Dynamic Performance Characteristics, Part 2

Abstract

The first-order model discussed in chap. 6 is inadequate when there is more than one energy storage reservoir in the system to be modeled. If the sensor is linear it can be modeled with a higher-order dynamic performance model. Here the term ‘system’ refers to a physical device such as a sensor while the equation refers to the corresponding mathematical model. There exists a dual set of terms corresponding to consideration of the physical system or of the mathematical model. For example, an are coefficients of the mathematical model (see eqn. 8.1) but they also represent some physical aspect of the sensor being modeled; thus they can also be called system parameters. The general dynamic performance model is the linear ordinary differential equation where t = time, the independent variable, x = the dependent variable, an = equation coefficients or system parameters, and xi(t) = input or forcing function. This equation is ordinary because there is only one independent variable. It is linear because the dependent variable and its derivatives occur to the first degree only. This excludes powers, products, and functions such as sin(x). If the system parameters an are constant, the system is time invariant.