Evaluation of variance of time history response of the system based on time-constant analysis

The time history response and its variance of physical system are analyzed based on the functional model converted from physical domain to time-constant domain. Since a base unit of the model in time-constant domain is time, the relationship between the model and its time history response may be apparent for analysis of the response. This approach is firstly applied to the theoretical 1st and 2nd order system in time-constant domain and to give results: (1) a ratio of time-constant to input time of 1st and 2nd order system is an explanatory variable of the time history response and its variance, and thus (2) increasing the ratio can reduce the variance of time history response. This approach is then applied to a real system called the impact excitation system which converts input electrical energy to solenoid armature movement to excite a target plate. The measured time history responses of the system such as a current, armature velocity and impact force are analyzed by the corresponding functional model in time-constant domain and give results: (3) the rapid change of time history response and its variance of armature velocity and impact force at impacting on the target can be explained as a small time-constant of armature mass and contact stiffness relative to the input time, and thus (4) it is verified that the proposed approach can provide the insight for analysis and designing the time history response and its variance of physical system in an intuitive way.