Optimal tracking with fixed order controllers

For discrete-time scalar systems, we propose an approach for designing feedback controllers of fixed order to minimize an upper bound on the peak magnitude of the tracking error to a given command input. The work makes use of linear programming to design over a class of closed-loop systems proposed for the rejection of non-zero initial conditions and bounded disturbances. Performance robustness in the form of a guaranteed upper bound on the peak magnitude of the tracking error under plant uncertainty is incorporated into the formulation.

[1]  M. Dahleh,et al.  Minimization of a regulated response to a fixed input , 1988 .

[2]  Boris Polyak,et al.  The use of a new optimization criterion for discrete-time feedback controller design , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  Robin J. Evans,et al.  Optimal pole placement design for SISO discrete-time systems , 1996, IEEE Trans. Autom. Control..

[4]  E. Mosca,et al.  Minimization of a closed-loop response to a fixed input for SISO systems , 1997, IEEE Trans. Autom. Control..

[5]  Boris T. Polyak,et al.  Robust stability and design of linear discrete-time SISO systems under l1 uncertainties , 1999, IEEE Trans. Autom. Control..

[6]  M. E. Halpern.  Modified pole-assignment controller for plant models with exact or near pole-zero cancellation , 1988 .

[7]  N. Elia,et al.  Robust performance for both fixed and worst case inputs , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[8]  S. Bhattacharyya,et al.  A technique for choosing zero locations for minimal overshoot , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[9]  Franco Blanchini,et al.  A convex optimization approach to fixed-order controller design for disturbance rejection in SISO systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[10]  Mustafa Khammash.  Robust performance: unknown disturbances and known fixed inputs , 1997, IEEE Trans. Autom. Control..

[11]  J. Pearson,et al.  l^{1} -optimal feedback controllers for MIMO discrete-time systems , 1987 .

[12]  M. Halpern.  Minimum magnitude response to a fixed input , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).