Pole assignment for linear and quadratic systems with time‐delay in control

SUMMARY We consider the pole assignment problems for time-invariant linear and quadratic control systems, with time-delay in the control. Closed-loop eigenvectors in X D Œx1, x2, ��� � are chosen from their corresponding invariant subspaces, possibly optimizing some robustness measure, and explicit expressions for the feedback matrices are given in terms of X. Condition of the problems is also investigated. Our approach extends the well-known Kautsky, Nichols, and Van Dooren algorithm. Consequently, the results are similar to those for systems without time-delay, except for the presence of the ‘secondary’ eigenvalues and the condition of the problems. Simple illustrative numerical examples are given. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  John E. Mottershead,et al.  State feedback control with time delay , 2009 .

[2]  Wen-Wei Lin,et al.  A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems , 2010, J. Comput. Appl. Math..

[3]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[4]  Tiexiang Li,et al.  A SCHUR-NEWTON ALGORITHM FOR ROBUST POLE ASSIGNMENT OF DESCRIPTOR SYSTEMS , 2008 .

[5]  John E. Mottershead,et al.  Partial pole placement with time delay in structures using the receptance and the system matrices , 2011 .

[6]  Tiexiang Li,et al.  Robust Pole Assignment for Ordinary and Descriptor Systems via the Schur Form , 2011 .

[7]  H. K. Tam,et al.  Pole assignment with minimum eigenvalue differential sensitivity , 1997 .

[8]  Y. Saad.  Projection and deflation method for partial pole assignment in linear state feedback , 1988 .

[9]  Chang-Chieh Hang,et al.  Approximate pole placement with dominance for continuous delay systems by pid controllers , 2008 .

[10]  E. Chu,et al.  Optimization and pole assignment in control system design , 2001 .

[11]  Jun Wang,et al.  A gradient flow approach to on-line robust pole assignment for synthesizing output feedback control systems , 2002, Autom..

[12]  Sylvan Elhay,et al.  POLE ASSIGNMENT IN VIBRATORY SYSTEMS BY MULTI-INPUT CONTROL , 2000 .

[13]  Gene H. Golub,et al.  Matrix computations , 1983 .

[14]  H. Faßbender,et al.  A STRUCTURED POLYNOMIAL EIGENPROBLEM ARISING IN THE ANALYSIS OF TIME DELAY SYSTEMS AND RELATED POLYNOMIAL EIGENPROBLEMS , 2007 .

[15]  Eric K-W Chu.  POLE ASSIGNMENT FOR SECOND-ORDER SYSTEMS , 2002 .

[16]  Biswa Nath Datta,et al.  Numerically robust pole assignment for second-order systems , 1996 .

[17]  N. Nichols,et al.  Robust pole assignment in linear state feedback , 1985 .

[18]  B. Datta,et al.  ORTHOGONALITY AND PARTIAL POLE ASSIGNMENT FOR THE SYMMETRIC DEFINITE QUADRATIC PENCIL , 1997 .

[19]  Biswa Nath Datta,et al.  Quadratic Partial Eigenvalue Assignment Problem with Time Delay for Active Vibration Control , 2009 .

[20]  K W E Chu.  A pole-assignment algorithm for linear state feedback , 1986 .

[21]  Tiexiang Li,et al.  A SCHUR-NEWTON ALGORITHM FOR ROBUST POLE ASSIGNMENT , 2007 .

[22]  K.-W.E. Chu.  A controllability condensed form and a state feedback pole assignment algorithm for descriptor systems , 1988 .

[23]  Mohsen Razzaghi.  A pole assignment technique for multivariable systems with input delay , 1986, Kybernetika.

[24]  A. Tits,et al.  Globally convergent algorithms for robust pole assignment by state feedback , 1996, IEEE Trans. Autom. Control..

[25]  K. Chu.  Approximate pole assignment , 1993 .

[26]  John E. Mottershead,et al.  Receptance Method in Active Vibration Control , 2006 .