Natural entrainment of collocated mechanical systems via decentralized multi-agent feedback

This paper considers the design of feedback controllers for a class of collocated mechanical systems, aiming to achieve a natural mode of oscillation as a stable limit cycle of the closed-loop system. Motivated by recent results on central pattern generators, the controller is formed as a collection of multiple identical agents without direct communications to each other. Each agent is described as a transfer function followed by a static nonlinearity, and is placed between a sensor/actuator pair. Several simple linear dynamics are considered for the agents. The method of multivariable harmonic balance (MHB) is used to obtain approximate conditions for achieving entrainment to a natural oscillation, and numerical examples suggest that the proposed design conditions are fairly reliable in spite of sinusoidal approximations adopted in the MHB method. It is found that a band-pass filtering property is essential for the linear dynamics of each agent to achieve entrainment to an arbitrarily specified mode of natural oscillation.