# How do you get the transfer function from the state space model?

## How do you get the transfer function from the state space model?

3.12 Converting State Space Models to Transfer Functions

1. Take the Laplace transform of each term, assuming zero initial conditions.
2. Solving for x(s), then y(s) (it should be noted that often D = 0)
3. where G(s) is a transfer function matrix.
4. or in matrix form (with m inputs and r outputs)
5. Example 3.9: Isothermal CSTR.

Can we derive transfer function from state space model?

Converting from state space form to a transfer function is straightforward because the transfer function form is unique. Converting from transfer function to state space is more involved, largely because there are many state space forms to describe a system.

How do you get state-space in Matlab?

sys = ss( A , B , C , D , ltiSys ) creates a state-space model with properties such as input and output names, internal delays and sample time values inherited from the model ltisys . sys = ss( D ) creates a state-space model that represents the static gain, D .

### How do you use the transfer function in Matlab?

Create the transfer function G ( s ) = s s 2 + 3 s + 2 : num = [1 0]; den = [1 3 2]; G = tf(num,den); num and den are the numerator and denominator polynomial coefficients in descending powers of s. For example, den = [1 3 2] represents the denominator polynomial s2 + 3s + 2.

What is transfer matrix of a control system?

In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. The matrix relates the outputs of the system to its inputs.

What is required to represent a system in state space?

The state space representation of a system is given by two equations : Note: Bold face characters denote a vector or matrix. The variable x is more commonly used in textbooks and other references than is the variable q when state variables are discussed.