Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case

This paper deals with the direct solution of the pole placement problem by state-derivative feedback for multi- input linear systems. The paper describes the solution of this pole placement problem for any controllable system with nonsingular system matrix and nonzero desired poles. Then closed-loop poles can be placed in order to achieve the desired system performance. The solving procedure results into a formula similar to Ackermann one. Its derivation is based on the transformation of linear multi-input systems into Frobenius canonical form by coordinate transformation, then solving the pole placement problem by state derivative feedback and transforming the solution into original coordinates. The procedure is demonstrated on examples. In the present work, both time- invariant and time-varying systems are treated.

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

[2]  Martin Hosek,et al.  Active Vibration Control of Distributed Systems Using Delayed Resonator With Acceleration Feedback , 1997 .

[3]  N. Peric,et al.  A comparative study of servosystems with acceleration feedback , 2000, Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy (Cat. No.00CH37129).

[4]  Sathya Hanagud,et al.  A COMPARISON OF H2 OPTIMIZED DESIGN AND CROSS-OVER POINT DESIGN FOR ACCELERATION FEEDBACK CONTROL , 1998 .

[5]  Jean Jacques Loiseau,et al.  Dynamics assignment by PD state feedback in linear reachable systems , 1994, Kybernetika.

[6]  W. Wonham,et al.  On pole assignment in multi-input controllable linear systems , 1967, IEEE Transactions on Automatic Control.

[7]  André Preumont,et al.  Active Damping of Optical Test Benches with Acceleration Feedback , 1993 .

[8]  Nejat Olgac,et al.  Efficient pole placement technique for linear time-variant SISO systems , 1995 .

[9]  Michael Valásek,et al.  Pole placement for linear time-varying non-lexicographically fixed MIMO systems , 1999, Autom..

[10]  D. Luenberger.  Canonical forms for linear multivariable systems , 1967, IEEE Transactions on Automatic Control.

[11]  Frank L. Lewis,et al.  A geometric theory for derivative feedback , 1991 .

[12]  M. Valasek,et al.  Pole-placement for SISO linear systems by state-derivative feedback , 2004 .

[13]  K. Hunt.  APPLIED OPTIMAL CONTROL AND ESTIMATION : DIGITAL DESIGN AND IMPLEMENTATION , 1993 .

[14]  Maxime P. Bayon de Noyer,et al.  Single Actuator and Multi-Mode Acceleration Feedback Control , 1998 .

[15]  Michael Valásek,et al.  Efficient eigenvalue assignments for general linear MIMO systems , 1995, Autom..

[16]  Frank L. Lewis,et al.  Applied Optimal Control and Estimation , 1992 .

[17]  W. Wonham.  On pole assignment in multi-input controllable linear systems , 1967 .

[18]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[19]  Michael Valášek,et al.  A Direct Algorithm for Pole Placement by State-derivative Feedback for Single-input Linear Systems , 2003 .

[20]  A. Preumont.  Vibration Control of Active Structures , 1997 .

[21]  O. R. Ainsworth,et al.  On the transformation to phase-variable canonical form , 1967 .