Delay Handling Method in Dominant Pole Placement Based PID Controller Design

Das, Saptarshi; Halder, Kaushik; Gupta, Amitava

doi:10.1109/tii.2019.2918252

Cited by 28 publications

(43 citation statements)

References 33 publications

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“…However, for simulation purposes, we have also shown the time and frequency responses using different order of Pade approximation for highlighting the credibility of the method over existing literature. Recently, a similar dominant pole placement method based PID controller design has been proposed in (Das et al 2020) where the Euler's discretization formula was used for the PID controller. This paper differs in the methodology as compared to (Das et al 2020) since it uses a more accurate -Tustin's discretization formula for the PID controller.…”

Section: Discussionmentioning

confidence: 99%

Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling

Halder

Das

Gupta

2020

International Journal of Control

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This paper proposes a new formulation of proportional-integral-derivative (PID) controller design using the dominant pole placement method for handling second order plus time delay (SOPTD) systems. The proposed method does not contain any finite term approximation like different orders of Pade for handling the time-delay term, in the quasi-polynomial characteristic equation. Rather it transforms the transcendental exponential delay term of the plant into finite number of discrete-time poles by a suitable choice of the sampling time. The PID controller has been represented by Tustin's discretization method and the PID controller gains are obtained using the dominant pole placement criterion where the plant is discretized using the pole-zero matching method. A random search and optimization method has been used to obtain the stability region in the desired closed loop parameters space by minimising the integral squared error (ISE) criterion by randomly sampling from the stabilizable region and then these closed loop parameters are mapped on to the PID controller gains. Effectiveness of the proposed methodology is shown for nine test-bench plants with different lag to delay ratios and open loop damping levels, and the effect of choosing different sampling times, using credible numerical simulations.

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Section: Discussionmentioning

confidence: 99%

Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling

Halder

Das

Gupta

2020

International Journal of Control

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“…From substitution (6) the substitution for time variable, 3 3 t t c = , results. Thus, the delay length is expressed by the ratio 3 3 c   = (15) and this delay parameter is further referred to as laggardness number of the plant. Using the introduced similarity numbers the plant model ( 1) is transformed to the form point of the 1  , 2  , ϑ and K parameter space from where steady-state gain K can be still excluded as shown below.…”

Section:  =mentioning

confidence: 99%

“…and gain K is merged with the proportional, derivative and integration gains in (21). Then the P  , D  and I  are the loop gains absorbing the gain K and the filter time constant is in analogy with (15) expressed in dimensionless form…”

Section: Dimensionless Control Loop Descriptionmentioning

confidence: 99%

Filtered PID Control Loop for Third Order Plants With Delay: Dominant Pole Placement Approach

Fišer

Zı́tek

2021

IEEE Access

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The paper deals with tuning the filtered PID controller applied to third order plants with delay. This model option is chosen as a representative case where the loop characteristic quasi-polynomial is of higher order than three. Applying the similarity theory for introducing dimensionless parameterization a comparative model of third order plant dynamics is obtained. Four dominant polesfrom the infinite spectrum of the control loopare assigned by means of tuning three controller gains and a filter time constant where a specific argument increment criterion proves their dominance. The pole prescription coordinates are parameterized via damping, root and natural frequency ratios optimized in the space of the introduced similarity numbers according to the IAE criterion with respect to robustness and filtering constraints. Particularly the natural frequency ratio is a new parameter introduced to tune robustly the PID together with its filter. For the constrained IAE optimization the response of disturbance rejection is used as a representative of control loop behavior. In the space of similarity numbers of the plant it is shown that a limited range of plants is suited to be controlled on the PID control principle and the boundaries of this range are outlined. Survey maps of optimum controller parameters are presented and a comparative study on benchmark application example is added.

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“…Apart from the Ziegler-Nichols method, many efforts have concentrated on finding improved PID control synthesis methods. Some of them are related to classic control design approaches such as the frequency-domain [7] or root locus method [8] and other extensions for nonlinear plants [9], while other more sophisticated methods for PID control design aimed at improving performance are available under fractional order PID [10]- [12], or PID with time predictors [13]. Other related works have addressed the PID control synthesis by means of complex numerical optimizations [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Enhanced 2-DOF PID Controller Tuning Based on an Uncertainty and Disturbance Estimator With Experimental Validation

et al. 2021

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In this paper a novel tuning procedure for Two-Degree-of-Freedom (2-DOF) PID controllers is proposed. The tuning methodology is based on an Uncertainty and Disturbance Estimator. As a result, an equivalent 2-DOF PID controller with simpler tuning rules is obtained. One advantage of the proposed method is that tracking performance and disturbance rejection can be accommodated separately in control synthesis. Moreover, the trade-off between disturbance rejection and robustness can easily be adjusted by tuning a single parameter without affecting the desired set-point tracking specifications. Numerical comparisons with well-known tuning methods are performed to illustrate the advantages of the proposed method. Finally, the effectiveness of the proposal is experimentally validated in an open-loop unstable plant consisting of a test-bed quadrotor platform.

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Delay Handling Method in Dominant Pole Placement Based PID Controller Design

Cited by 28 publications

References 33 publications

Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling

Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling

Filtered PID Control Loop for Third Order Plants With Delay: Dominant Pole Placement Approach

Enhanced 2-DOF PID Controller Tuning Based on an Uncertainty and Disturbance Estimator With Experimental Validation

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