A graphical method to analyze the transient responses of second-order relay-control systems subjected to periodic input is proposed in this paper. The phase-plane representation is employed in studying the behavior of system variables. There will be derived formulae showing the relation between the two points on the phase-plane, which give the position of a solution at the beginning and at the end of a certain definite interval of time, provided that the number of commutation of the relay element during the interval is less than or equal to one.
The behavior of system variables on the phase-plane is determined by using these formulae. By repetitive application of these formulae, the behavior of solutions can be investigated by every definite period of time, which is usually chosen equal to some multiples of half a cycle of input signal.
It is suggested that by using the method proposed in this paper, regions of initial conditions leading to different types of periodic oscillations may be determined.
抄録全体を表示