Proportional Integral Derivative Algorithm Research Articles

Temperature control algorithm for polymerase chain reaction (PCR) instrumentation based upon improved hybrid fuzzy proportional integral derivative (PID) control

Here is reported an adaptive polymerase chain reaction (PCR) temperature control algorithm based on improved hybrid fuzzy proportional integral derivative (PID) control. The algorithm adopts fuzzy control in the rapid temperature changing stage for monitoring and reduces the overshoot. In the constant temperature stage, the PID controller's initial parameters are automatically calculated online through the relay self-tuning algorithm. The output of the system is pre-compensated by feedforward compensation algorithm, and adjusted by the variable universe fuzzy PID algorithm, which avoids the explosion of fuzzy rules to a certain extent. The experimental results show that the average heating rate of the improved hybrid fuzzy PID control algorithm is 4.2 °C/s, with an average cooling rate is 3.2 °C/s. The system stabilizes within 5 s with a maximum overshoot of less than 1.2 °C and a static error of ± 0.1 °C at various ambient temperatures.

Performance Comparison of PID and NARX Neural Network for Attitude Control of a Quadcopter UAV

ABSTRACT: In this study, two different types of controllers have been designed and tested for altitude and motion control of an autonomous quadrotor to compare the control performance under the influence of parametric uncertainty and disturbances. The first controller is a proportional-integral-derivative (PID) controller which is a conventional linear controller. The closed-loop PID algorithms calculate the results of the system by using the error values that consist of the difference between the sensor values measured by the closed-loop feedback method and the reference inputs. The second method that has been used is artificial neural network (ANN) algorithms, which provide both advantages and convenience in defining and controlling linear systems and non-linear systems with the closed-loop feedback method used in PID. The most important feature of the ANN algorithms is their high performance as a result of training with different input values. Therefore, the ANN control system has been trained with the input data used with Gaussian noise and the desired target data. A dynamic time series non-linear autoregressive with Exogenous input (NARX) neural network has been chosen as an ANN controller because of the time-delayed backpropagation learning performance. In this study, PID, and NARX NN control algorithms to control the maneuvers and altitude of the quadcopter and the mathematical model have been designed on Matlab Simulink. Motion control performances of the PID and NARX controllers are tested on the model. The design was tested on a real-time simulation environment with a one-millisecond fixed-step size. This paper proposes an alternative approach to control attitude and altitude on a quadcopter with the NARX NN algorithm.

A Summary of PID Control Algorithms Based on AI-Enabled Embedded Systems

Proportional-integral-derivative (PID) controllers are extensively used in engineering practices for their simple structures, robustness to model errors, and easy operations. At present, there is a great variety of PID controllers. Companies have developed intelligent regulators with functions for automatically tuning PID parameters. For present PID controllers, strategies such as intelligence, self-adaptation, and self-correction are extended to transmission PID. PID controllers and corresponding improved ones are utilized in 90% of industrial control processes. In this paper, PID control algorithms are summarized. This paper focuses on advanced control strategies such as PID control, predictive PID control, adaptive PID control, fuzzy PID control, neural network PID control, expert intelligent PID control, PID control based on genetic algorithms, and PID control based on ant colony algorithms. Besides, these kinds of algorithms are compared, and prospects of PID algorithms are forecast at the end of this paper.

Predictive functional control for challenging dynamic processes using a simple prestabilization strategy

AbstractPredictive functional control (PFC) is a straightforward and cheap model‐based technique for systematic control of well‐damped open‐loop processes. Nevertheless, its oversimplified design characteristics are often the cause of diminished efficacy in more challenging applications; processes involving lightly damped and/or unstable dynamics have been particularly difficult to control with PFC. This paper presents a more sustainable solution for such applications by integrating the concept of prestabilization within the predictive functional control formulation. This is essentially a two‐stage synthesis wherein the undesirable open‐loop dynamics are first compensated, using a well‐understood classical approach such as proportional integral derivative (PID), before implementing predictive control in a cascade structure. The proposal, although comes with significant implications for tuning and constraint handling, is, nonetheless, straightforward and provides improved closed‐loop control in the presence of external perturbations compared to the standard PFC and the PID algorithms, as demonstrated with two industrial case studies.

Competent and uncomplicated PID control algorithm design expressions for controlling second order systems

Proportional-integral-derivative (PID) control algorithm with its various forms, namely P (proportional), PI (proportional-integral), PD (proportional-derivative), PID, and compensators, is considered the most applied and widely used control algorithms in industry; this is because of its simple construction, robustness and capabilities to achieve desired control over plant performance. Designing PID algorithm is accomplished with a compromise to result in an overall system responds with acceptable levels of stability, response fastness, smoothness and costs. Various PID design methodologies and expressions have been introduced in text and literature,each has its advantages, disadvantages and limitations. In the present work, a new, efficient, simple, easy to apply and linear expressions for PID algorithmP-. PI, PD, and PID modes design are derived and presented. Expressions are derived based on relating parameters of both controller and plant. The expressions are intended to control the behavior of second order systems and approximated as such systems, such that it responds with acceptable stability level, minimum possible overshoot, oscillations and steady state error. To further improve the resulted response, only one tuning parameter α, is introduced To test, analyze, and evaluate the design expressions, MATLAB/Simulink software was used. A simulation model was built by integrating the next sub-models; PID control algorithm modes, drive with limitation and saturation blocks, sensor, desired output signal generator and finally various forms of second order systems. The simulation model was developed and refined to be as close as possible to real life conditions and processing. Studying the recorded testing, graphical and numerical results show that the suggested expressions are being simple and easy to apply, and also efficient in providing better control over controlled system’s behavior in terms of response measures and performance indices.Moreover, expressions are efficient to speed up response and eliminate or reduce overshoot, rise time and settling time. Studying results show that, the overall system responds with acceptable fast response, in most cases without overshoot, oscillation and with minimum steady state error and better ISE and IAE indices values.

Simple and efficient PID algorithm design method for controlling first order systems with a time delay

Many processes in industry are characterized by delay time or by slow aperiodic dynamics called lag behavior. In addition, many plants in the industry are described mathematically by higher order systems that are approximated with the lower order systems, most frequently such processes and systems are described mathematically as first-order-systems-with time-delay (FOSTD), also called first-order-plus-dead-time (FOPDT). The presence of time delays causes degradation and limitation of achieving desired performance, moreover, it can induce instability. In such cases, design of feedback control algorithm becomes difficult and tedious task. The present work suggests an efficient, simple, linear, and easy to apply design expressions for designing continuous PID (proportional-integral-derivative) control algorithm modes to control the behavior of FOPDT systems. The design expressions are intended to overcome negative effects of time delay presence, as well as, to simplify the control algorithm design process and help designer, in easy and simple way, to get system under control with acceptable system stability, medium fastness of response and without or with minimum possible overshoot, oscillation and error. For testing and evaluating the correctness, applicability and efficiency of the derived expressions, MATLAB/Simulink software was applied to develop refined software simulation model that simulates real life values and returns maximum needed numerical and graphical data for assessment process. In addition, various FOSTD systems’ types and forms were used in the simulation model, in particular, systems with small, medium and large time constants, DC gains, and time delay, unstable systems, systems with variable delay. Furthermore, to assess the efficiency of suggested design expressions, the resulted overall system response were compared with resulted responses when two design methods were applied; worldwide known Ziegler Nichols method and MATLAB/Simulink auto-tuned PID block. Analysis of numerical and graphical testing results, show that, The designed control algorithm applying the suggested expressions can, not only simplify the design process, but also, efficient for successful in getting system under control and improving controlling system performance, speeding up response, reduce overshoot, and minimize error, but also stabilize an unstable plants.

Adaptive Fuzzy Neural Network PID Algorithm for BLDCM Speed Control System

Because of its simple structure, high efficiency, low noise, and high reliability, the brushless direct current motor (BLDCM) has an irreplaceable role compared with other types of motors in many aspects. The traditional proportional integral derivative (PID) control algorithm has been widely used in practical engineering because of its simple structure and convenient adjustment, but it has many shortcomings in control accuracy and other aspects. Therefore, in this paper, a fuzzy single neuron neural network (FSNNN) PID algorithm based on an automatic speed regulator (ASR) is designed and applied to a BLDCM control system. This paper introduces a BLDCM mathematical model and its control system and designs an FSNNN PID algorithm that takes speed deviation e at different sampling times as inputs of a neural network to adjust the PID parameters, and then it uses a fuzzy system to adjust gain K of the neural network. In addition, the frequency domain stability of a double closed loop PID control system is analyzed, and the control effect of traditional PID, fuzzy PID, and FSNNN PID algorithms are compared by setting different reference speeds, as well as the change rules of three-phase current, back electromotive force (EMF), electromagnetic torque, and rotor angle position. Finally, results show that a motor controlled by the FSNNN PID algorithm has certain superiority compared with traditional PID and fuzzy PID algorithms and also has better control effects.

Dynamic Model and Numerical Simulation of Maximum Turbidity Zone Formation in River Inlet

The estuary of a river can be seen as a relatively free and partially closed coastal body. It is connected to the ocean and is a transitional zone of rivers, which contains processes from land to sea and from fresh water to salt water. The estuary is one of the most productive natural habitats in the world and carries a large number of sediments due to natural factors such as changes in runoff and tides. Therefore, many coastal areas with river estuaries have become the most densely populated areas in the human population. In this paper, the RSM (Reynolds stress model) turbulence model and the PID (proportional integral derivative) algorithm are successfully used to simulate the dynamic model and for the numerical simulation of the formation of turbidity maximum zone in the estuary, which provides a theoretical basis for the follow-up of the similar research studies.

Stirring System Design for Automatic Coffee Maker Using OMRON PLC and PID Control

The implementation of the use of PLC in this study was designed for a small scale in the process of stirring coffee drinks at a speed of 600 RPM. To get a stable speed so that the water does not overflow, a control system is needed. To get optimal results, a system design that can control the stirring speed is arranged automatically using a Programmable Logic Controller (PLC). This system is designed using a rotary encoder sensor C38S6G5-600B-G24N as a speed reader obtained from the movement of the motor, DC Motor JGA25-370 12V as an actuator or stirrer. PLC OMRON CP1E-NA20DR-A is used as a motor speed control device using the Proportional Integral Derivative (PID) algorithm to control the system according to the setpoint entered. The motor speed control system with the PID algorithm shows a system response that works well according to the researchers' expectations. The response of the system obtained is fast enough to achieve a stable speed with a small overshoot value. Thus this system was successfully designed to control the stirring process of coffee drinks automatically and produce stable stirring by giving a set point of 600 RPM at the parameter constant Proportional band is 720%; Integral time is 1.6s; and Derivative time is 0.2s with a rise time value is 1.3s; settling time is 11s; overshoot is 1.1%; and steady-state error is 0.5%.

Dynamic Vehicle and Rigid Road Interaction Analysis and Vibration Control of the Quarter Car Model Using Adaptive Neuro Fuzzy Algorithm

In this study 3-DOF quarter car model with the three bumps on the rigid road, the assumption has been modeled with the non-random irregularity. To reduce the excessive vibrations occurred on the vehicle body, an active suspension system with the linear actuator has been considered. Moreover, to control this actuator, an adaptive neuro-fuzzy algorithm is designed. The training and testing data of the ANFIS has been obtained from Proportional Integral Derivative (PID) control algorithm. After that the successful training process, a testing procedure has been applied to ANFIS for the measure of the adaptive neuro-fuzzy system with data that are not considered in the training process. Then, the performance of the ANFIS is compared by the PID algorithm and passive suspension system in terms of vehicle body vertical acceleration, vehicle body vertical displacement, and control force. The road model used in the study has been modeled according to non-random road profile mathematical formulation considering periodical and discrete road profile cases. In this formulation, one can easily determine the height, width, and number of the road defect with the series mathematical formulation. Consequently, with the results obtained from the presented study, it is proven that ANFIS is a very effective controlling algorithm to suppress vibration occurred on the vehicle body due to vehicle road interaction. Furthermore, the performance of the ANFIS has been tested with different parameters, for example, different number membership functions (MF), which used the fuzzification of the input parameters.

Hexarotor Longitudinal Flight Control with Deep Neural Network, PID Algorithm and Morphing

Unmanned Aerial Vehicles (UAV) have become an integral part of life, from military operations to entertainment. With this popularity, the interest of researchers on these UAVs has gradually increased. The use of UAVs in many areas and the researches carried out by researchers have revealed the limitations of these devices. At the beginning of these restrictions is the passage through the narrow space. In this study, longitudinal flight control of a hexarotor UAV is discussed with morphing. The limitation of this study is that it is difficult to estimate the moment of inertia and proportional integral derivative (PID) coefficient values according to the arm length, since there is a change in the hexarotor arm lengths with the morphing and the rigid body model changes accordingly. In this study, it is aimed to obtain these parameters with the Deep Neural Network(Artificial Neural Network(ANN) with two or more hidden layers) to overcome this problem. 15 drawings of hexarotor morphing states were drawn in Solidworks program. A training set was created by obtaining the PID coefficients for the longitudinal flight of these drawings from the Matlab/Simulink program. The training set was taught to the Deep Neural Network and moments of inertia and PID coefficients were obtained according to the arbitrarily estimated arm extension or shortening rates. In addition, the hexarotor dynamic model was derived according to the Newton-Euler approach and modeled using the state space model. The longitudinal flight of the hexarotor is simulated with the state space model. The moment of inertia and PID coefficients were estimated by Deep Neural Network according to the values determined by the program randomly together with the initial state. Simulations were made with these parameters and the results were given in graphics.

Isothermal extrusion speed curve design for porthole die of hollow aluminium profile based on PID algorithm and finite element simulations

The isothermal extrusion process of hollow aluminium profile was investigated using incremental proportional–integral–derivative (PID) control algorithm and finite element simulations. The range of extrusion speed was determined by considering the maximum extrusion load and production efficiency. By taking the optimal solution temperature of the secondary phase as the target temperature, the extrusion speed–stroke curve for realizing the isothermal extrusion of the aluminium profile was obtained. Results show that in the traditional constant extrusion speed process, the average temperature of the cross-section of the aluminium profile at the die exit rapidly increases and then slowly rises with the increase in ram displacement. As the extrusion speed increases, the temperature difference at the die exit of the profile along the extrusion direction increases. The exit temperature difference between the front and back ends of the extrudate along the extrusion direction obtained by adopting isothermal extrusion is about 6.9 °C. Furthermore, the heat generated by plastic deformation and friction during extrusion is balanced with the heat transfer from the workpiece to the container, porthole die and external environment.

Design and Experiment of Row-Controlled Fertilizing–Weeding Machine for Rice Cultivation

Current approaches to topdressing and weeding operations for rice cultivation present several disadvantages, such as poor precision, low efficiency, serious environmental pollution, and so on. This paper presents a row-controlled fertilizing–weeding machine to improve the precision of fertilizing and weeding operations and to reduce the heavy pollution associated with rice cultivation. A proportional–integral–derivative algorithm was adopted to realize accurate fertilization control, and an automatic driving system for agricultural machinery based on BeiDou navigation was used for accurate row-controlled operation. Accuracy testing and field experiments were carried out. The results show that the fertilization control system can stabilize the speed to within 0.55 s of the desired speed with a standard deviation of around 0.32 r·min−1. The row-controlled operation ensures the lateral deviation is within ± 5 cm at operating speeds below 5 km·h−1. The high uniformity and accuracy of fertilization meet agronomic requirements and rice cultivation standards, and the weeding performance is acceptable at working speeds below 5 km·h−1.

Speed regulation strategy and algorithm for the variable-belt-speed energy-saving control of a belt conveyor based on the material flow rate.

As an important transportation, the belt conveyor has been widely used and researched. It is urgent to solve the problem of energy saving and consumption reduction of belt conveyor. Aiming at reducing high energy consumption in the rated-speed operation of a belt conveyor, the present paper establishes an energy-saving belt-speed model of a belt conveyor using a polynomial regression-fitting algorithm and a small number of sample observations, and proposes a speed regulation strategy and particle swarm optimization–proportional–integral–derivative algorithm for the variable-belt-speed energy-saving control of a belt conveyor based on the material flow rate. The control strategy and algorithm adjust the running speed of the belt conveyor accurately according to changes in the material flow rate, thus reducing damage of frequent speed regulation to the belt conveyor and saving energy. Simulation analysis of a practical case shows that energy-saving belt-speed model, speed regulation strategy, and algorithm effectively reduce the energy consumption of a belt conveyor, and they thus have high application value in coal, ports, power, mine, metallurgy, chemical, and other industries. Further work in this field can be focused on the prediction of material flow rate of belt conveyor, the controllable adjustment duration of algorithm and the reduction of overshoot.

Composite control of the SiC arc welding power source based on the expert system and neuron PID

A third generation wide-band-gap SiC semiconductor device is used in the SiC arc welding power source, which has a higher inverter frequency and greatly improves the dynamic characteristics of the arc welding power source, providing opportunities for control algorithm optimization. A composite control method of the arc welding power source combining the expert system and single neuron Proportional-Integral-Derivative (PID) is proposed in this paper, aimed at the fact that the proportional cofficient of neuron PID can hardly be adapted to rapid welding current changes. The SiC arc welding power source is taken as the plant of study in this paper. A mathematical model of the arc welding power source-arc system is established, and the controller of the arc welding power source based on the neuron PID and corresponding expert rules are defined to adjust the proportional coefficient of neuron PID Finally, the neuron PID controller (SNC) and the composite controller based on the expert system and neuron PID (ESNC) are simulated and verified. The results show that compared with the neuron PID algorithm, this method can adjust the proportional neuron PID coefficient in real time according to the welding current and has a better adaptive ability and superior tracking performance for arc welding power source control.

How to Apply Fuzzy MISO PID in the Industry? An Empirical Study Case on Simulation of Crane Relocating Containers

The proportional-integral-derivative (PID) algorithm automatically adjusts the control output based on the difference between a set point and a measured process variable. The classical approach is broadly used in the majority of control systems. However, in complex problems, this approach is not efficient, especially when the exact mathematical formula is difficult to specify. Besides, it was already proven that highly nonlinear situations are also significantly limiting the usage of the PID algorithm, in contrast to the fuzzy algorithms, which often work correctly under such conditions. In the case of multidimensional objects, where many independently operating PID algorithms are currently used, it is worth considering the use of one fuzzy algorithm with many-input single-output (MISO) or many-input many-output (MIMO) structure. In this work, a MISO type chip is investigated in the study case on simulation of crane relocating container with the external distribution. It is an example of control objects that due to badly conditioned dynamic features (strong non-linearities) require the operator’s intervention in manual or semi-automatic mode. The possibility of fuzzy algorithm synthesis is analyzed with two linguistic variable inputs (distance from −100 to 500 mm and angle from −45° to 45°). The output signal is the speed which is modelled as a linguistic power variable (in the domain from −100% to 100%). Based on 36 fuzzy rules, we present the main contribution, the control system with external disturbance, to show the effectiveness of the identified fuzzy PID approach with different gain values. The fuzzy control system and PID control are implemented and compared concerning the time taken for the container to reach the set point. The results show that fuzzy MISO PID is more effective than the classical one because fuzzy set theory helps to deal with the environmental uncertainty. The container’s angle deviations are taken into consideration, as mitigating them and simultaneously maintaining the fastest speed possible is an essential factor of this challenge.

Speed Profile Tracking by an Adaptive Controller for Subway Train Based on Neural Network and PID Algorithm

Train running performance largely depends on the controller. In order to improve the controller performance of speed profile tracking, an adaptive control method for subway trains is addressed in this paper. Considered time-varying parameters of train motion, the train model with dynamic parameters is constructed. The model free adaptive controller combined with neural network and proportional-integral-derivative (PID) algorithm is proposed to realize adaptive control. The control laws and parameter tuning laws of the proposed controller are both illustrated, and PID gain range and actuator saturation are taken into consideration. Compared with other controllers, numerical tests are provided to verify the effectiveness and stability of the proposed controller. The controller is also applied on a real line, and the results show that the proposed controller outperforms the currently used controller. More specifically, the proposed controller reduces average absolute running time error by 0.67 s, average absolute stopping position error by 0.09 m, average maximum absolute speed tracking error by 1.22 m/s, and total energy consumption by 2.73 kWh.

Fast Detection Using PID Pre-Interpolation Algorithm for Magnetic Particle Testing

The current tracing scheme is based on a silicon-controlled rectifier (SCR) with phase shift triggering, which is utilized in traditional magnetic particle testing. In industrial applications, the popularization and implementation of magnetic particle flaw detection technology could be degraded by various problems such as poor real-time performance of current tracing, the significant error of current tracing, and low precision of flaw detection. In this work, the magnetization current waveforms under different control angles of the SCR are studied to obtain a real-time magnetization current tracking in less than 0.5 s and a current tracking error smaller than 5%. A fast three-phase electric zero detection circuit is designed in which the current tracking method is optimized by combining a high-speed analog to digital (AD) converter with a true root-mean-square (true-rms) device. Moreover, a Newton interpolation-based fast proportional integral derivative (PID) algorithm is proposed to achieve a precise real-time current tracking. The experimental results show that the real-time magnetic particle flaw detection for current tracking is performed in less than 0.2 s with a current tracking error below 2%, which meets the technical requirements of magnetic particle flaw detection. The fast three-phase electric zero detection method using the PID algorithm can improve the real-time performance and accuracy of current tracking in magnetic particle flaw detection.

Integrated control strategy of tractor hydromechanical continuously variable transmission

Given the transmission efficiency fluctuation and response lag problem of hydromechanical continuous variable transmission combined with the complex and variable working environment of a tractor, an integrated control strategy of engine throttle compensation–hydromechanical continuous variable transmission speed regulation is adopted for dual-flow transmission control. On the basis of the estimation of working resistance, a fuzzy algorithm is used to design the throttle compensation law. Considering the maximum driving power of a tractor as the target of variable speed control, an hydromechanical continuous variable transmission efficiency model is established, and the control law of an hydromechanical continuous variable transmission displacement ratio with the maximum driving power of the tractor under any working condition is determined. On the basis of the wavelet neural network proportional–integral–derivative algorithm, the control law of the hydromechanical continuous variable transmission speed regulation is designed, and the parameters of proportional–integral–derivative control are corrected in real time during the control process. Based on MATLAB/Simulink modelling and simulation and the real vehicle verification test, results showed that the influence of hydromechanical continuous variable transmission efficiency fluctuation on the driving power of the entire vehicle, the response lag of the pump-controlled motor system, and the effect of the leakage on the variable speed control and the fluctuation of the working resistance are solved by studying the hydromechanical continuous variable transmission variable speed transmission control strategy. This strategy improves the stability of the tractor speed and ensured the quality of the work, thereby improving the ability of the tractor to adapt to complex working environments.

A Fuzzy PID Algorithm for a Novel Miniature Spherical Robots with Three-dimensional Underwater Motion Control

We proposed and developed a small bionic amphibious spherical robot system for tasks such as coastal environment monitoring and offshore autonomous search and rescue. Our third-generation bionic small amphibious spherical robots have many disadvantages, such as the lack of maneuverability and a small operating range. It is difficult to accomplish underwater autonomous motion control with these robots. Therefore, we proposed a fourth-generation amphibious spherical robot. However, the amphibious spherical robot developed in this project has a small and compact design, with limited sensors and external sensing options. This means that the robot has weak external information collection capabilities. We need to make the real time operation of the robot’s underwater motion control system more reliable. In this paper, we mainly used a fuzzy Proportional-Integral-Derivative (PID) control algorithm to design an underwater motion control system for a novel robot. Moreover, we compared PID with fuzzy PID control methods by carrying out experiments on heading and turning bow motions to verify that the fuzzy PID is more robust and exhibits good dynamic performance. We also carried out experiments on the three-dimensional (3D) motion control to validate the design of the underwater motion control system.