PID controller synthesis for a class of unstable MIMO plants with I/O delays

Conditions are presented for closed-loop stabilizability of linear time-invariant (LTI) multi-input, multi-output (MIMO) plants with I/O delays (time delays in the input and/or output channels) using PID (Proportional+Integral+Derivative) controllers. We show that systems with at most two unstable poles can be stabilized by PID controllers provided a small gain condition is satisfied. For systems with only one unstable pole, this condition is equivalent to having sufficiently small delay-unstable pole product. Our method of synthesis of such controllers identify some free parameters that can be used to satisfy further design criteria than stability.

[1]  Tong Heng Lee,et al.  On the design of multivariable PID controllers via LMI approach , 2002, Autom..

[2]  K. Saadaoui,et al.  A new method for the computation of all stabilizing controllers of a given order , 2005 .

[3]  Tong Heng Lee,et al.  An improvement on multivariable PID controller design via iterative LMI approach , 2004, Autom..

[4]  Malcolm C. Smith.  On stabilization and the existence of coprime factorizations , 1989 .

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

[6]  Graham C. Goodwin,et al.  Control System Design , 2000 .

[7]  Jürgen Ackermann,et al.  Computing stable regions in parameter spaces for a class of quasipolynomials , 2003 .

[8]  M. Gevers,et al.  Simultaneous Stabilization of Three or More Plants: Conditions on the Positive Real Axis Do Not Suffice , 1994 .

[9]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[10]  Hitay Özbay,et al.  RESILIENT PI AND PD CONTROLLERS FOR A CLASS OF UNSTABLE MIMO PLANTS WITH I/O DELAYS , 2006 .

[11]  Wim Michiels,et al.  Stabilizing a chain of integrators using multiple delays , 2004, IEEE Transactions on Automatic Control.

[12]  M. Vidyasagar.  Control System Synthesis : A Factorization Approach , 1988 .

[13]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[14]  Allen Tannenbaum,et al.  Abstract model and controller design for an unstable aircraft , 1992 .

[15]  Wim Michiels,et al.  Static output feedback stabilization: necessary conditions for multiple delay controllers , 2005, IEEE Transactions on Automatic Control.

[16]  Shankar P. Bhattacharyya,et al.  PID Controllers for Time Delay Systems , 2004 .

[17]  Bernard Friedland,et al.  Control System Design: An Introduction to State-Space Methods , 1987 .

[18]  G. Stein,et al.  Respect the unstable , 2003 .