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Robust PID ‐ PSD Controller Design: BMI Approach
Author(s) -
Veselý Vojtech,
Rosinová Danica
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.559
Subject(s) - pid controller , control theory (sociology) , mathematics , affine transformation , quadratic equation , mathematical optimization , computer science , engineering , control (management) , control engineering , temperature control , artificial intelligence , pure mathematics , geometry
A new robust proportional‐integral‐derivative ( PID )–proportional‐sum‐derivative ( PSD ) controller design method based on linear (bilinear) matrix inequalities ( LMI , BMI ) is proposed for uncertain affine linear system. The design procedure guarantees the parameter dependent quadratic stability, and guaranteed cost control with a new quadratic cost function ( LQRS ) including the derivative term for the state vector as a tool to influence the overshoot and response rate. The second approach to the PSD controller design procedure is based on a Lyapunov function with a special term corresponding to the time‐delay part of the control algorithm. The results obtained are illustrated on three examples to show the robust PID , PSD control design procedure and the influence of the choice of matrix S in the extended cost function.