining useful life population to the versatile Birnbaum–Saunders distribution, and adopt a segmenting piecewise polynomials algorithm to learn the mapping between the distribution parameters and degradation index from degradation and failure data of similar systems. By this way, the remaining useful life distribution of deteriorating feedback control systems can be predicted in real-time given the system input/output at an inspection time. We numerically experiment our method on a stabilization loop control device driven by proportional–integral–differential controller in an inertial platform. Numerous sensitivity results under various configurations of system characteristics and training data corroborate the outperformance of proposed degradation index and the learning-based prognostics method.

Magnetic Levitation Belt Conveyor Control System Based on Multi-Sensor Fusion

Belt conveyors are critical in coal transportation systems; however, they are supported by rollers, which incur high energy costs. Magnetic levitation support is adopted. The measurement of a magnetic levitation air gap is important, and a displacement sensor is usually used in real-time. To address the problems of poor linearity and low measurement stability of single displacement sensors in magnetic levitation systems, a magnetic levitation support system based on multi-sensor data fusion is proposed. First, an industrial camera sensor is used to collect images, and the suspended air gap is obtained through image processing. Second, using an extended Kalman filter, the photoelectric position sensor and industrial camera sensor are fused to the suspension air gap value in the process of suspension. The electromagnet current is controlled by the PID (proportion integration differentiation) control algorithm, and experiments are carried out. Experimental results showed that, compared with an estimation of the suspension state of two sensors before and after EKF fusion, the root mean square error is reduced by 0.0597 and 0.0081, respectively, compared with the measurement value of a single sensor. Moreover, the fusion data were more robust, thereby meeting the requirements of magnetic levitation control.

Model Establishment of Chip Air Cooling Process and Its Proportional Integral Differential Tuning

Abstract Chip junction temperature is a key factor affecting the normal operation of the chip. The development of integrated circuit technology brings about high integration and low cost, but it also puts forward higher requirements for the cooling system. This paper focuses on the air cooling of the chip, builds a hardware test platform based on MCS-52, the general name of the intel series microcontroller unit, and sets up a mathematical model of the air cooling process of the chip on the matlab platform based on the principle of energy conservation, heat transfer theory and finite element method. By proposing the equivalent convective heat transfer coefficient, the thermal resistance of the system can be well estimated. This model can easily realize the joint simulation of chip, heat radiator, and control strategy, which overcomes the disadvantage that traditional finite element simulation software are difficult to combine with control strategy. In addition, based on the model, the proportional integral differential (PID) control parameters are automatically optimized, achieving excellent temperature control effect, and proving the feasibility of optimizing the control parameters through the model.

Incremental proportion integration differentiation control of all-terrain vehicle magnetorheological suspension system under low-frequency disturbances

In intelligent control systems of magnetorheological (MR) suspension of all-terrain vehicle (ATV), low-frequency disturbance (LFD) in the measured feedback signal (acceleration) makes the controller unable to calculate the theoretical control force accurately. In particular, when the frequency of the LFD signal is close to that of the actual acceleration signal, the LFD cannot be filtered by designing a traditional filter. Based on the above questions, this paper proposes an incremental proportion integration differentiation (IPID) strategy to address the issue of LFD in the measured feedback acceleration signal of the MR suspension system of ATV. First of all, the model of 1/4 vehicle suspension in consideration of LFD is established, the source of LFD is analyzed which is due to the transformation of Coriolis acceleration under the condition of vehicle body pitch and roll. Next, a semi-active IPID controller is designed by utilizing differential derivation of discrete PID and semi-active principle to eliminate the LFD component mixed in the acceleration signal by making a difference. The particle swarm optimization (PSO) algorithm is utilized to optimize the parameters of the controller, which is then verified through numerical simulation. Subsequently, a real vehicle control experiment is carried out based on a 4 × 4 ATV equipped with the MR suspension system and implemented by DSP controller with the designed IPID algorithm. The effectiveness of the proposed method is evaluated under the speed 10 km h−1 and E road, and the designed method is compared with the traditional proportion integration differentiation (PID) control algorithm through simulation and experimentation to demonstrate the superiority and rationality of ‘filtering out’ LFD signal and improving control effectiveness.

Tracking performance of the coaxial counter-paddle flight system using fractional active disturbance rejection controller

Stable aerial flight capability is crucial for amphibious vehicles to perform cross-domain motion, yet it is often influenced by unpredictable cross-domain environments and model uncertainties. A fractional-order active disturbance rejection controller based on finite-time convergent extended state observer is proposed for the anti-interference control problem in the attitude trajectory tracking of bullet-shaped trans-domain amphibious vehicle in complex environments. Firstly, a complete dynamic model of the airborne flight system of the bullet-shaped trans-domain amphibious vehicle is established. A hierarchical control scheme based on the proposed controller is designed assuming that all states of the system are available, in order to improve the control reliability and robustness of the flight system in multi-source interference environments. Then, based on a novel hybrid particle swarm search technique called the Particle Swarm Optimization with Lévy Flight and Wavelet Mutation algorithm, which combines Lévy flight and wavelet mutation, a new parameter identification and tuning algorithm is proposed for the proposed controller to obtain optimal control parameters for attitude and position. To provide a comprehensive comparison, the stability of the optimization algorithm and the robustness performance of the controller were evaluated. Finally, all controllers were tested under three different disturbance scenarios. The results show that the proposed controller can achieve better stability in flight attitude and trajectory tracking tasks compared to Proportion Integration Differentiation controller, Fractional-order Proportion Integration Differentiation controller, and Active Disturbance Rejection controller in all scenarios.

FusionPID: A PID control system for the fusion of infrared and visible light images

The purpose of infrared and visible image fusion is to compensate for the incomplete imaging of a single sensor. Although there are existing fusion algorithms, they tend to overlook the guidance that infrared and visible light images can provide in formulating fusion strategies. Consequently, the resulting fused image lacks a genuine reference, and the designed fusion strategy lacks adaptive ability. To overcome this challenge, this study proposes a novel fusion framework based on cybernetics, referred to as FusionPID, that utilizes a proportional integral differential (PID) control system to fuse infrared and visible images. The framework first extracts source map features through an improved Mean Shift feature clustering algorithm in the field of machine vision. This information is then used to construct the transfer function of the control system, enhancing the potential of the fused images for downstream target detection tasks. Secondly, a comprehensive measurement function is designed to judge the difference between the fused image and the source image. The target of the fused process is guided by the source image through the measurement value and the feedback function of the control system. Finally, a PID controller is designed, which can adjust the output adaptively according to the difference between the source image and the fusion result. FusionPID can rely on the feedback ability of the control system for different fusion tasks, so that the fusion image can maintain both the thermal radiation in the infrared image and the texture in the visible image. Experiments show that our FusionPID has advantages over the most advanced methods in maintaining significant contrast and rich texture. In addition, the fused image generated by this method can be applied to downstream target detection tasks to improve the detection performance.

Control strategy analysis of multistage speed compressor for vehicle air conditioning based on particle swarm optimization

For electric vehicles (EVs), there is an urgent need to reduce the energy consumption of the air conditioning (AC) system while ensuring the cabin's comfort. This paper proposes a particle swarm optimization-based multistage compressor speed (PSO-MCS) control strategy to reduce compressor energy consumption. The multistage compressor speed (MCS) allows the compressor speed to be as near to the high-efficiency cooling zone as possible, outputting different speeds in different temperature zones to achieve temperature control. The particle swarm optimization (PSO) algorithm is used to reduce the compressor energy consumption by searching for the optimal compressor speed. The AC system mathematical model based on PSO-MCS is built and compared with the conventional proportional-integral-differential (PID) control. The results show that PSO-MCS control can improve the coefficient of performance (COP) by 2.41% and 2.71%, respectively, compared to PID control at 35 °C and 40 °C. And PSO-MCS control can reduce 4.07% and 3.89% energy consumption, respectively.

Design of Observer-Based Discrete-Type PID Control for Reconstructed Jump Model of Interconnected Power System Under Hybrid Attacks

In this article, observed-based discrete proportion-integration-differentiation (PID) control for multi-area interconnected power systems is addressed under hybrid attacks. Firstly, a reconstructed jump model for interconnected power systems is proposed by taking the circumstance of data packet loss into consideration, which caused by the stochastic transmission delay of sampled data. Then, different from the traditional continuous-type PID control, an observer-based discrete-type PID control strategy is designed for discrete-time power system. Besides, due to the sampled data may be tampered or shield in open communication networks, the hybrid attacks, i.e., deception attacks and denial-of-service attacks, with random manners are considered. Furthermore, an input-to-state stable criterion is derived by constructing appropriate Lyapunov-Krasovskii functionals. Finally, the discrete-type PID controllers and observer are achieved, and the validity of proposed approach are also demonstrated in the illustrative examples section.

Vehicle-Mounted Solar Occultation Flux Fourier Transform Infrared Spectrometer and Its Remote Sensing Application.

For the demand of rapid monitoring of pollution gas disorganized emissions in industrial parks, this paper studies the solar fast tracker system of vehicle-mounted SOF-FTIR (Solar Occultation Flux Fourier Transform Infrared Spectroscopy) system, where the spectrometer directly measures the broadband absorption spectrum of solar radiation light. A fast portable solar tracking system based on PSD (position sensitive detector) is designed, the mathematical model of solar spot position on the PSD surface source is established, and the optimal optical design parameters are simulated using the model. The dead-zone integral separation PID (Proportion Integration Differentiation) control algorithm is used to track the trajectory of the solar, and the light spot position model is used to nonlinearly compensate the output of PID control so that the PID controller has the same control precision and response speed in different error areas. Experimental analysis of the solar tracking performance of the vehicle-mounted SOF-FTIR under static and dynamic conditions, as well as the spectral effects on the measurements under static vehicle, constant speed, and turning driving conditions. The remote sensing application experiment of vehicle-mounted SOF-FTIR pollution gas emission flux was carried out in a tire factory in Hefei City, Anhui Province. A vehicle-mounted SOF-FTIR system realized the qualitative and quantitative analysis of the pollution gas at the boundary of the tire plant and calculated the flux of each component pollution gas. The emission flux of pollution gas was highly consistent with the actual pollution distribution of the tire plant. The results show that the positioning accuracy of PSD in the vehicle tracking experiment can also meet SOF-FTIR requirements for solar tracking. The remote sensing system will be useful in the field of atmospheric environment monitoring, and the mobile monitoring of regional pollutant gases based on solar infrared spectroscopy has application value.

Nonlinear Tank-Level Control Using Dahlin Algorithm Design and PID Control

Liquid-level control in tanks is widely used in various industrial sectors. Due to problems arising from the case that the liquid level is above or below the recommended, the process of its control is of great significance. The proportional integral differential (PID) controller is one of the most widely used controllers in applications that require accuracy and optimal automatic control. In this paper, single and coupled ship fuel tank systems are discussed. In addition, mathematical models and their linearization using two different approaches are presented. The two control approaches are used to maintain the specified liquid level in tanks. The first is based on the design of standard PID controllers, with the application of the Ziegler–Nichols, Takahashi tuning, and Auto-tuning methods. The second approach, proposed by the authors, is based on the application of the Dahlin algorithm. The simple modification of the Dahlin controller, which can avoid the “ringing” of the control signal, is suggested in the paper. Moreover, the lower limit of the decrease in the desired time constant, which ensures the desired behavior of the system, is determined. The comparisons provided for different performance indexes show the advantages of the modified Dahlin algorithm approach compared to the standard PID controllers. Furthermore, the comparison with the literature-known approaches is realized.

Investigation on Li-plating prevention optimal charging protocol of nickel-rich/graphite-SiOx lithium ion battery

Improving the fast-charging capability of power batteries is crucial to increase the widespread adoption of electric vehicles. Nevertheless, lithium metal will plate on the surface of the anode electrode when the batteries are charged at a heavy current or worked at a low temperature, thus resulting in the deterioration of battery performance, and even thermal runaway. Therefore, preventing Li plating in electrical batteries has become an urgent problem to be solved. In addition to the development of novel materials with improved dynamics, electrochemical simulation also provides a tool that can elucidate the internal processes of the battery in real time, which can be used to explore the optimization of battery usage policies, such as Li plating prevention. In this research, an electrochemical model of NCM811/SiOx-Graphite battery is built for optimizing fast charge protocol. The model takes into account Li plating/stripping and solid electrolyte interphase (SEI) formation to better quantify the effect of charging protocol changes on battery performance. The optimal charging protocol at varying temperatures (−5 °C–25 °C) is obtained from the proportion integral differential (PID) controller. In addition, the multistage optimal charging protocol is discussed for conventional charging piles, and the effectiveness is verified through experiments.

Predictive Control of a Heaving Compensation System Based on Machine Learning Prediction Algorithm

Floating structures have become a major part of offshore structure communities as offshore engineering moves from shallow waters to deeper ones. Floating installation ships or platforms are widely used in these engineering operations. Unexpected wave-induced motions affect floating structures, especially in harsh sea conditions. Horizontal motions on the sea surface can be offset by a dynamic positioning system, and heave motions can be controlled by a heave compensation system. Active heave compensation (AHC) systems are applied to control vertical heave motions and improve safety and efficiency. Predictive control based on machine learning prediction algorithms further improves the performance of active heave compensation control systems. This study proposes a predictive control strategy for an active heave compensation system with a machine learning prediction algorithm to minimise the heave motion of crane payload. A predictive active compensation model is presented to verify the proposed predictive control strategy, and proportion–integration–differentiation control with predictive control is adopted. The reliability of back propagation neural network (BPNN) and long short-term memory recurrent neural network (LSTM RNN) prediction algorithms is proven. The influence of the predictive error on compensation performance is analysed by comparing predictive feedforward cases with actual-data feedforward cases. Predictive feedforward control with regular and irregular wave conditions is discussed, and the possible strategies are examined. After implementing the proposed predictive control strategy based on a machine learning algorithm in an active heave compensation system, the heave motion of the payload is reduced considerably. This investigation is expected to contribute to the motion control strategy of floating structures.

PID Control Model Based on Back Propagation Neural Network Optimized by Adversarial Learning-Based Grey Wolf Optimization

In processes of industrial production, the online adaptive tuning method of proportional-integral-differential (PID) parameters using a neural network is found to be more appropriate than a conventional controller with PID for controlling different industrial processes with varying characteristics. However, real-time implementation and high reliability require the adjustment of specific model parameters. Therefore, this paper proposes a PID controller that combines a back-propagation neural network (BPNN) and adversarial learning-based grey wolf optimization (ALGWO). To enhance the unpredictable behavior and capacity for exploration of the grey wolf, this study develops a new parameter-learning technique. Alpha gray wolves use the random walk of levy flight as their hunting method. In beta and delta gray wolves, a search strategy centering on the top gray wolf is employed, and in omega gray wolves, the decision wolves handle the confrontation strategy. A fair balance between exploration and exploitation can be achieved, as evidenced by the success of the adversarial learning-based grey wolf optimization technique in ten widely used benchmark functions. The effectiveness of different activation functions in conjunction with ALGWO were evaluated in resolving the parameter adjustment issue of the BPNN model. The results demonstrate that no unique activation function outperforms others in different controlled systems, but their fitnesses are significantly inferior to those of the conventional PID controller.

FPGA based hardware platform for trapped-ion-based multi-level quantum systems

We report a design and implementation of a field-programmable-gate-arrays (FPGA) based hardware platform, which is used to realize control and signal readout of trapped-ion-based multi-level quantum systems. This platform integrates a four-channel 2.8 Gsps@14 bits arbitrary waveform generator, a 16-channel 1 Gsps@14 bits direct-digital-synthesis-based radio-frequency generator, a 16-channel 8 ns resolution pulse generator, a 10-channel 16 bits digital-to-analog-converter module, and a 2-channel proportion integration differentiation controller. The hardware platform can be applied in the trapped-ion-based multi-level quantum systems, enabling quantum control of multi-level quantum system and high-dimensional quantum simulation. The platform is scalable and more channels for control and signal readout can be implemented by utilizing more parallel duplications of the hardware. The hardware platform also has a bright future to be applied in scaled trapped-ion-based quantum systems.