Controls System Question

1. Jun 7, 2014

Lancelot59

I'm attempting to solve a control systems problem, however I'm stuck on the first step.

The system is specified with a difference equation:
$$y(k+2)+y(k+1)+0.16y(k)=u(k+1)+2u(k)$$

So I need to convert this back onto the usual pulse transfer function form to use one of the standard methods of deriving the matrix.

The thing is I can't get to the transfer function. Due to the k shifts there are all of the initial condition constant terms such as z*y(0) that don't appear in the solutions at all.

Neither the problem or the solution specify that those conditions are zero. Are the initial conditions just being ignored, or am I missing something here?

Thanks!

Last edited: Jun 7, 2014
2. Jun 9, 2014

rude man

By definition, a transfer function assumes zero initial conditions.

What matrix? Are you looking for the z transform?

3. Jun 9, 2014

Lancelot59

I need to get the whole system into some form of state space equation.

So I was going to take the z transform of that difference equation, then take the zeros and poles of that z domain transfer function to get the G and H matrices of the state space representation.

4. Jun 9, 2014

donpacino

Yes that is a correct method

note: I have always referred to the state space matrices as A,B,C & D.
I am assuming G & H are the system dynamics and input effects matrices respectivly

5. Jun 9, 2014

Lancelot59

Yes. For reference I'm using the Discrete Time Controls systems textbook by Ogata.