A circularly coupled oscillator system for relative phase regulation and its application to timing control of a multicylinder engine

In this paper, distributed systems that consist of many locally connected subsystems, especially oscillators, and produce linear state relations, such as a state difference, are treated. The relations are defined between two connected subsystems, where their references are also assigned as a goal behavior simultaneously. The problem is: how subsystem dynamics are constructed to converge the relations to their references by only use of local operations, and how these references are adjusted if they are unachievable. To solve the above problems, a mathematical description of the subsystem interactions are clarified by extending a method based on the gradient dynamics. Then, the reference adjustment is defined so that the subsystem interactions decreases. As an example of this formulation, the relative phase control of the circularly coupled oscillator system is considered, where the oscillation with the uniform phase lag should be achieved. This oscillator system is applied to the timing controller for the multicylinder engine, and its effectiveness is discussed based on the simulation results.