Flatness-based linear output feedback control for disturbance rejection and tracking tasks on a Chua's circuit

Abstract

A linear output feedback controller is developed for trajectory tracking problems defined on a modified version of Chua's circuit. The circuit modification considers the introduction of a flat input, i.e. a suitable external control input channel guided by (a) the induction of the flatness property on a measurable output signal of the circuit and (b) the physical viability of the control input. A linear active disturbance rejection control based on a high-gain linear disturbance observer, is implemented on a laboratory prototype. We show that the state-dependent disturbance can be approximately, but arbitrarily closely, estimated through a linear high-gain observer, called a generalised proportional integral (GPI) observer, which contains a linear combination of a sufficient number of extra iterated integrals of the output estimation error. Experimental results are presented in the output reference trajectory tracking of a signal generated by an unrelated chaotic system of the Lorenz type. Laboratory experiments illustrate the proposed linear methodology for effectively controlling chaos.

Keywords:

• Chua's circuit
• linear control of chaotic systems
• observers

Acknowledgements

This work was supported by SIP-IPN México and CINVESTAV-IPN México.

Notes

Note

1. This assumption cannot be verified a priori when φ(·) is completely unknown. However, in cases where the nonlinearity is known except for some of its parameters, as it is the case of the Chua's system, its validity can be assessed with some work.