Feedback control for oscillations with CPG architecture

This paper presents a method for designing a nonlinear feedback controller for a linear plant to achieve an oscillation with a prescribed profile as a projection of a stable limit cycle of the closed-loop system. The controller architecture is based on the central pattern generator, a biological oscillator composed of interconnected neurons that control rhythmic body movements during animal locomotion. The nonlinear control design problem is reduced, approximately, to a linear eigenstructure assignment problem through describing functions and the multivariable harmonic balance method. We then provide a necessary and sufficient condition for existence of a feasible controller assigning a given eigenstructure, as well as a parametrization of all such controllers. A numerical example demonstrates the efficacy of the proposed design method.