Robust PI/PID controller for interval first order system with time delay

Farkh, Rihem; Laabidi, Kaouther; Ksouri, Mekki

doi:10.1504/ijmic.2011.040491

Cited by 12 publications

(4 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Ho et al [13] and Silva et al [14], the Hermite-Biehler theorem was used for the formulation of P, PI, and PID controllers to stabilize a delay-free interval plant family. In Silva et al [14], the stabilizing problem of a PI/PID controller for the first-order delay system was analyzed, and then used to obtain all PI and PID gains that stabilize an interval first-order delay system [15].…”

Section: Introductionmentioning

confidence: 99%

Optimal Robust Control for Unstable Delay System

Farkh¹,

Ksouri²,

Bouani³

2021

Computer Systems Science and Engineering

Self Cite

View full text Add to dashboard Cite

Proportional-Integral-Derivative control system has been widely used in industrial applications. For uncertain and unstable systems, tuning controller parameters to satisfy the process requirements is very challenging. In general, the whole system's performance strongly depends on the controller's efficiency and hence the tuning process plays a key role in the system's response. This paper presents a robust optimal Proportional-Integral-Derivative controller design methodology for the control of unstable delay system with parametric uncertainty using a combination of Kharitonov theorem and genetic algorithm optimization based approaches. In this study, the Generalized Kharitonov Theorem (GKT) for quasi-polynomials is employed for the purpose of designing a robust controller that can simultaneously stabilize a given unstable second-order interval plant family with time delay. Using a constructive procedure based on the Hermite-Biehler theorem, we obtain all the Proportional-Integral-Derivative gains that stabilize the uncertain and unstable second-order delay system. Genetic Algorithms (GAs) are utilized to optimize the three parameters of the PID controllers and the three parameters of the system which provide the best control that makes the system robust stable under uncertainties. Specifically, the method uses genetic algorithms to determine the optimum parameters by minimizing the integral of time-weighted absolute error ITAE, the Integral-Square-Error ISE, the integral of absolute error IAE and the integral of time-weighted Square-Error ITSE. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example.

show abstract

Section: Introductionmentioning

confidence: 99%

Optimal Robust Control for Unstable Delay System

Farkh¹,

Ksouri²,

Bouani³

2021

Computer Systems Science and Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…18 The Kharitonov region in the PID parameter space is computed, which is the set of PID parameters stabilizing the parameter uncertain processes. 19,20 Nevertheless, it should be noted that the Kharitonov theorem does not directly address the control performance issues for PID design. Another drawback of the Kharitonov-based methods is that they can hardly deal with the uncertainty of time delay.…”

Section: Introductionmentioning

confidence: 99%

“…A significant number of PID design methods for parameter uncertainty are based on Kharitonov’s theorem, which investigates the stability region of interval processes (with fixed delays) . The Kharitonov region is computed, which is the set of PID parameters that can stabilize the parameter uncertain processes. , Nevertheless, it should be noted that Kharitonov’s theorem does not directly address the control performance issues for PID design. Another drawback of Kharitonov-based methods is that the uncertainty in time delay is not addressed.…”

Section: Introductionmentioning

confidence: 99%

Robust Proportional–Integral–Derivative (PID) Design for Parameter Uncertain Second-Order Plus Time Delay (SOPTD) Processes Based on Reference Model Approximation

Gao

Zhang

Yang

et al. 2017

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

To design robust PID controllers for second-order plus time delay (SOPTD) processes with parameter uncertainty, a reference model approximation method is proposed in this study. The central idea is to enable the frequency response of the PID controller to approximate that of a user-specified reference model. A convex hull is utilized to approximate the frequency template of the parameter uncertain process, and the maximum approximation error of the reference model among all candidate processes is bounded. To guarantee that the PID

show abstract

“…However, these results are not applicable to the second order delay system. In [28,29], the stabilizing problem of PI/PID controller for second order delay system is analyzed and then used to obtain all PI and PID gains that stabilize a first and a second order delay interval systems [30,31] . In this paper, we employed a version of the HermiteBiehler theorem applicable to quasi-polynomials to investigate the complete set of stabilizing PI/PID parameters for unstable second order process with time delay.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

Farkh

Laabidi

Ksouri

2014

Int. J. Autom. Comput.

Self Cite

View full text Add to dashboard Cite

Abstract:In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative (PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.

show abstract

Robust PI/PID controller for interval first order system with time delay

Cited by 12 publications

References 40 publications

Optimal Robust Control for Unstable Delay System

Optimal Robust Control for Unstable Delay System

Robust Proportional–Integral–Derivative (PID) Design for Parameter Uncertain Second-Order Plus Time Delay (SOPTD) Processes Based on Reference Model Approximation

Stabilizing Sets of PI/PID Controllers for Unstable Second Order Delay System

Contact Info

Product

Resources

About