Digital Pid Design for Maximally Deadbeat and Time-Delay Tolerance

Keel, L.H.; Rego, J.I.; Bhattacharyya, S.P.

doi:10.3182/20020721-6-es-1901.00141

Cited by 4 publications

(6 citation statements)

References 3 publications

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“…Example To have a geometric insight into the

K_{3}

critical points and the new characterization of the entire set of discrete PID controllers for a given plant, we consider the discrete PID control system shown in Figure 1 with the plant

z - italictransfer

function given by [42]

G_{p} ((), z) goodbreak= \frac{N_{p} ((), z)}{D_{p} ((), z)} goodbreak= \frac{100 z^{3} + 2 z^{3} + 3 z + 11}{100 z^{5} + 2 z^{4} + 5 z^{3} - 41 z^{2} + 52 z + 70}

For

ρ = 1

, we have

A ((), z) = z ((), z - 1) D_{p} ((), z)

and

B ((), z) = N_{p} ((), z)

, where the factor

z ((), z - 1)

A ((), z)

comes from the denominator of the

z - transfer

function of the digital PID controller. Thus, from Equation (11), we have the following polynomials associated with the real and imaginary parts of

A ((), z)

and

B ((), z)

.…”

Section: A New and Complete Characterization Of Stabilizing Discrete ...mentioning

confidence: 99%

“…The objective of this paper is to provide, in parallel manner to the continuous-time case [38], a discrete PID controller design procedure based on the characterization of stabilizing set for maximizing stability margins. A PID controller designed to achieve a maximum stability margin provides stability robustness when the plant is subject to parametric and/or operating variations and maximally deadbeat time responses [42] for set-point changes. To achieve this goal, we present a new and complete characterization of entire set of stabilizing discrete PID controllers for a given plant.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, digital PID controllers are now extensively used in various fields of control applications. The characterization of the complete set of stabilizing discrete PID controllers and its applications have also been studied by several authors [40–51]. Using the bilinear transformation

z = ((), w + 1) / ((), w - 1)

and the parameter substitution

k_{i} = k_{s} - k_{p}

, Xu et al [40] have extended the continuous‐time approach to construct stabilizing discrete PID controller sets.…”

Section: Introductionmentioning

confidence: 99%

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Design of discrete PID controllers for maximizing stability margins

Guo

Hwang

2022

Asian Journal of Control

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The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed-loop poles being inside the circle of radius ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number ε, a minimum value ρ Ã ε and the corresponding ρ Ã ε À stabilizing discrete PID controller set for achieving at least 1 À ρ Ã ε of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability-margin discrete PID controller design, two numerical examples are provided.

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“…Example To have a geometric insight into the

K_{3}

critical points and the new characterization of the entire set of discrete PID controllers for a given plant, we consider the discrete PID control system shown in Figure 1 with the plant

z - italictransfer

function given by [42]

G_{p} ((), z) goodbreak= \frac{N_{p} ((), z)}{D_{p} ((), z)} goodbreak= \frac{100 z^{3} + 2 z^{3} + 3 z + 11}{100 z^{5} + 2 z^{4} + 5 z^{3} - 41 z^{2} + 52 z + 70}

For

ρ = 1

, we have

A ((), z) = z ((), z - 1) D_{p} ((), z)

and

B ((), z) = N_{p} ((), z)

, where the factor

z ((), z - 1)

A ((), z)

comes from the denominator of the

z - transfer

function of the digital PID controller. Thus, from Equation (11), we have the following polynomials associated with the real and imaginary parts of

A ((), z)

and

B ((), z)

.…”

Section: A New and Complete Characterization Of Stabilizing Discrete ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

z = ((), w + 1) / ((), w - 1)

and the parameter substitution

k_{i} = k_{s} - k_{p}

, Xu et al [40] have extended the continuous‐time approach to construct stabilizing discrete PID controller sets.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Design of discrete PID controllers for maximizing stability margins

Guo

Hwang

2022

Asian Journal of Control

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show abstract

“…This allows one to get a fixed number of poles to handle in the complex z-plane for pole placement based PID controller design [14], rather than a variable or [11]. Thus, mapping of the dominant pole placement design in discrete time, transforms the quasipolynomial in s-domain to a finite term rational polynomial in z-domain [15], [8], which can easily accommodate user's specifications using a coefficient matching method. Therefore, the dominant poles can now be individually mapped between the complex sz  domain after their locations are determined from the continuous time domain specifications, set by the control designer.…”

Section:  mentioning

confidence: 99%

“…Now, after mapping of the poles in (15) with sampling time Ts, the z-plane locations of the closed loop dominant and nondominant poles are:…”

Section: A All Non-dominant Real Polesmentioning

confidence: 99%

Delay Handling Method in Dominant Pole Placement Based PID Controller Design

Das

Halder

Gupta

2020

IEEE Trans. Ind. Inf.

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Time delay handling is a major challenge in dominant pole placement design due to variable number of poles and zeros arising from the approximation of the delay term. We propose a new theory for continuous time PID controller design using dominant pole placement method mapped on to the discrete time domain with an appropriate choice of the sampling time to convert the delays in to finite number of poles. The method is developed to handle linear systems, represented by second order plus time delay (SOPTD) transfer function models. The proposed method does not contain finite term approximations like various orders of Pade, for handling the time delays which may affect the number and orientation of the resulting poles/zeros. Effectiveness of the proposed method have been shown using numerical simulations on nine SOPTD testbench processes and another six challenging processes including single, double integrators and process with zero damping.

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Design of Digital PID Control Systems Based on Sensitivity Analysis and Genetic Algorithms

Perng

Hsieh

2019

Int. J. Control Autom. Syst.

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Digital Pid Design for Maximally Deadbeat and Time-Delay Tolerance

Cited by 4 publications

References 3 publications

Design of discrete PID controllers for maximizing stability margins

Design of discrete PID controllers for maximizing stability margins

Delay Handling Method in Dominant Pole Placement Based PID Controller Design

Design of Digital PID Control Systems Based on Sensitivity Analysis and Genetic Algorithms

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