Final answer:
To determine the state variable model from the given transfer function, we would convert it into a set of differential equations, forming the state-space representation. Matrices A, B, C, and D describe this system, involving assigning state variables for each integrator based on the transfer function order.
Step-by-step explanation:
To determine the state variable model from a given transfer function Y(s)/R(s). To create a state variable model, we would typically rewrite the transfer function into a set of first-order differential equations that represent the system in the time domain. However, without further context or system descriptions, it is not possible to provide the exact steps. We would usually look for the matrices A, B, C, and sometimes D that describe the state-space representation of the system, expressed as:
- ∆x(t) = Ax(t) + Bu(t)
- y(t) = Cx(t) + Du(t)
To find these matrices, you may need to decompose the transfer function into partial fractions if applicable, then assign state variables to each integrator in the system. For a third-order denominator as seen in the provided transfer function, you would generally have three state variables.