Control and trajectory tracking by flatness of a time-variant stator flux motor

By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Thus point of view has been used to enlighten the design of RST controllers in the linear system case with constant parameters. We will see in the present paper that in the case of time-varying linear systems thus point of view can also be adopted and leads to design a feedback in terms of the flat output and its derivatives. To implement this feedback a constant gain reduced order observer can be used. The observer poles are also chosen with respect to the trajectory to follow. All these developments are exemplified on a DC motor with a time-variant stator flux, and lead to a simple but powerfull control for tracking a given trajectory for the angular velocity of the motor.

[1]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[2]  Michel Fliess,et al.  A flatness based control synthesis of linear systems and application to windshield wipers , 1997, 1997 European Control Conference (ECC).

[3]  Mounir Ayadi,et al.  Polynomial controller design based on flatness , 2001, Kybernetika.

[4]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[5]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[6]  A. Isidori.  Nonlinear Control Systems , 1985 .

[7]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[8]  Thomas Kailath,et al.  Linear Systems , 1980 .

[9]  I. Horowitz.  Synthesis of feedback systems , 1963 .

[10]  Mounir Ayadi,et al.  Digital flatness-based robust controller applied to a thermal process , 2001, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204).

[11]  M. Fliess,et al.  On Differentially Flat Nonlinear Systems , 1992 .

[12]  J. A. Richards.  Analysis of periodically time-varying systems , 1983 .

[13]  Vladimír Kučera,et al.  Analysis and design of discrete linear control systems , 1991 .

[14]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[15]  L. Silverman,et al.  Transformation of time-variable systems to canonical (phase-variable) form , 1966 .

[16]  L. Silverman,et al.  Controllability and Observability in Time-Variable Linear Systems , 1967 .

[17]  Philippe Martin,et al.  A Lie-Backlund approach to equivalence and flatness of nonlinear systems , 1999, IEEE Trans. Autom. Control..

[18]  Karl Johan Åström,et al.  Solution Using Robust Adaptive Pole Placement , 1991 .