Design of PI controllers for achieving time and frequency domain specifications simultaneously

Introduction. The research of linear dynamic systems of regulation of the process of biological purification of contaminated water with fractional regulators was conducted in order to determine the boundaries of D-domains of their global stability and to determine the space of the parameters of the adjustment of the fractional controller for fixed orders of the diereintegrators in its composition.Materials and methods. Studies were conducted on the stability of the automatic control of the water treatment process. Using the Dsplit method, we obtain analytical formulas that determine the limits of the region of stable stabilization of the "object" + "fractionalregulator" system.Result and discussion. Automatic control systems of fractional order are more precisely described by dynamic equations, in which the order of derivatives can be any number, valid and not only integer. Proportional-integral-differential (PID-) regulators that are widely used in practice of automation also fall under a fractional generalization, if in their structure, instead of ordinary integer derivatives and integrals, fractional analogues are used. The

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“…To select the region of stable system stabilization (control object with the controller) we use the D-split method, the parameters space [6].…”

Section: Resultsmentioning

confidence: 99%

Isolation of domains of stability of linear dynamic systems with fractional regulators

Лобок¹,

Goncharenko²,

Vykhrova³

et al. 2017

UJFS

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“…Here, all or some of the coefficients p i are the function of k p and k i depending on the order of N (s) and D(s) polynomials. The boundaries between the stability and instability domains in the parameter space P are defined by the following three parts [20]:…”

Section: Stabilization Using Fractional-order Pi λ Controllermentioning

confidence: 99%

“…Changing ω from 0 to ∞, a CRB curve is constructed in the (k p , k i )-plane using Equations (20) and (21).…”

Section: Stabilization Using Fractional-order Pi λ Controllermentioning

confidence: 99%

“…On the other hand, controller design for the systems containing uncertainties has been studied in [17,18]. More recently, a controller design technique based on the stability boundary locus has been given in [19,20]. However, the stabilization problems considered in these methods completely deal with systems dynamics whose behaviors are described by integer-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization using fractional-order PI and PID controllers

2007

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This paper presents a solution to the problem of stabilizing a given fractional dynamic system using fractional-order PI λ and PI λ D μ controllers. It is based on plotting the global stability region in the (k p , k i )-plane for the PI λ controller and in the (k p , k i , k d )-space for the PI λ D μ controller. Analytical expressions are derived for the purpose of describing the stability domain boundaries which are described by real root boundary, infinite root boundary and complex root boundary. Thus, the complete set of stabilizing parameters of the fractional-order controller is obtained. The algorithm has a simple and reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of fractional-order control systems.

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“…Jeng et al [9] designed PID controller based on plant step response data. Hamamci and Tan [10] proposed a tuning method based frequency domain specifications. Panda [11] proposed analytical method of PID tuning for various processes.…”

Section: Introductionmentioning

confidence: 99%

Design Of Pid Controller With Compensator Using Direct Synthesis Method For Unstable System

Atchaya¹,

Pandey²

2016

IJECS

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In industrial processes, unstable system produces undesirable peak overshoot. So, PID controller with compensator and set point filter is designed using direct synthesis method. The set point filter reduces the peak overshoot. PID controller with compensator improves the overall response of the system. In this method, the characteristics equation of the system with PID controller and a compensator is compared with a desired characteristics equation. A single tuning parameter is used to find controller parameters, compensator and set point filter.

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Design of PI controllers for achieving time and frequency domain specifications simultaneously

Cited by 61 publications

References 9 publications

Isolation of domains of stability of linear dynamic systems with fractional regulators

Isolation of domains of stability of linear dynamic systems with fractional regulators

Stabilization using fractional-order PI and PID controllers

Design Of Pid Controller With Compensator Using Direct Synthesis Method For Unstable System

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