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Reduced gain pi/pid controllers for foptd/soptd processes under load disturbance

Bożek Andrzej, Trybus Leszek

Acta Mechanica et Automatica

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2024

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Vol. 18, no. 2

212--222

EN

In practical applications, an engineer is sometimes expected to execute the step test for tuning the controller without waiting much for the steady-state or a low level of disturbances. Hence, knowing that the initial settings may not be quite reliable, he/she detunes the controller by reducing its gain as a precaution against possible poor behaviour of the closed-loop system. It is up to their experience to choose by how much to detune. Therefore, the development of a practically oriented approach that would assist the engineer to choose the degree of gain reduction is the goal of this paper. The approach assumes that process parameters are determined by the least-squares approximation of the step response. Accuracy of the approximation is evaluated by a relative approximation error involving integrals of the error and the process response itself. The SIMC tuning rules are applied to choose the initial controller settings. The approach relies on detecting by simulation the worst case that may happen when the step response is triggered at any time. Detuning nomograms specify by how much to reduce the initial gain for PI-FOPTD and PID-SOPTD designs, given the relative approximation error. Two long-lasting lab experiments involving temperature control identify a plant, verify the load disturbance model through multiple step tests and demonstrate usage of the approach in the closed-loop system.

2

Krok dyskretyzacji i nastawy PID w dyskretnym serwomechanizmie napięciowym

Bożek Andrzej, Trybus Leszek

Pomiary Automatyka Robotyka

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2022

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R. 26, nr 1

5--10

PL

Przedstawiono metodę doboru kroku dyskretyzacji i nastaw dyskretnego regulatora PID dla modelu serwomechanizmu z silnikiem sterowanym napięciowo, opisanym jako integrator ze stałą czasową. Założeniem metody jest lokalizacja potrójnego bieguna układu zamkniętego, aby zapewnić gładkie przebiegi regulacyjne. Daną projektową stanowi czas regulacji. Zbadano, w jakim stopniu filtracja składowej różniczkującej regulatora skraca wymagany krok dyskretyzacji. Rozważono także rozszerzony problem projektowy z zadanym dodatkowo stopniem filtracji.

EN

A method for selection of discretization step and discrete PID controller settings is presented for a model of servo with voltage controlled motor, described by an integrator with time constant. The method assumes a triple pole location of the closed-loop system to provide smooth control transients. Settling time is a design data. Influence of filtering degree in controller derivative component on reduction of discretization step is examined. Extended design problem with the filtering degree being an additional requirement is also considered.

3

Tuning PID and PI-PI servo controllers by multiple pole placement

Bożek Andrzej, Trybus Leszek

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 1

art. no. e139957

EN

Tuning rules for PID and PI-PI servo controllers are developed using a pole placement approach with a multiple pole, i.e. a triple one in the case of PID and a quadruple for PI-PI. The controllers involve complex roots in the numerators of the transfer functions. This is not possible in the classical P-PI structure which admits real roots only. The settling time of the servos determined by the multiple time constant is the only design parameter. Nomograms to read out discrete controller settings in terms of the time constant and control cycle are given. As compared to the classical structures, the upper limit on the control cycle is now twice longer in the case of PID, and four times in the case of PI-PI. This implies that the settling times can be shortened by the same ratios. Responses of a PLC-controlled servo confirm the validity of the design.