Integer Order Proportional Integral Research Articles

A theoretical demonstration for reinforcement learning of PI control dynamics for optimal speed control of DC motors by using Twin Delay Deep Deterministic Policy Gradient Algorithm

To benefit from the advantages of Reinforcement Learning (RL) in industrial control applications, RL methods can be used for optimal tuning of the classical controllers based on the simulation scenarios of operating conditions. In this study, the Twin Delay Deep Deterministic (TD3) policy gradient method, which is an effective actor-critic RL strategy, is implemented to learn optimal Proportional Integral (PI) controller dynamics from a Direct Current (DC) motor speed control simulation environment. For this purpose, the PI controller dynamics are introduced to the actor-network by using the PI-based observer states from the control simulation environment. A suitable Simulink simulation environment is adapted to perform the training process of the TD3 algorithm. The actor-network learns the optimal PI controller dynamics by using the reward mechanism that implements the minimization of the optimal control objective function. A setpoint filter is used to describe the desired setpoint response, and step disturbance signals with random amplitude are incorporated in the simulation environment to improve disturbance rejection control skills with the help of experience based learning in the designed control simulation environment. When the training task is completed, the optimal PI controller coefficients are obtained from the weight coefficients of the actor-network. The performance of the optimal PI dynamics, which were learned by using the TD3 algorithm and Deep Deterministic Policy Gradient algorithm, are compared. Moreover, control performance improvement of this RL based PI controller tuning method (RL-PI) is demonstrated relative to performances of both integer and fractional order PI controllers that were tuned by using several popular metaheuristic optimization algorithms such as Genetic Algorithm, Particle Swarm Optimization, Grey Wolf Optimization and Differential Evolution.

Non-integer Order Control Scheme for Pressurized Water Reactor Core Power

Tracking load changes in a pressurized water reactor (PWR) with the help of an efficient core power control scheme in a nuclear power station is very important. The reason is that it is challenging to maintain a stable core power according to the reference value within an acceptable tolerance for the safety of PWR. To overcome the uncertainties, a non-integer-based fractional order control method is demonstrated to control the core power of PWR. The available dynamic model of the reactor core is used in this analysis. Core power is controlled using a modified state feedback approach with a non-integer integral scheme through two different approximations, CRONE (Commande Robuste d'Ordre Non Entier, meaning Non-integer order Robust Control) and FOMCON (non-integer order modeling and control). Simulation results are produced using MATLAB® program. Both non-integer results are compared with an integer order PI (Proportional Integral) algorithm to justify the effectiveness of the proposed scheme. Sate-space model Core power control Non-integer control Pressurized water reactor PI controller CRONE FOMCON.

Fractional order zero phase error tracking control of a novel decoupled 2-DOF compliant micro-positioning stage

This study focuses on a piezo-actuated two-degrees-of-freedom (2-DOF) decoupled compliant micro-positioning stage driven by a novel compound bridge-type amplification mechanism embedded with Scott-Russell mechanism. According to the system identification, the transfer functions of two working directions are obtained. Both of the measured dynamic cross couplings between them are also lower than −40 dB, demonstrating that the single-input-single-output control strategy can be adopted reasonably. Based on the identified frequency response, a fractional order proportional-integral (FOPI) controller is designed for the 2-DOF compliant micro-positioning stage. Compared with the integer order proportional-integral (IOPI) controller using same parameters, the amplitude error of the FOPI controller is 2% lower than that of IOPI controller. Additionally, a fractional order zero phase error controller (FOZPETC) is designed by obtaining the inverse of the fractional order closed-loop system in a large frequency range. And the gain of the corrected control system is 1 in a wide frequency band to eliminate the phase error in the close-loop control system. Finally, using the compound control strategy of FOZPETC+FOPI, a series of trajectory tracking tests are carried out on the proposed novel 2-DOF compliant micro-positioning stage. All the experimental results prove that the designed controller can achieve good positioning and tracking performance of the micro-positioning stage, and confirm the effectiveness of the compound control strategy of FOZPETC+FOPI.

Intelligent Proportional Integral Terminal Sliding Mode Control for variable speed standalone wind energy conversion system

AbstractThis study investigates the design of robust nonlinear controller for control of voltage and frequency of variable‐speed standalone Wind Energy Conversion System (WECS). The variation in wind‐speed and load raise the oscillation in terminal‐voltage and frequency. These oscillation need to be minimized for enhancing the power management. To overcome this issue, an Intelligent Proportional Integral Terminal Sliding Mode Controller (iPI‐TSMC) is proposed. Proposed iPI‐TSMC establishes a fast‐finite‐time convergence with minimum steady‐state error. Also this controller is robust against the wind velocity perturbation, load variations, and external disturbances. Closed‐loop stability of the proposed controller is validated using Lyapunov‐stability‐theorem. The cogency of the proposed iPI‐TSMC has been validated through MATLAB/simulink environment for different operating conditions. Also performance of iPI‐TSMC is compared with fractional‐order‐proportional‐integral (FOPI) and conventional integer‐order‐proportional‐integral (IOPI) controllers. The simulation results, signifies the efficacy of iPI‐TSMC as compared to other controllers. Feasibility of proposed iPI‐TSMC controller is verified in real‐time HIL simulator using op4510 platform.Statement of Industrial RelevanceSimulation analysis and the comparative study of iPI‐TSMC with FOPI, and IOPI shows better performance to keep constant terminal‐voltage during different wind‐profiles, load variation, and external disturbance. Also, performance assessment of iPI‐TSMC for different matrices during varying wind‐profiles is found superior than FOPI and IOPI controllers. Performance validation of proposed iPI‐TSMC for varying wind‐velocity and load in real‐time HIL simulator op4510 platform shows the feasibility of the proposed controller, which makes it suitable for real‐time application.

Performance enhancement of electric vehicle traction system using FO‐PI controller

This work improves the performance of an electric vehicle (EV) traction system by using non-linear fractional-order proportional–integral (FO-PI) controller. The functionality of FO-PI controller is benchmarked against integer-order proportional–integral (IO-PI) controller. A 400 V, 6.6 Ah Li-ion battery bank is designed to power an indirect field-oriented induction motor driven prototype EV traction system. The appeal of this study is to reveal the simplicity, robustness, and effectiveness of FO-PI speed regulator for EV traction system. The efficacy of FO-PI speed regulator for EV applications is validated through rigorous experimentation. The FO-PI controller due to its non-linear nature proves to be more robust and effective under variation of a system's parameters and external disturbances as compared to IO-PI controller. Furthermore, the experimental results show that FO-PI control strategy provides higher torque per amp output while maintaining better voltage and state-of-charge profiles of the Li-ion battery bank.

Comparative analysis of fractional order PI and integer order PI based controller for hybrid standalone wind energy conversion system

AbstractThis article presents a comprehensive analysis of fractional order proportional integral (FOPI) and integer order proportional integral (IOPI) controllers for voltage and frequency control of a variable speed hybrid standalone wind energy conversion system. Variations in wind velocity and load introduce the changes in terminal voltage and frequency. This can be controlled by an appropriate controller with satisfactory response. In this work, FOPI controller is proposed for controlling the terminal voltage and frequency. Dual second order generalized integral phase locked loop (DSOGI‐PLL) is utilized to track the system frequency. Fractional‐order controller is implemented for voltage source converter, which makes it robust due to their fractional characteristics. FOPI (PIλ) provides an additional degree of freedom (λ), along with proportional gain (Kp) and integral gain (Ki). The robustness of the controller is validated through simulations in MATLAB/simulink and its performance is compared with IOPI under various operating conditions. The results show that, FOPI based controller is able to maintain the terminal voltage and frequency constant with improved transient response in comparison to IOPI. Finally, performance assessment of the controllers is carried out using performance metrics.

Fractional-order proportional integral controller based on Al-Alaoui operator for resonant optical gyro

The first- and second-order fractional-order proportional integral (FOPI) controllers based on the Al-Alaoui operator and the continued fraction expansion method are designed and applied to the closed-loop control system of a resonant optical gyro. The phase margin method is used to tune the control parameters. The characteristics of the unit step responses of the integer order proportional integral (IOPI) and the FOPI controllers are calculated and compared. Responses to perturbations at different positions of the closed-loop control system are simulated. Results show that for the resonant optical gyro, the FOPI closed-loop control system has much better unit-step-response performance and noise-resistance ability than the IOPI control system, which is important for improving the dynamic response characteristics and the robustness of the gyro’s feedback system and enhancing the detection ability of the gyro. Experiments on a resonant optical gyro experimental system also verify the advantages of the FOPI controller in step response and bias stability.

Effects of fractional-order PI controller on delay margin in single-area delayed load frequency control systems

This study aims to determine the improvement effect on the delay margin if fractional-order proportional integral (PI) controller is used in the control of a single-area delayed load frequency control (LFC) system. The delay margin of the system with fractional-order PI control has been obtained for various fractional integral orders and the effect of them has been shown on the delay margin as a third controller parameter. Furthermore, the stability of the system that is either under or over the delay margin is examined by generalized modified Mikhailov criterion. The stability results obtained have been confirmed numerically in time domain. It is demonstrated that the proposed controller for delayed LFC system provides more flexibility on delay margin according to integer-order PI controller.

Fractional order modeling and two loop control of PEM fuel cell for voltage regulation considering both source and load perturbations

The growing demand for renewable energy sources has favored attention towards fuel cell and in particular towards Polymer Electrolyte Membrane Fuel Cell (PEMFC) as an alternative energy source. Despite the advantage of possessing high current density, standalone isolated fuel cell operate at low voltage and the output is heavily dependent on the operating condition. This demands the integration of fuel cells with suitable power conditioning units. The present work aims at designing a controller which achieves the objective of regulated output voltage irrespective of variation in both load and source operating condition. The design and integration of the converter with PEMFC necessitates the development of a mathematical model, which can represent the PEMFC dynamics under different operating conditions. PEMFCs are known to exhibit distributed dynamics and possess long term memory, which are more accurately represented by fractional calculus. In this regard, a hybrid optimization based approach for fractional order modeling of PEMFC has been proposed. Further using the model, a fractional order Proportional Integral (FOPI) controller has been designed for regulating the load voltage. The presence of an extra tuning parameter in FOPI allows greater flexibility in achieving the system specification as compared to the classical Integer Order Proportional Integral (IOPI) controller. The effectiveness of the proposed FOPI controller for PEMFC fed PWM DC/DC converter has been validated under varying operating condition of the PEMFC and load perturbations in real time environment.

Fractional Order PI‐PD Control of Liquid Level in Coupled Two Tank System and its Experimental Validation

AbstractThis paper presents a level control problem of a coupled two tank single input single output (SISO) system. A cascade control strategy is adopted having a fractional order proportional integral (FOPI) controller and fractional order proportional derivative (FOPD) controller in the outer and the inner loops, respectively. Cascaded integer order proportional integral (IOPI) and integer order proportional derivative (IOPD) controllers are also designed to compare the performances. A frequency domain approach is followed to design all the controllers. It is mathematically shown that the FOPI and FOPD controllers can achieve less steady state error and consume less energy than that of the IOPI and IOPD controllers while meeting the same phase margin and gain crossover frequency. All propositions are validated on an experimental setup.

Fractional Order PI Controller Based PMSM Drive under Dynamic Loading Conditions

Objective: The main objective of this paper is to examine the permanent magnet synchronous motor (PMSM) drive using controller under dynamics. Statistical Analysis: The method adapted for analyzing dynamics occurring in PMSM drive is fractional calculus on PI (proportional-integral) controller. The vector control scheme was applied for speed control and stimulated in MATLAB and Simulink under various operating conditions. Findings: The FOPI controlled drive shows better control execution property and robustness over traditional integer order PI controller. The dynamics during load and speed variations are figured out to be normal than the actual case by use of FOPI as speed controller. Improvement: The stimulation result shows the performance and adequacy of the proposed FOPI controlled PMSM drive system.

Fractional Order PI Controller Design for Non-Monotonic Phase Systems

Abstract In this paper, a fractional order proportional-integral (FOPI) controller is proposed for controlling the non-monotonic decreasing phase DC-buck regulator system. The parameters of FOPI controller are optimized by Nelder's-Mead (NM) method. The FOPI controller provides fast closed-loop performance as well as improves the robust properties of the system in time and frequency domain. The controller preserves the monotonic phase between the desired bandwidth and improves the characteristic performance of the system. The proposed method is validated by comparing the time domain as well as frequency domain characteristics with the integer order proportional-integral (IOPI) controllers tuned using various techniques.

Fractional order ultra low-speed position servo: Improved performance via describing function analysis

In a reference of the previous work, a new systematic design method for fractional order proportional and derivative (FOPD) controller is proposed for a class of typical second-order plants. Simulation and experimental results in the reference show that, the dynamic performance and robustness with the designed FOPD controller outperforms that with the optimized traditional integer order proportional integral (IOPI) controller at normal speed. Furthermore, it is found that, for the ultra low-speed position tracking with a significant friction effect, the tracking performance using the designed FOPD controller is much better than that using the optimized IOPI controller. However, the reason of this advantage is unclear. In this paper, using the describing function method and Bode plots analysis, the observed advantage of the designed FOPD controller over the optimized IOPI controller, for the nonlinear low-speed position tracking system with friction effect, is explained with the theoretical analysis. This explanation for the priority of the designed FOPD controller is consistently demonstrated by the extended experimental results in this paper.