The state-variable diagram provides a physical picture that is useful in understanding the state-variable concept. In addition, the differential equations relating the state variables are easily obtained by inspection of the diagram. A state-variable diagram consists of integrators, summing devices, and amplifiers. Outputs from the integrators denote the state variables. It should be noted that the state-variable diagram is the same as an analog computer simulation diagram .
Example 1. As an example of determining the state-variable diagram, consider a system whose transfer function is given by
Dividing numerator and denominator by s3, to obtain the result in terms of integrators:
Defining the error node of the control system to be E(s),
Eq. (2.223) may be rewritten as follows:
From Eq. (2.225) and the relation