## Transfer Function from Difference Equations

## Transfer Function from Difference Equations

(OP)

If you had a difference equation model of say x(k+1) = 0.2x(k)+u(k) and y(k+1)=-0.4y(k)+x(k)+u(k-1), how would you develop a transfer function in the discrete time domain.

Likewise, working backwards, if you were given a transfer function in the continous domain of say (s+3)/(s^2+4s+16), sampled every 0.05s, how would you find a set of difference equations.

Thanks for your time.

Likewise, working backwards, if you were given a transfer function in the continous domain of say (s+3)/(s^2+4s+16), sampled every 0.05s, how would you find a set of difference equations.

Thanks for your time.

## RE: Transfer Function from Difference Equations

This is for what kind of application because it doesn't make much sense.

I looks like you just made this up.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: Transfer Function from Difference Equations

I did not make this up.

## RE: Transfer Function from Difference Equations

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: Transfer Function from Difference Equations

## RE: Transfer Function from Difference Equations

For instance a digital PID controller can be implemented as

u(n)=u(n-1)+K0*e(n)+K1*e(n-1)+K2*e(n-2)

where

K0=Ki*T+Kp+Kd/T

K1=-Kp-2*Kd/T

K2=Kd/T

So if I know K0,K1,K2 and T I can calculate Ki, Kp and Kd but why? Usually one starts with Ki,Kp, and Kd then calculates K0, K1, K2.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: Transfer Function from Difference Equations

## RE: Transfer Function from Difference Equations