Computation of robustly stabilizing PID controllers for interval systems

The paper is focused on the computation of all possible robustly stabilizing Proportional-Integral-Derivative (PID) controllers for plants with interval uncertainty. The main idea of the proposed method is based on Tan’s (et al.) technique for calculation of (nominally) stabilizing PI and PID controllers or robustly stabilizing PI controllers by means of plotting the stability boundary locus in either P-I plane or P-I-D space. Refinement of the existing method by consideration of 16 segment plants instead of 16 Kharitonov plants provides an elegant and efficient tool for finding all robustly stabilizing PID controllers for an interval system. The validity and relatively effortless application of presented theoretical concepts are demonstrated through a computation and simulation example in which the uncertain mathematical model of an experimental oblique wing aircraft is robustly stabilized.

[1]  Ibraheem,et al.  Decentralized automatic generation control of interconnected power systems incorporating asynchronous tie-lines , 2014, SpringerPlus.

[2]  Radek Matušů,et al.  Graphical analysis of robust stability for systems with parametric uncertainty: an overview , 2011 .

[3]  ASYMPTOTIC STABILITY OF AN EQUILIBRIUM P . OSITION OF A FAMILY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS , 2022 .

[4]  Samira Chouraqui,et al.  Neuro-fuzzy controller to navigate an unmanned vehicle , 2013, SpringerPlus.

[5]  Celaleddin Yeroglu,et al.  Computation of Stabilizing PI and PID Controllers using the Stability Boundary Locus , 2006 .

[6]  Nusret Tan,et al.  COMPUTATION OF STABILIZING PI CONTROLLERS FOR INTERVAL SYSTEMS , .

[7]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1995 .

[8]  Roberto Tempo,et al.  Extreme point results for robust stabilization of interval plants with first-order compensators , 1992 .

[9]  Zhengyun Ren,et al.  Computation of stabilizing PI and PID controllers by using Kronecker summation method , 2009 .

[10]  Aniruddha Datta,et al.  Design of P, PI and PID controllers for interval plants , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[11]  Ren Zhengyun,et al.  Computation of stabilizing PI and PID controllers by using Kronecker summation method , 2008, 2008 27th Chinese Control Conference.

[12]  Roman Prokop,et al.  Design of Robust PI Controllers and their Application to a Nonlinear Electronic System , 2010 .

[13]  B. R. Barmish,et al.  Extreme Point Results for Robust Stabilization of Interval Plants with First Order Compensators , 1990, 1990 American Control Conference.

[14]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[15]  Radek Matušů,et al.  Robust stabilization of interval plants using Kronecker summation method , 2010 .

[16]  Radek Matuš.  Calculation of all stabilizing PI and PID controllers , .

[17]  Neil Munro,et al.  Fast calculation of stabilizing PID controllers , 2003, Autom..

[18]  Aidan O'Dwyer,et al.  Handbook of PI and PID controller tuning rules , 2003 .

[19]  Shankar P. Bhattacharyya,et al.  A linear programming characterization of all stabilizing PID controllers , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[20]  Naresh K. Sinha,et al.  Modern Control Systems , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Sidhartha Panda,et al.  Design of Static Synchronous Series Compensator Based Damping Controller Employing Real Coded Genetic Algorithm , 2011 .

[22]  Shankar P. Bhattacharyya,et al.  Robust and Non-fragile PID Controller Design , 2001 .

[23]  L. R. Pujara,et al.  On computing stabilizing controllers for SISO interval plants , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[24]  Ashik Ahmed,et al.  Design of static synchronous series compensator based damping controller employing invasive weed optimization algorithm , 2014, SpringerPlus.

[25]  S. Bhattacharyya,et al.  A generalization of Kharitonov's theorem; Robust stability of interval plants , 1989 .

[26]  Radek Matušů,et al.  Robust Stabilization of Oblique Wing Aircraft Model Using PID Controller , 2015 .

[27]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .

[28]  Shankar P. Bhattacharyya,et al.  Linear Control Theory , 2009 .

[29]  J. Závacká,et al.  The Kronecker summation method for robust stabilization applied to a chemical reactor , 2011 .

[30]  Yilun Shang.  Consensus seeking over Markovian switching networks with time-varying delays and uncertain topologies , 2016, Appl. Math. Comput..