Disturbance-observer-based LQR control of singularly perturbed systems via recursive decoupling methods

ABSTRACT

This paper addresses the disturbance-observer-based linear quadratic regulation (LQR) problem of singularly perturbed systems subject to harmonic disturbances. To reduce the computational burden and facilitate the on-board implementation, a recursive matrix decoupling method is proposed to decompose the stiff singularly perturbed model into the block-diagonal form. Then, a robust LQR controller is designed based on the equivalent decoupled system, which consists of a state feedback controller for performance optimisation and a robust controller for disturbance compensation. Moreover, the designed controller is integrated with a finite frequency disturbance observer to attenuate the effect of harmonic disturbances. Finally, a simulation example on a DC motor system is provided to verify the effectiveness of the proposed design method.

Keywords:

• Disturbance observer
• iterative algorithm
• LQR control
• singularly perturbed systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [61803156], the Natural Science Foundation of Shanghai [18ZR1409300], the China Postdoctoral Science Foundation [2017M620136], and the Fundamental Research Funds for the Central Universities [222201814044].