PID Parameters Research Articles

Towards a theoretical foundation of PID control for uncertain nonlinear systems

As is well-known, the classical PID control plays a dominating role in various control loops of industrial processes. However, a theory that can explain the rationale why the linear PID can successfully deal with the ubiquitous uncertain nonlinear dynamical systems and a method that can provide explicit design formulae for the PID parameters are still lacking. This paper is a continuation of the authors recent endeavor towards establishing a theoretical foundation of PID for nonlinear uncertain systems. In contrary to most of the existing literature on linear or affine nonlinear systems, we will consider a class of non-affine nonlinear uncertain systems, and will show that a three dimensional parameter set can be constructed explicitly, such that whenever the PID parameters are chosen from this set, the closed-loop systems will be globally stable and the regulation error will converge to zero exponentially fast, under some suitable conditions on the system uncertainties. Moreover, we will also consider the simpler PI and PD control, and provide a necessary and sufficient condition for the choice of the PI parameters for a class of one dimensional non-affine uncertain systems, by applying the Markus–Yamabe theorem in differential equations. These theoretical results show explicitly that the ubiquitous PID control does indeed have strong robustness with respect to both the system nonlinear uncertainties and the selection of the controller parameters.

Performance Investigation of EMFO-Based Perpetual Online Tuned Variable SR-Controller in Simulated Real Environment

This study uses the enhanced moth flame optimization (EMFO) algorithm with an online tuning approach to optimize the parameters of a variable range split range PID (SRPID) controller. Before implementing the developed EMFO algorithm in the actual plant, it is necessary to investigate the performance of the same in the simulated real environment. Therefore, in the present work, an electrical analogous model of the practical environment is simulated for investigation by considering several effects, namely imperfect insulation, density, viscosity, and compressibility. Further, to check the effectiveness of the proposed algorithm, the controller performance using the EMFO algorithm is compared with the performance using the original MFO algorithm. The validation results show a substantial improvement in the case of EMFO-based controller with an online tuning method in comparison to MFO-based controller. EMFO algorithm exhibits superior performance as it combines the benefits of three modifications (change the spiral path, opposition learning-based initialization, and change in flames selection) in the original MFO algorithm. Furthermore, the system is also investigated for the effect of system dynamics and process disturbance. It is concluded that the developed EMFO algorithm gives superior performance in a simulated real environment paving the way for possible implementation in practical situations.

Design of High Precision Semiconductor Laser System

In PCR technology, the suitability and stability of the light source used to excite fluorescence is particularly important. Semiconductor laser not only plays an important role in medical, science and technology, aerospace, transportation, communications and other fields, but also brings great changes to society. In this paper, the research background and the overall design architecture of the laser are described first, and then the circuit design of the key modules of the system is described in detail, the optical control closed-loop feedback system ensures the stability of laser drive current, and the temperature control closed-loop and PID algorithm reduce the adverse effects of temperature on laser power. At the same time, the sparrow search algorithm is used to optimize the three parameters of PID, the simulation results and test data show that: The whole design fully meets the needs of the application scene.

Analysis methodology of compatibility between motion control and mechanical architecture of a newly designed gantry virtual track train and the path-tracking control strategy

This study aimed to propose a gantry virtual track train (G-VTT) architecture and investigate the path-tracking control of it. Based on the decoupling control theory, the concept and judgment criterion of the path-tracking independence of the G-VTT was proposed to provide a method to analyzing the compatibility between motion control and mechanical architecture, and instructing the design of the architecture of the G-VTT that could realize autonomous path-tracking with simple control strategy. The controllability and observability of the path-tracking control system were discussed from the perspective of vehicle kinematics and the decouplibility of each tracking point's lateral motion and the path-tracking independence of the vehicle was proved. The distributed virtual driving (DVD) model based on self-adaptive preview PID algorithm was proposed to achieve independent path-tracking of each axle. This model consists of two parts: forward preview model based on the fractional calculus theory simulating the driver's visual field and the parameter self-tuning PID controller based on variable universe fuzzy control theory (VUF-PID controller). The effectiveness and adaptability of the DVD model were verified by co-simulation test. The results show that the VUF-PID controller has an excellent control performance and could realize the self-tuning of PID parameters effectively and could adapt to the noticeable hysteresis effect with the forward preview model introduced. Moreover, the VUF-PID controller could significantly improve the curve-passing stability of the G-VTT, and exhibits excellent adaptability to the traveling speed, curve radius, and vehicle payload. Even when the train travels under an adverse operating condition with lateral acceleration about 3.2m/s2, the maximum tracking error could still be kept below ±0.02 m.

Optimized Active Control of a Smart Cantilever Beam Using Genetic Algorithm

Vibration is one of the most dangerous phenomena that happens to a structure. It leads to premature fatigue and eventually failure, with potentially fatal consequences. A smart structure is an excellent solution to this problem; it adds an actuator, a sensor, and an appropriate control law to the system to reduce/eliminate the vibration. This study developed a complete analytical model for a cantilever beam with a collocated PZT sensor/actuator pair. First, we used a coupling of a collocated PZT sensor and an actuator to measure and control vibration levels based on a PID control law considering the physical constraints associated with PZT operation as the voltage level of the actuator. Next, the damping coefficient of the structure was determined by using genetic algorithms best fit to satisfy specific vibration conditions. Finally, we conducted a complete optimization for sensor/actuator position and PID parameters, using genetic algorithms. Thus, this paper gives a thorough understanding of the potential vibration control of the cantilever beam.

Tracking moving target for 6 degree-of-freedom robot manipulator with adaptive visual servoing based on deep reinforcement learning PID controller.

In this paper, an image-based visual servoing (IBVS) controller with a 6 degree-of-freedom robotic manipulator that tracks moving objects is investigated using the proposed Deep Q-Networks and proportional-integral-derivative (DQN-PID) controller. First, the classical IBVS controller and the problem of feature loss and large steady-state error for tracking moving targets are introduced. Then, a DQN-PID based IBVS method is proposed to solve the problem of feature loss and large steady-state error and improve the servo precision, as the existing methods are hard to use for solve the problems. Specifically, the IBVS method is inherited by our controller to build the tracking model, and a value-based reinforcement learning method is proposed as an adaptive law for dynamically tuning the PID parameters in the discrete space, which can track the moving target and keep the servo feature in the field of the camera. Finally, compared with the different existing methods, the DQN-PID based IBVS method has merits of higher accuracy and more stable tracking, or generalization.

Research on speed control of permanent magnet synchronous motor based on RBF neural network tuning PID

Abstract In order to solve the problem of insufficient speed regulation performance of conventional PID controller in multi gear switching of electric drive fracturing PMSM, RBF neural network parameter identification is used to set the PID parameters and improve the control effect of conventional PID controller. By analyzing the application characteristics of PMSM in electric drive fracturing truck, the RBF-PID controller and the speed control system model of PMSM are established based on s-function in MATLAB/SIMLINK, and the simulation research is carried out in combination with the application requirements. The results show that compared with the conventional PID controller, the RBF-PID controller has better real-time performance and robustness. The real-time response characteristics of the PMSM speed regulation control system are improved by 84% and the robustness is improved by 62%. The RBF-PID controller can effectively improve the working stability of PMSM.

The Experimental Study of Attitude Stabilization Control for Programmable Nano Quadcopter

Rotary-wing nano-quadcopters are unmanned technologies used for reconnaissance and surveillance operations in many areas, especially strategic missions such as security and military operations. The main problem for these devices, which reached a wide audience with the widespread use of civilian production, is stabilization. The most important parameter affecting the stable, effective and reliable flight of these UAVs in the air is PID elements. In this study, experimental studies are carried out in [x, y, z] coordinates using a programmable Nano-quadcopter Crazyflie 2.0 drone. In order to determine the relationship between stabilization and PID control parameters of these systems, each coordinate axis is analyzed statistically. As far as is known, there is no study in the literature regarding the performance of the PID parameters of the Crazyflie 2.0 drone. At the end of the analysis study with the SPSS program, it is determined that the related drone moves with a very high level of efficiency in the "z" axis and performs the task related to the high level of efficiency on the y-axis. It is also confirmed that the drone performs poorly in the stabilization movement on the "x" axis and as a result of the analysis study, the system becomes more stable by making the necessary adjustments in the "yaw_p" parameter. Thanks to the study, it is aimed to create a decision support system for the optimization of the PID control parameters of UAVs, which are used extensively in every sector.

Fuzzy Logic-Based Load Frequency Control in an Island Hybrid Power System Model Using Artificial Bee Colony Optimization

This study presents the implementation of Artificial Bee Colony (ABC) optimization in an island hybrid power system model using fuzzy logic-based load frequency control. The Island Hybrid Power System considered in this study consisted of various generation units and an energy storage system. The optimized control parameters of PID using ABC were used in an intelligent fuzzy logic controller. The profiles (power & Frequency) of isolated hybrid power system were improved using a Super Conducting Magnetic Energy Storage (SMES) System. Individual controllers were used for wind turbine and diesel generators to control the power output for balancing the demand (frequency change control). Comparative analysis of power and frequency with the help of various classical and intelligent control configurations is presented. The outcome of the study shows that a minimum deviation in frequency and power is obtained through the proposed Intelligent Fuzzy Control approach for the considered isolated power system model.

Controller Design of Tracking WMR System Based on Deep Reinforcement Learning

Traditional PID controllers are widely used in industrial applications due to their simple computational architecture. However, the gain parameters of this simple computing architecture are fixed, and in response to environmental changes, the PID parameters must be continuously adjusted until the system is optimized. This research proposes to use the most important deep reinforcement learning (DRL) algorithm in deep learning as the basis and to modulate the gain parameters of the PID controller with fuzzy control. The research has the ability and advantages of reinforcement learning and fuzzy control and constructs a tracking unmanned wheel system. The mobile robotic platform uses a normalization system during computation to reduce the effects of reading errors caused by the wheeled mobile robot (WMR) of environment and sensor processes. The DRL-Fuzzy-PID controller architecture proposed in this paper utilizes degree operation to avoid the data error of negative input in the absolute value judgment, thereby reducing the amount of calculation. In addition to improving the accuracy of fuzzy control, it also uses reinforcement learning to quickly respond and minimize steady-state error to achieve accurate calculation performance. The experimental results of this study show that in complex trajectory sites, the tracking stability of the system using DRL-fuzzy PID is improved by 15.2% compared with conventional PID control, the maximum overshoot is reduced by 35.6%, and the tracking time ratio is shortened by 6.78%. If reinforcement learning is added, the convergence time of the WMR system will be about 0.5 s, and the accuracy rate will reach 95%. This study combines the computation of deep reinforcement learning to enhance the experimentally superior performance of the WMR system. In the future, intelligent unmanned vehicles with automatic tracking functions can be developed, and the combination of IoT and cloud computing can enhance the innovation of this research.

PID Controller Parameter Tables for Time-Delayed Systems Optimized Using Hill-Climbing

Several parameter tables for PID controllers are known from the literature, for the control of time-delayed systems. The best known is that of Ziegler and Nichols, but there are others also. In this publication, a parameter table is presented that minimizes the quality criteria IAE, ITAE and ISE for the control of time-delayed systems that can be identified with PTn systems. The controller output limitation is also taken into account. Since it is very computationally intensive to calculate these PID parameter sets, a well-known approach from the field of artificial intelligence was chosen. This was hill-climbing, which can find the parameter sets with much less computational effort than is needed for nested loops. With this method, the PID parameter tables for the minimized quality criteria were found and compared, each on the basis of many randomized starting parameter values. The application of the hill-climbing method shows rapid convergence. The parameters are discussed with two examples of time-delayed systems: a PT3 and a PT5. The results are regulated systems which show very good transient behavior. Furthermore, it is also possible to use the procedure presented for optimal PID parameters to control general, stable systems.

Energy-Efficient Robot Configuration and Motion Planning Using Genetic Algorithm and Particle Swarm Optimization

The implementation of Industry 5.0 necessitates a decrease in the energy consumption of industrial robots. This research investigates energy optimization for optimal motion planning for a dual-arm industrial robot. The objective function for the energy minimization problem is stated based on the execution time and total energy consumption of the robot arm configurations in its workspace for pick-and-place operation. Firstly, the PID controller is being used to achieve the optimal parameters. The parameters of PID are then fine-tuned using metaheuristic algorithms such as Genetic Algorithms and Particle Swarm Optimization methods to create a more precise robot motion trajectory, resulting in an energy-efficient robot configuration. The results for different robot configurations were compared with both motion planning algorithms, which shows better compatibility in terms of both execution time and energy efficiency. The feasibility of the algorithms is demonstrated by conducting experiments on a dual-arm robot, named as duAro. In terms of energy efficiency, the results show that dual-arm motions can save more energy than single-arm motions for an industrial robot. Furthermore, combining the robot configuration problem with metaheuristic approaches saves energy consumption and robot execution time when compared to motion planning with PID controllers alone.

Adaptive Fuzzy-PID Controller for Liquid Flow Control in theHeating Tank System

Liquid flow control systems are often used in some industrial processes. One of theproblems is the existence of disturbance that can cause the flow response to become unstable. Thus, it is necessary to re-tuning the controller when the disturbance occurs. This study aims to design and implement an Adaptive Fuzzy-PID (AF-PID) controller for the liquid flow control in the heating tank system. We develop an industrial plant prototype of a heating tank process to test the designed controller on a laboratory scale. AF-PID controller is used to controlling the flow rate when the disturbance occurs. This controller was chosen because it has the ability to adapt PID parameters when a disturbance occurs based on fuzzy logic.The nominal PID controller constants will adjust by additional PID parameters when there is a disturbance based on the Mamdani type fuzzy logic rule. The hardware experimental result shows that the designed controller can maintain the stability of the liquid flow when given 50% and 100% pipe leakages with maximum undershot by 3.33% and 24% respectively

Adaptive Fuzzy-PID Controller for Liquid Flow Control in theHeating Tank System

Liquid flow control systems are often used in some industrial processes. One of theproblems is the existence of disturbance that can cause the flow response to become unstable. Thus, it is necessary to re-tuning the controller when the disturbance occurs. This study aims to design and implement an Adaptive Fuzzy-PID (AF-PID) controller for the liquid flow control in the heating tank system. We develop an industrial plant prototype of a heating tank process to test the designed controller on a laboratory scale. AF-PID controller is used to controlling the flow rate when the disturbance occurs. This controller was chosen because it has the ability to adapt PID parameters when a disturbance occurs based on fuzzy logic.The nominal PID controller constants will adjust by additional PID parameters when there is a disturbance based on the Mamdani type fuzzy logic rule. The hardware experimental result shows that the designed controller can maintain the stability of the liquid flow when given 50% and 100% pipe leakages with maximum undershot by 3.33% and 24% respectively.

Simulation on the effects of the Arduino PID controller parameters using the WOKWI online simulator

PID controllers are known in the industrial world as reliable controllers and are studied in universities. The explanation of the ideal PID mathematically often makes it difficult for students to understand the computational process and the implementation that occurs. Often there is difficulty in selecting the correct controller parameters, for example, the Kp, Ki, and Kd parameters. In this study, PID parameters were selected in the form of Kp, Ti, and Td and observed controller output. The Ti parameter as the time integral is easier to understand than the Ki parameter as the gain integral. The Arduino simulator used is wokwi which is an online Arduino simulator. The PID library used is the Arduino Brett Beauregard PID. The results obtained are the effect of changes in the parameters of Kp, Ti, and Td on the controller output. For larger Kp, the controller output is proportional to the amount of input. The larger the Ti, the slower the system output, while the effect of Td is used when the input changes frequently

Optimal Control of Chilled Water System Based on Improved Sparrow Search Algorithm

Chilled water systems have large time delays and large inertia, and the traditional PID controller has a poor control effect. In this paper, an improved sparrow search algorithm is proposed to optimize the control of chilled water systems. Firstly, the random walk strategy was used to randomly perturb the sparrows to improve the searching ability of the sparrows. Then, a Gauss mutation was added in the iteration process of sparrows to enhance the local search ability. Finally, the values of the PID parameters as obtained by the above methods were substituted into the controller for simulation. The simulation results show that the method proposed in this paper improves the search accuracy of the sparrow search algorithm and effectively solves the problems of large time delays and large inertia in the chilled water system. The method in this paper took the least amount of time for the system to reach the steady state at only 12.75 s. The control effect of the proposed method was also better than that of the improved ant colony optimization algorithm. The rise time was 2.713 s, and the adjustment time was 4.95 s.

The Design and Experimentation of EVPIVS-PID Harvesters’ Header Height Control System Based on Sensor Ground Profiling Monitoring

In this paper, an adaptive header height control system is designed. Through the influence of the natural frequency, ωn, and damping ratio, ζ, on the system’s dynamic index, the optimal hydraulic cylinder parameters are determined comprehensively. The ground profiling monitoring mechanism and the header height feedback mechanism based on the angle sensor are designed. An integrated electromagnetic proportional valve was installed to replace the original header-controlled, electronically-controlled reversing valve, and a PWM (pulse width modulation) control-simulated counterweight test was performed. The limitation of traditional PID facing the integral saturation state is analysed, and a new EVPIVS-PID algorithm is proposed and simulated. Through the analysis of multiple groups of sample data in the field test, the accuracy of the control system in the header height control and output PWM value is demonstrated. The effectiveness of the EVPIVS-PID control algorithm to change the corresponding PID parameters based on the monitoring operation speed is analysed and demonstrated. Experiments show that the adaptive control system of header height based on ground profiling has a stable control effect. The height error of cutting stubble is not more than 2 cm, which can meet the requirements of a 5–11 km/h harvesting speed in plain areas.

An Improved Mayfly Optimization Algorithm Based on Median Position and Its Application in the Optimization of PID Parameters of Hydro-Turbine Governor

Mayfly algorithm is a new intelligent optimization algorithm with unique optimization capabilities recently proposed. It has strong research value, but there are also insufficient explorations, and it is easy to fall into the problem of local optimization. This paper aims to improve the optimization performance of the mayfly algorithm and explore its application value in practical engineering optimization problems. An improved mayfly algorithm based on the median position of the group is proposed. In its velocity update, the median position of the group is introduced with emphasis, and a non-linear gravity coefficient is introduced at the same time. Through the benchmark test function, its superiority in exploitation, convergence speed and accuracy and the improvement of exploration are verified. At the same time, the simulation model of the hydro-turbine governor using MATLAB/Simulink is established, and 10% frequency disturbance experiments of this model are carried out separately in two typical working conditions. The experiments results show that the optimal ITAE index value of the system obtained by the improved mayfly algorithm is smaller, and 16.5 and 18.1 iterations to complete on average. In addition, the experiments results reveal that the PID parameters optimized by the improved mayfly algorithm can make the dynamic performance of the regulation system better than other popular swarm intelligence algorithms, where the overshoot decreased by more than 3.1%, and the adjustment time also decreased in different degrees. The proposal of the median position of the group provides a new idea for the improvement of the swarm intelligence optimization algorithm. Meanwhile, a new effective method for optimizing the PID parameters of the hydro-turbine governor has been found.

PID Controller Parameter Optimized by Reformative Artificial Bee Colony Algorithm

The PID parameters determine the PID controller performance. A reformative artificial bee colony (RABC) algorithm is proposed for the PID parameter optimization problem. The algorithm balances the exploitation capability and exploration capability of the ABC algorithm by introducing a global optimal solution and improving the food source probability. The proposed algorithm is validated by simulation with six benchmark functions, and the results show that the RABC algorithm has higher search accuracy and faster search speed than other variants of the artificial bee colony algorithm. The RABC algorithm‐optimized PID controller has better control with minimum overshoot and fast response, as verified by comparison with PSO‐PID, DE‐PID, and GA‐PID methods in three typical systems.

Layer thickness controlling in Direct Energy Deposition process by adjusting the powder flow rate

Additive manufacturing by direct energy deposition is highly suitable to manufacture metal structures of nearly arbitrary geometry by locally melting powder or wire in a layer-by-layer manner. The layer thickness varies throughout the process due to uncontrollable and dynamic influences. The implementation of process control can be used to ensure a more constant layer thickness. Hence, target component height is achieved more precisely. This paper presents an approach to control the layer thickness by varying the powder flow rate of the powder feeder. A thermographic camera was used to measure the current structure height during manufacturing. The powder flow rate was adjusted by a PID controller operating layer-by-layer or in an alterable frequency. Different PID parameters were compared based on the manufacturing process of a wall, a cuboid, and a cross-shaped structure. As a result, a more precise match between manufactured component height and target component height was achieved.