From transfer function to differential equation

1. How do you write a differential equation from a transfer function?
2. How do you find the differential equation of a function?
3. How do you find the difference equation from Z transform?
4. How do you convert a transfer function to state space?

How do you write a differential equation from a transfer function?

Transfer Function to Single Differential Equation

To find the transfer function, first write an equation for X(s) and Y(s), and then take the inverse Laplace Transform. Recall that multiplication by "s" in the Laplace domain is equivalent to differentiation in the time domain.

How do you find the differential equation of a function?

Differential Equation

Taking an initial condition, rewrite this problem as 1/f(y)dy= g(x)dx and then integrate on both sides. Integrating factor technique is used when the differential equation is of the form dy/dx + p(x)y = q(x) where p and q are both the functions of x only.

How do you find the difference equation from Z transform?

In order to solve the difference equation, first it is converted into the algebraic equation by taking its Z-transform. Then, the solution of the equation is calculated in z-domain and finally, the time-domain solution of the equation is obtained by taking its inverse Z-transform.

How do you convert a transfer function to state space?

Probably the most straightforward method for converting from the transfer function of a system to a state space model is to generate a model in "controllable canonical form." This term comes from Control Theory but its exact meaning is not important to us.