Avoiding feedback-linearization singularity using a quotient method — The field-controlled DC motor case

Abstract

Feedback linearization requires a unique feedback law and a unique diffeomorphism to bring a system to Brunovský normal form. Unfortunately, singularities might arise both in the feedback law and in the diffeomorphism. This paper demonstrates the ability of a quotient method to avoid or mitigate the singularities that typically arise with feedback linearization. The quotient method does it by relaxing the conditions on diffeomorphism, which can be achieved since there is an additional degree of freedom at each step of the iterative procedure. This freedom in choosing quotients and the resulting advantage are demonstrated for a field-controlled DC motor. Using a Lyapunov function, the domain of attraction of the control law obtained with the quotient method is proved to be larger than the domain of attraction of a control law obtained using feedback linearization.

Controlled zero dynamics feedback linearization with application to free-floating redundant orbital manipulator

“…Among the numerous new theoretical works, Wilson et al proposed a method of avoiding the singularity in feedback linearization with using quotient method [2], Menini et al formulated a feedback linearization without a controllability assumption [3]. Interesting example of applications is a work of Rehman et al which presents a feedback linearization control system for hypersonic flight vehicle [4].…”