Rejection of nonharmonic disturbances in nonlinear systems via the internal model approach

Abstract

This paper proposes an asymptotic rejection algorithm for rejecting exotic disturbances in nonlinear systems. Disturbances produced by nonlinear exosystems are nonharmonic and periodic. The proposed algorithm extends the rejection of nonlinear disturbances for nonlinear dynamic systems from systems in the strict feedback form and output feedback form to general nonlinear systems. A new nonlinear internal model is proposed to deal with these disturbances. Furthermore, a state feedback controller is designed to ensure that the system’s state variables asymptotically converge to zero, and disturbances can be completely rejected. The proposed algorithm has various applications, such as active vibration control. The proposed algorithm is demonstrated to completely reject the nonharmonic periodic disturbances produced by a van der Pol oscillator.

Keywords

Disturbance rejection global stability internal model approach nonharmonic periodic signal vibration control

Get full access to this article

View all access options for this article.

References

Bodson

Douglas

(1997) Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequencies. Automatica 33: 2213–2221.

Byrnes

Isidori

(2004) Nonlinear internal model for output regulation. IEEE Transactions on Automatic Control 49: 2244–2247.

Chen

Ding

Lennox

(2008) Rejection of nonharmonic disturbances in nonlinear systems with semi-global stability. IEEE Transactions on Circuits and Systems Part II: Express Briefs 55: 1289–1293.

Chen

Huang

(2005) Robust output regulation with nonlinear exosystems. Automatica 41: 1447–1454.

Ding

(2006) Output regulation of uncertain nonlinear systems with nonlinear exosystems. IEEE Transactions on Automatic Control 51: 498–503.

Ding

(2007) Asymptotic rejection of unknown sinusoidal disturbances in nonlinear Systems. Automatica 43: 174–177.

Teel

(2007) Characterization of forced vibration for difference inclusions: A Lyapunov approach. IEEE Transactions on Circuits and Systems I: Regular Papers 54: 1367–1379.

Huang

(2004) Nonlinear Output Regulation: Theory and Application. Philadelphia, PA: SIAM.

Huang

Chen

(2004) A general framework for tackling the output regulation problem. IEEE Transactions on Automatic Control 49: 2203–2218.

10.

Huang

Rugh

(1990) On a nonlinear multivariable servomechanism problem. Automatica 26: 963–972.

11.

Isidori

(1995) Nonlinear Control Systems, 3rd ed. Berlin: Springer.

12.

Isidori

Byrnes

(1990) Output regulation of nonlinear systems. IEEE Transactions on Automatic Control 35: 131–140.

13.

Khalil

(2002) Nonlinear Systems, 3rd ed. New Jersey: Prentice-Hall.

14.

Leyva-Ramos

Escobar

Martinez

Mattavelli

(2005) Analog circuits to implement repetitive controller for tracking and disturbance rejection of periodic signals. IEEE Transactions on Circuits and Systems Part II: Express Briefs 52: 466–470.

15.

Marino

Santosuosso

Tomei

(2003) Robust adaptive compensation of biased sinusoidal disturbances with unknown frequencies. Automatica 39: 1755–1761.

16.

Ding

(2007) Global adaptive output regulation of a class of nonlinear systems with nonlinear exosystems. Automatica 43: 143–149.