Robust PI-D controller design for descriptor systems using regional pole placement and/or H 2 performance

Vojtech Veselý; Ladislav Körösi

Kybernetika (2020)

  • Volume: 56, Issue: 4, page 810-820
  • ISSN: 0023-5954

Abstract

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The paper deals with the problem of obtaining a robust PI-D controller design procedure for linear time invariant descriptor uncertain polytopic systems using the regional pole placement and/or H 2 criterion approach in the form of a quadratic cost function with the state, derivative state and plant input (QSR). In the frame of Lyapunov Linear Matrix Inequality (LMI) regional pole placement approach and/or H 2 quadratic cost function based on Bellman-Lyapunov equation, the designed novel design procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure the designer could use controller with different structures such as P, PI, PID, PI-D. For the PI-D’s D-part of controller feedback the designer could choose any available output/state derivative variables of descriptor systems. Obtained design procedure is in the form of Bilinear Matrix Inequality (BMI). The effectiveness of the obtained results is demonstrated on two examples.

How to cite

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Veselý, Vojtech, and Körösi, Ladislav. "Robust PI-D controller design for descriptor systems using regional pole placement and/or $H_2$ performance." Kybernetika 56.4 (2020): 810-820. <http://eudml.org/doc/297017>.

@article{Veselý2020,
abstract = {The paper deals with the problem of obtaining a robust PI-D controller design procedure for linear time invariant descriptor uncertain polytopic systems using the regional pole placement and/or $H_2$ criterion approach in the form of a quadratic cost function with the state, derivative state and plant input (QSR). In the frame of Lyapunov Linear Matrix Inequality (LMI) regional pole placement approach and/or $H_2$ quadratic cost function based on Bellman-Lyapunov equation, the designed novel design procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure the designer could use controller with different structures such as P, PI, PID, PI-D. For the PI-D’s D-part of controller feedback the designer could choose any available output/state derivative variables of descriptor systems. Obtained design procedure is in the form of Bilinear Matrix Inequality (BMI). The effectiveness of the obtained results is demonstrated on two examples.},
author = {Veselý, Vojtech, Körösi, Ladislav},
journal = {Kybernetika},
keywords = {descriptor system; robust PI-D controller; state derivative feedback; output feedback; pole placement},
language = {eng},
number = {4},
pages = {810-820},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust PI-D controller design for descriptor systems using regional pole placement and/or $H_2$ performance},
url = {http://eudml.org/doc/297017},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Veselý, Vojtech
AU - Körösi, Ladislav
TI - Robust PI-D controller design for descriptor systems using regional pole placement and/or $H_2$ performance
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 4
SP - 810
EP - 820
AB - The paper deals with the problem of obtaining a robust PI-D controller design procedure for linear time invariant descriptor uncertain polytopic systems using the regional pole placement and/or $H_2$ criterion approach in the form of a quadratic cost function with the state, derivative state and plant input (QSR). In the frame of Lyapunov Linear Matrix Inequality (LMI) regional pole placement approach and/or $H_2$ quadratic cost function based on Bellman-Lyapunov equation, the designed novel design procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure the designer could use controller with different structures such as P, PI, PID, PI-D. For the PI-D’s D-part of controller feedback the designer could choose any available output/state derivative variables of descriptor systems. Obtained design procedure is in the form of Bilinear Matrix Inequality (BMI). The effectiveness of the obtained results is demonstrated on two examples.
LA - eng
KW - descriptor system; robust PI-D controller; state derivative feedback; output feedback; pole placement
UR - http://eudml.org/doc/297017
ER -

References

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