Research

15 pages, 2869 KiB

Open AccessArticle

Quadratic Model-Based Dynamically Updated PID Control of CSTR System with Varying Parameters

by Dushko Stavrov, Gorjan Nadzinski, Stojche Deskovski and Mile Stankovski

Algorithms 2021, 14(2), 31; https://doi.org/10.3390/a14020031 - 21 Jan 2021

Cited by 9 | Viewed by 2734

In this paper, we discuss an improved version of the conventional PID (Proportional–Integral–Derivative) controller, the Dynamically Updated PID (DUPID) controller. The DUPID is a control solution which preserves the advantages of the PID controller and tends to improve them by introducing a quadratic [...] Read more.

In this paper, we discuss an improved version of the conventional PID (Proportional–Integral–Derivative) controller, the Dynamically Updated PID (DUPID) controller. The DUPID is a control solution which preserves the advantages of the PID controller and tends to improve them by introducing a quadratic error model in the PID control structure. The quadratic error model is constructed over a window of past error points. The objective is to use the model to give the conventional PID controller the awareness needed to battle the effects caused by the variation of the parameters. The quality of the predictions that the model is able to deliver depends on the appropriate selection of data used for its construction. In this regard, the paper discusses two algorithms, named 1D (one dimensional) and 2D (two dimensional) DUPID. Appropriate to their names, the former selects data based on one coordinate, whereas the latter selects the data based on two coordinates. Both these versions of the DUPID controller are compared to the conventional PID controller with respect to their capabilities of controlling a Continuous Stirred Tank Reactor (CSTR) system with varying parameters in three different scenarios. As a quantifying measure of the control performance, the integral of absolute error (IAE) metric is used. The results from the performed simulations indicated that the two versions of the DUPID controller improved the control performance of the conventional PID controller in all scenarios. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

17 pages, 4454 KiB

Open AccessArticle

Swarm-Based Design of Proportional Integral and Derivative Controllers Using a Compromise Cost Function: An Arduino Temperature Laboratory Case Study

by P. B. de Moura Oliveira, John D. Hedengren and E. J. Solteiro Pires

Algorithms 2020, 13(12), 315; https://doi.org/10.3390/a13120315 - 30 Nov 2020

Cited by 24 | Viewed by 3116

Abstract

Simple and easy to use methods are of great practical demand in the design of Proportional, Integral, and Derivative (PID) controllers. Controller design criteria are to achieve a good set-point tracking and disturbance rejection with minimal actuator variation. Achieving satisfactory trade-offs between these [...] Read more.

Simple and easy to use methods are of great practical demand in the design of Proportional, Integral, and Derivative (PID) controllers. Controller design criteria are to achieve a good set-point tracking and disturbance rejection with minimal actuator variation. Achieving satisfactory trade-offs between these performance criteria is not easily accomplished with classical tuning methods. A particle swarm optimization technique is proposed to design PID controllers. The design method minimizes a compromise cost function based on both the integral absolute error and control signal total variation criteria. The proposed technique is tested on an Arduino-based Temperature Control Laboratory (TCLab) and compared with the Grey Wolf Optimization algorithm. Both TCLab simulation and physical data show that satisfactory trade-offs between the performance and control effort are enabled with the proposed technique. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

27 pages, 1770 KiB

Open AccessArticle

A NARX Model Reference Adaptive Control Scheme: Improved Disturbance Rejection Fractional-Order PID Control of an Experimental Magnetic Levitation System

by Hossein Alimohammadi, Baris Baykant Alagoz, Aleksei Tepljakov, Kristina Vassiljeva and Eduard Petlenkov

Algorithms 2020, 13(8), 201; https://doi.org/10.3390/a13080201 - 18 Aug 2020

Cited by 17 | Viewed by 3924

Abstract

Real control systems require robust control performance to deal with unpredictable and altering operating conditions of real-world systems. Improvement of disturbance rejection control performance should be considered as one of the essential control objectives in practical control system design tasks. This study presents [...] Read more.

Real control systems require robust control performance to deal with unpredictable and altering operating conditions of real-world systems. Improvement of disturbance rejection control performance should be considered as one of the essential control objectives in practical control system design tasks. This study presents a multi-loop Model Reference Adaptive Control (MRAC) scheme that leverages a nonlinear autoregressive neural network with external inputs (NARX) model in as the reference model. Authors observed that the performance of multi-loop MRAC-fractional-order proportional integral derivative (FOPID) control with MIT rule largely depends on the capability of the reference model to represent leading closed-loop dynamics of the experimental ML system. As such, the NARX model is used to represent disturbance-free dynamical behavior of PID control loop. It is remarkable that the obtained reference model is independent of the tuning of other control loops in the control system. The multi-loop MRAC-FOPID control structure detects impacts of disturbance incidents on control performance of the closed-loop FOPID control system and adapts the response of the FOPID control system to reduce the negative effects of the additive input disturbance. This multi-loop control structure deploys two specialized control loops: an inner loop, which is the closed-loop FOPID control system for stability and set-point control, and an outer loop, which involves a NARX reference model and an MIT rule to increase the adaptation ability of the system. Thus, the two-loop MRAC structure allows improvement of disturbance rejection performance without deteriorating precise set-point control and stability characteristics of the FOPID control loop. This is an important benefit of this control structure. To demonstrate disturbance rejection performance improvements of the proposed multi-loop MRAC-FOPID control with NARX model, an experimental study is conducted for disturbance rejection control of magnetic levitation test setup in the laboratory. Simulation and experimental results indicate an improvement of disturbance rejection performance. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

17 pages, 8080 KiB

Open AccessArticle

PD Steering Controller Utilizing the Predicted Position on Track for Autonomous Vehicles Driven on Slippery Roads

by Natalia Alekseeva, Ivan Tanev and Katsunori Shimohara

Algorithms 2020, 13(2), 48; https://doi.org/10.3390/a13020048 - 21 Feb 2020

Cited by 1 | Viewed by 3979

Abstract

Among the most important characteristics of autonomous vehicles are the safety and robustness in various traffic situations and road conditions. In this paper, we focus on the development and analysis of the extended version of the canonical proportional-derivative PD controllers that are known [...] Read more.

Among the most important characteristics of autonomous vehicles are the safety and robustness in various traffic situations and road conditions. In this paper, we focus on the development and analysis of the extended version of the canonical proportional-derivative PD controllers that are known to provide a good quality of steering on non-slippery (dry) roads. However, on slippery roads, due to the poor yaw controllability of the vehicle (suffering from understeering and oversteering), the quality of control of such controllers deteriorates. The proposed predicted PD controller (PPD controller) overcomes the main drawback of PD controllers, namely, the reactiveness of their steering behavior. The latter implies that steering output is a direct result of the currently perceived lateral- and angular deviation of the vehicle from its intended, ideal trajectory, which is the center of the lane. This reactiveness, combined with the tardiness of the yaw control of the vehicle on slippery roads, results in a significant lag in the control loop that could not be compensated completely by the predictive (derivative) component of these controllers. In our approach, keeping the controller efforts at the same level as in PD controllers by avoiding (i) complex computations and (ii) adding additional variables, the PPD controller shows better quality of steering than that of the evolved (via genetic programming) models. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

18 pages, 1716 KiB

Open AccessArticle

Neural PD Controller for an Unmanned Aerial Vehicle Trained with Extended Kalman Filter

by Javier Gomez-Avila, Carlos Villaseñor, Jesus Hernandez-Barragan, Nancy Arana-Daniel, Alma Y. Alanis and Carlos Lopez-Franco

Algorithms 2020, 13(2), 40; https://doi.org/10.3390/a13020040 - 18 Feb 2020

Cited by 5 | Viewed by 3758

Abstract

Flying robots have gained great interest because of their numerous applications. For this reason, the control of Unmanned Aerial Vehicles (UAVs) is one of the most important challenges in mobile robotics. These kinds of robots are commonly controlled with Proportional-Integral-Derivative (PID) controllers; however, [...] Read more.

Flying robots have gained great interest because of their numerous applications. For this reason, the control of Unmanned Aerial Vehicles (UAVs) is one of the most important challenges in mobile robotics. These kinds of robots are commonly controlled with Proportional-Integral-Derivative (PID) controllers; however, traditional linear controllers have limitations when controlling highly nonlinear and uncertain systems such as UAVs. In this paper, a control scheme for the pose of a quadrotor is presented. The scheme presented has the behavior of a PD controller and it is based on a Multilayer Perceptron trained with an Extended Kalman Filter. The Neural Network is trained online in order to ensure adaptation to changes in the presence of dynamics and uncertainties. The control scheme is tested in real time experiments in order to show its effectiveness. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

26 pages, 4835 KiB

Open AccessArticle

Multi-Loop Model Reference Proportional Integral Derivative Controls: Design and Performance Evaluations

by Baris Baykant Alagoz, Aleksei Tepljakov, Eduard Petlenkov and Celaleddin Yeroglu

Algorithms 2020, 13(2), 38; https://doi.org/10.3390/a13020038 - 13 Feb 2020

Cited by 9 | Viewed by 4852

Abstract

Due to unpredictable and fluctuating conditions in real-world control system applications, disturbance rejection is a substantial factor in robust control performance. The inherent disturbance rejection capacity of classical closed loop control systems is limited, and an increase in disturbance rejection performance of single-loop [...] Read more.

Due to unpredictable and fluctuating conditions in real-world control system applications, disturbance rejection is a substantial factor in robust control performance. The inherent disturbance rejection capacity of classical closed loop control systems is limited, and an increase in disturbance rejection performance of single-loop control systems affects the set-point control performance. Multi-loop control structures, which involve model reference control loops, can enhance the inherent disturbance rejection capacity of classical control loops without degrading set-point control performance; while the classical closed Proportional Integral Derivative (PID) control loop deals with stability and set-point control, the additional model reference control loop performs disturbance rejection control. This adaptive disturbance rejection, which does not influence set-point control performance, is achieved by selecting reference models as transfer functions of real control systems. This study investigates six types of multi-loop model reference (ML-MR) control structures for PID control loops and presents straightforward design schemes to enhance the disturbance rejection control performance of existing PID control loops. For this purpose, linear and non-linear ML-MR control structures are introduced, and their control performance improvements and certain inherent drawbacks of these structures are discussed. Design examples demonstrate the benefits of the ML-MR control structures for disturbance rejection performance improvement of PID control loops without severely deteriorating their set-point performance. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

13 pages, 6398 KiB

Open AccessEditor’s ChoiceArticle

Optimal Learning and Self-Awareness Versus PDI

by Brendon Smeresky, Alex Rizzo and Timothy Sands

Algorithms 2020, 13(1), 23; https://doi.org/10.3390/a13010023 - 11 Jan 2020

Cited by 31 | Viewed by 6443

Abstract

This manuscript will explore and analyze the effects of different paradigms for the control of rigid body motion mechanics. The experimental setup will include deterministic artificial intelligence composed of optimal self-awareness statements together with a novel, optimal learning algorithm, and these will be [...] Read more.

This manuscript will explore and analyze the effects of different paradigms for the control of rigid body motion mechanics. The experimental setup will include deterministic artificial intelligence composed of optimal self-awareness statements together with a novel, optimal learning algorithm, and these will be re-parameterized as ideal nonlinear feedforward and feedback evaluated within a Simulink simulation. Comparison is made to a custom proportional, derivative, integral controller (modified versions of classical proportional-integral-derivative control) implemented as a feedback control with a specific term to account for the nonlinear coupled motion. Consistent proportional, derivative, and integral gains were used throughout the duration of the experiments. The simulation results will show that akin feedforward control, deterministic self-awareness statements lack an error correction mechanism, relying on learning (which stands in place of feedback control), and the proposed combination of optimal self-awareness statements and a newly demonstrated analytically optimal learning yielded the highest accuracy with the lowest execution time. This highlights the potential effectiveness of a learning control system. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

23 pages, 1752 KiB

Open AccessArticle

Learning Output Reference Model Tracking for Higher-Order Nonlinear Systems with Unknown Dynamics

by Mircea-Bogdan Radac and Timotei Lala

Algorithms 2019, 12(6), 121; https://doi.org/10.3390/a12060121 - 12 Jun 2019

Cited by 8 | Viewed by 3638

Abstract

This work suggests a solution for the output reference model (ORM) tracking control problem, based on approximate dynamic programming. General nonlinear systems are included in a control system (CS) and subjected to state feedback. By linear ORM selection, indirect CS feedback linearization is [...] Read more.

This work suggests a solution for the output reference model (ORM) tracking control problem, based on approximate dynamic programming. General nonlinear systems are included in a control system (CS) and subjected to state feedback. By linear ORM selection, indirect CS feedback linearization is obtained, leading to favorable linear behavior of the CS. The Value Iteration (VI) algorithm ensures model-free nonlinear state feedback controller learning, without relying on the process dynamics. From linear to nonlinear parameterizations, a reliable approximate VI implementation in continuous state-action spaces depends on several key parameters such as problem dimension, exploration of the state-action space, the state-transitions dataset size, and a suitable selection of the function approximators. Herein, we find that, given a transition sample dataset and a general linear parameterization of the Q-function, the ORM tracking performance obtained with an approximate VI scheme can reach the performance level of a more general implementation using neural networks (NNs). Although the NN-based implementation takes more time to learn due to its higher complexity (more parameters), it is less sensitive to exploration settings, number of transition samples, and to the selected hyper-parameters, hence it is recommending as the de facto practical implementation. Contributions of this work include the following: VI convergence is guaranteed under general function approximators; a case study for a low-order linear system in order to generalize the more complex ORM tracking validation on a real-world nonlinear multivariable aerodynamic process; comparisons with an offline deep deterministic policy gradient solution; implementation details and further discussions on the obtained results. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

13 pages, 4671 KiB

Open AccessArticle

Kalman-Filter-Based Tension Control Design for Industrial Roll-to-Roll System

by Hyeongjin Hwang, Jehwon Lee, Sangjune Eum and Kanghyun Nam

Algorithms 2019, 12(4), 86; https://doi.org/10.3390/a12040086 - 24 Apr 2019

Cited by 9 | Viewed by 5714

Abstract

This paper presents a robust and precise tension control method for a roll-to-roll (R2R) system. In R2R processing, robust and precise tension control is very important because improper web tension control leads to deterioration in the quality of web material. However, tension control [...] Read more.

This paper presents a robust and precise tension control method for a roll-to-roll (R2R) system. In R2R processing, robust and precise tension control is very important because improper web tension control leads to deterioration in the quality of web material. However, tension control is not easy because the R2R system has a model variation in which the inertia of the web in roll form is changed and external disturbances caused by web slip and crumpled web. Therefore, a disturbance observer (DOB) was proposed to achieve robustness against model variations and external disturbances. DOB is a robust control method widely used in various fields because of its simple structure and excellent performance. Moreover, the web passes through various process steps to achieve the finished product in the R2R process. Particularly, it is important to track the tension when magnitude of the tension varies during process. Feedforward (FF) controller was applied to minimize the tracking error in the transient section where tension changes. Moreover, the signal processing of a sensor using the Kalman filter (KF) in the R2R system greatly improved control performance. Finally, the effectiveness of the proposed control scheme is discussed using experimental results. Full article

(This article belongs to the Special Issue Algorithms for PID Controller 2019)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Algorithms for PID Controller 2019

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI