Discretization Method of Continuous-Time Dynamic Linear Model

Abstract

The article presents a new discretization method
of a continuous-time linear model of sensor dynamics. It can be useful to reduce measuring errors related to the inertia of the sensor. For example it is important in the measurement of rapid processes as temperature changes in combustion chambers, or for shortening the time needed to establish the sensor readings in a transition state. There is assumed that sensor dynamics can be approximated by linear differential equation or transfer function. The searched coefficients of equivalent difference equation or discrete transfer function are obtained from Taylor expansion of a sensor output signal and then on the solution of the linear set of equations. The method does not require decomposition of sensor transfer function for zeros and poles and can be applied to the case of transfer function with zeros equal to zero. The method was used to compensate the dynamics of sensor measuring fast signals. The Bode characteristics of a compensator were compared with others derived using classical methods of discretization of linear models. Additionally, signals in time were presented to show the dynamic error before and after compensation.