Question

Represent the following transfer function in state space. Give your answer in vector-matrix form.

T(s) = s(s+2)/(s +1)(s² + 2s + 5)

Answer 1

To represent the transfer function T(s) in state space, we need to find the state variables and express T(s) as a vector-matrix form. The resulting state space representation includes the state matrix, input matrix, output matrix, and direct transmission matrix.

Step-by-step explanation:

To represent the given transfer function in state space, we need to first find the state variables. Let's assign x1, x2, and x3 as the state variables. Then, we can express the transfer function T(s) as:

T(s) = C*(sI - A)^-1*B + D

where A is the state matrix, B is the input matrix, C is the output matrix, and D is the direct transmission matrix.

By performing the necessary calculations, we can represent T(s) in state space as the following vector-matrix form:

x' = Ax + Bu

y = Cx + Du