6 - Framework for Modeling Agricultural Systems

Abstract

A model is a characterization of a real system. It may take the form of a drawing, a simple written verbal description, or may be a complicated set of equations to be used in the simulation of the system. The variables that are required for defining the mathematical model of a system are the time scale adopted for the system, input variables, state variables, and output variables. An input is anything admitted to the system either as physical objects or as information packages. States are traits that characterize the system, and outputs are anything produced by the system either in a physical form or as information packages, as a function of the state. Two types of functions, the free response and the forced response, represent the response of a linear system. The free response is the reaction of the system to initial conditions in the absence of inputs and the forced response is the system reaction due exclusively to inputs. The sum of the free and the forced response of the system are called the total response. A steady state is the response of the system when inputs and outputs are equal. A transfer function is the relation between the transform of the response function and the transform of the input function, when all the initial values are zero. Interactive coupled systems are systems interfacing by means of interconnected difference or differential equations. The number of interconnected equations corresponds to the number of components of the system.