PID controller for active magnetic levitation ball system

Due to the significant nonlinear characteristics of the magnetic bearing, it is difficult to establish an accurate mathematical model, and it is susceptible to external disturbances. Traditional control methods struggle to meet the control requirements. Active disturbance rejection control (ADRC) does not rely on accurate models and has outstanding anti-interference ability. In order to improve the anti-disturbance ability and control stability of the system, a cascaded linear–nonlinear active disturbance rejection control method (CL-NLADRC) based on the improved artificial jellyfish algorithm is proposed and applied to the magnetic levitation ball system. Firstly, the mathematical model of the magnetic levitation ball system is established, and based on this model, a cascaded linear–nonlinear extended state observer is constructed to estimate and compensate for the system state, thereby enhancing the dynamic response capability of the system. Subsequently, the tangent spiral motion and the lens reversal learning strategy are introduced to improve the artificial jellyfish algorithm to further improve the global optimization performance of the algorithm. Finally, the improved artificial jellyfish algorithm is used to optimize the CL-NLADRC controller parameters. The simulation and experimental results show that compared with the traditional LADRC and PID controllers, the proposed CL-NLADRC has a significant improvement in the steady-state error, response speed, and anti-disturbance performance of the system. Among them, the root mean square error decreased by 14% and 47%, respectively, which verified the effectiveness and stability of the method in the magnetic levitation ball system.

Based on the physical model of a magnetic levitation ball system, a linear state-space model of the system is established and a pole assignment design method for the magnetic levitation ball system is proposed. Its aim is to design a state feedback control law, such that the closed-loop system has the desired eigenvalues and the system has well performance indexes. In addition, the optimal choice of poles for the magnetic levitation ball system is studied. The simulation results offer the transient response and steady-state response of the magnetic levitation ball system, which shows the simplicity and effectiveness of the proposed design method.

Design of a Data-Driven PID Controller using Operating Data

Abstract. Problem. Speed control systems are used to ensure road safety and improve vehicle efficiency by controlling traffic speed. The main purpose of the speed control system is to ensure road safety, increase vehicle efficiency and reduce the negative impact of transport on the environment by controlling the speed of traffic. Reducing speed allows drivers to react in time to unforeseen situations, stop at traffic lights, and reduce the distance to other vehicles. In this paper, we have carried out mathematical modeling of a vehicle speed control system. Goal. As a result of the analysis, the purpose of the study was highlighted: to carry out mathematical modeling of the car speed control system. Job tasks: to model the speed control system using a proportional regulator and a PID controller. Methodology. Initially, we considered a vehicle speed control system using a proportional regulator. In the process of synthesis, it was found that the use of a P-controller provides insufficiently good quality of the vehicle speed control system. It was decided to use a PID controller to synthesize the speed control system. Results. The result of the study is: optimized settings of the PID controller provide a given control time tp≈40 s with practically no overshoot, which is a completely satisfactory quality of this system. Originality. The originality lies in the fact that a PID controller with an NCD block was used to determine the transient function of the system with optimal settings. Practical value. The use of the proposed results indicates the possibility of using a PID controller to ensure the set parameters.

This paper concerns design and implementation of PID and fractional-order PID (FOPID) controllers to control position of an electromagnetically suspended ferromagnetic ball in a magnetic levitation (Maglev) system in real time. The Maglev system, manufactured by Feedback Instruments (Model No 33-210) is used as a platform to test the performance of proposed controllers. Parameters of PID and FOPID controllers are tuned by firefly algorithm (FA). FA is a metaheuristic algorithm based on movement of fireflies toward more attractive and brighter ones. PID and FOPID controllers are implemented in MATLAB and SIMULINK environment inside PC using fractional-order modeling and control toolbox. Controller in the SIMULINK environment inside PC is connected to the Maglev system through Advantech card. Effectiveness of proposed controllers is tested by checking the ability of the suspended ball to track a reference signal. Step change, sine wave, and square wave are used as reference signals. Real-time results have revealed satisfactory transient and steady-state responses over the contemporary existing controllers. FOPID controller showed better results compared to PID.

This paper proposes a new offline learning algorithm for a data-driven proportional-integral-derivative (DD-PID) controller based on an extended fictitious reference iterative tuning (E-FRIT). PID controllers have been used in many process systems. However, it is difficult to maintain a good control performance using PID controllers with fixed control parameters because of the nonlinearity of the systems. The DD-PID controller has been proposed as an effective control system for nonlinear systems. This controller can tune its PID parameters adaptively at each equilibrium point of the system output. In the conventional DD-PID controller, the PID parameters are learned so as to minimize a criterion of the FRIT method. However, the FRIT method is based on minimization of the error in system output, and therefore, the criterion is insufficient for systems, such as chemical process systems, for which the stability of a closed loop system is essential. In order to solve this problem, the E-FRIT method has been proposed; a penalty for input variation is incorporated in the criterion for this method. In the present study, an offline learning rule of PID parameters was derived based on the E-FRIT criterion. According to the rule, the PID parameters that are taken into stability can be calculated. The effectiveness of the proposed method was evaluated by simulations of a polystyrene reactor system. The simulation confirmed that the proposed DD-PID controller yields better control result than the conventional learning method.

Single-input interval type-2 fuzzy PID (SI-IT2-FPID) control approach is a simple and effective way of adding nonlinear characteristics to linear PID controllers to increase the control performance and the capability of handling system nonlinearities. In the SI-IT2-FPID approach, the nonlinear characteristic of the PID controller is provided by a single-input–single-output interval type-2 fuzzy controller (IT2-FC) positioned before the PID controller. In the literature, a constant footprint of uncertainty (C-FOU) structure is used in SI-IT2-FPID controller design procedures in almost all studies. However, the C-FOU structure limits the performance of the SI-IT2-FPID controller. In this study, an online footprint of uncertainty (FOU) tuning mechanism is proposed for SI-IT2-FPID controllers in order to increase their control performances. Online tuning of FOUs of interval type-2 membership functions (IT2-MFs) enhances the capability of SI-IT2-FPID controllers to handle system nonlinearities since FOU levels of IT2-MFs have a dominant effect on the control and robustness performance of SI-IT2-FPID controllers. In the proposed method, FOUs of IT2-MFs of an IT2-FC are adjusted by an analytical function based on the system error and the change of the error. In this way, the simple structure of the SI-IT2-FPID controller is preserved. In order to illustrate the control and robustness performance of the proposed controller, simulation studies are carried out on three benchmark systems, namely a second-order nonlinear system, a ball and beam system, and a first-order plus dead time system. Additionally, the performance of the proposed controller is compared to a SI-IT2-FPID controller with C-FOU and a classical PID controller. The simulation results show that the proposed controller exhibits better control and robustness performance than the other controllers.

Under the research context of two axis digital control turntable, this paper has set up a mathematical model of control system of turntables. Proceeding from such model, it has made an analysis on the deficiencies of classical PID control during turntable control. Against the feature of PID parameters difficult to be tuned, the neural network is thus introduced in the optimizing process of turncontrol PID parameters, during which PID controller is designed based on BP network. In addition, the PID algorithm control based on BP network is simulated with results indicating PID controller designed so featuring high tracking accuracy, stable performance and strong robustness, which provides a solution to the problem of inadequate precision required by classic PID control as regards to the control precision.

The performance of active suspension systems is directly related to the mechanical design and control of the system. The stable operation of the controller improves driving comfort and handling. The quarter car model is frequently used in the analysis of suspension systems due to its simple structure. In this study, Matlab Simulink software was used in the modeling, control and simulation of the quarter car active suspension model. System performance was investigated for four different road profiles with PID and fuzzy logic control methods. Two of the road profiles used are in the form of impact signals consisting of pits and bumps. The other two road profiles are random road disturbances with high frequency. The effects of active and passive suspension systems on driving comfort are compared by taking into account the control methods used. As a result of the study, it has been determined that the fuzzy logic controller gives better results in pulse signals consisting of bumps and pits, and the PID controller gives better results in high-frequency random road disturbances. In addition, with the use of fuzzy logic control method in the active suspension system, a significant decrease in the actuator force has occurred. This result is very interesting in terms of minimizing energy, reducing actuator sizes and reducing costs.

A GBMO-based PI λ D μ controller for vibration mitigation of seismic-excited structures

In CNC lathe servo feed system, many parameters are uncertain, so it is difficult to establish accurate mathematical model of the feed system, and parameters of conventional PID controller can not change the parameters to adjust with the controlled object. Fuzzy PID controller, which has the advantages of conventional PID control and fuzzy control, can solve these problems very well. So we can make it applied in CNC lathe servo feed system. This paper has made a simulation of fuzzy self-turning PID controller in the MATLAB environment. The simulation shows that the fuzzy self-turning PID controller has a better control capability and a higher stability, and it improved the servo feed system dynamic performance.

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.

This paper presents a control technique for improving the thermodynamics characteristic of the hydrogen gas within metal hydride(MH) reactor by heating/cooling with a thermoelectric module, Peltier element. Practically, the uncertainty of the parameters, such as unexpected outside temperature of the reactor. Additionally, the complicated problem of the integrated system model, Peltier and MH reactor, make the system to be nonlinear which makes it hard to use the conventional controller like proportional+integral+derivative, PID, or conventional fuzzy control to improve dynamic response. To obtain a high performance of the thermal management for the MH reactor, the fuzzy adaptive PID is developed. The fuzzy rules based on the knowledge of MH system are used to adapt the gain parameters of the PID control. The mathematical model of the MH thermal system is determined for using as the knowledge base for fuzzy rules. The experimental results show the effectiveness of the proposed technique that compared to conventional control.

The PID controller and real-time monitoring system for a low-temperature furnace was developed. The system has two part, the PID controller, and the real-time monitoring part. An Arduino mega2560 microcontroller board was used for measuring and control the furnace temperature. A type-K thermocouple and a MAX31850 IC was applied for a furnace temperature measurement. The microcontroller board and a MAX31850 were connected via the One-wire bus for convert the temperature values and sent to a personal computer. The PID parameters can be varied by a user in the program, which developed by LabVIEW Software on a computer. The laboratory made furnace was established for testing the controller and monitoring system. The results have shown that the temperature with the range of 25-500 degree Celsius can be controlled. By the trial and error method with the PID parameters, kp was 250, Ti was 0.05 and Td was 0.20, the target temperature can be controlled with the maximum error of 1 degree Celsius.

An optimal PID controller with incomplete derivation is proposed based on fuzzy inference and the genetic algorithm, which is called the fuzzy-GA PID controller with incomplete derivation. It consists of the off-line part and the on-line part. In the off-line part, by taking the overshoot, rise time, and settling time of system unit step response as the performance indexes and by using the genetic algorithm, a group of optimal PID parameters K*p, T*i, and T*i are obtained, which are used as the inital values for the on-line tuning of PID parameters. In a on-line part, based on K*p, T*i, and T*d and according to the current system error e and its time derivative, a dedicated program is written, which is used to optimize and adjust the PID parameters on line through a fuzzy inference mechanism to ensure that the system response has optimal dynamic and steady-state performance. The controller has been used to control the D. C. motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation shows that this kind of optimal PID controller has excellent control performance and robust performance.