Optimal force-balance control of closed-loop sensing systems with time delay

Abstract

Differing from the response control in civil and engineering applications, the excitation in a closed-loop sensing system is unknown and the control is designed to balance and measure the unknown excitation in real time. In this paper, a novel optimal force-balance control for a closed-loop sensing system with time delay is proposed. By introducing the errors between the control force and the unknown input as new variables, the force-balance control problem is transformed into a response minimization one with a time delay. Then, the discretization method is applied, and the continuous time system with time delay is converted into an extended discrete system without time delay, from which the analytical expression of the optimal force-balance control force is obtained. To illustrate the effectiveness of the proposed control, the optimal control of a practical quartz flexible force-balance accelerometer (FBA) is solved as an application. Numerical results show that the proposed control can realize the accurate measurement of wide-band random acceleration signals with a time delay of up to 10 times of control period. Besides, the proposed control can also significantly inhibit the vibration response of the FBA while guaranteeing measurement accuracy, which will benefit the obtaining of a large dynamic measurement range as a sensing application.