In order to estimate the critical temperature ratio (CTR) of thermoacoustic engines experimentally, a constant oscillation control method which regulates the pressure amplitude to a reference (constant) value has been proposed: the control system has a non-negative state variable of the pressure amplitude; the control law is of a proportional-integral (PI) controller driven by the tracking error; the output of the PI controller is utilized as a time-varying gain in driving signal of a loudspeaker to absorb or inject a power in the acoustic tube. A condition on PI gains for the equilibrium point to be asymptotically stable has been derived, which was agreed with the stability condition in experiments. In this paper, we focus on the fact that the closed-loop system with the zero P-gain becomes a marginal stable system of which differential equation is in separation of variables, a Lyapunov function candidate is constructed by modifying the initial-condition dependent constant of the system. As a result, global asymptotic stability is shown on the basis of the Lyapunov stability criterion without linear approximation.

This paper presents a design framework for individualization of control system. Controllers in products are designed for the average user in general. To increase the control performance for a particular person, individual design of controller is required. However, design controller for individual users involve costs. The words “Internet of Things” is used in recent years. It is expected that low cost customization of the control system using individual characteristics observation and application of information of the individual characteristics for control system design. This propose a concept of the design framework of control systems for individual user based on individual user's parameters.