# Control System Gain design problem

1. May 18, 2014

### koochiee

Is it possible for a Type 0 Open Loop Transfer function to have 0 steady state error?
Context - Control System Gain design to meet a certain steady state error specification.

The open loop T.F - G(s)=3/(s^2 +4s+3) (This is type 0 (n=0))

The closed loop T.F is Gc(s)=G(s)/(1+KG(s)), But my problem is will changing the value of K or adding gain would make a difference? Because the Open loop T.F. is Type 0, the steady state error for 1. step i/p - constant
2. ramp & parabolic i/p - infinity, Any help is much appreciated. :)

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2. May 19, 2014

### donpacino

Typically 'H' is the feedback gain and 'K' is the amplifier before the plant, which is G in this case.

Are you sure you have your amplifier in the correct location?

3. May 19, 2014

### koochiee

And yes it is, the closed loop T.F is Gc(s)=G(s)/(1+KG(s)). Even after when I convert it to a unity feedback gain system it still is a type 0 system. Which can't have zero steady state error. And they're asking us to show that a gain (possibly in the forward path) of K+1 would enable it to maintain a zero steady state error.

4. May 20, 2014

### donpacino

with your system, you will always have a steady state error of 1/4*step input.

Now if your K was in the forward path (as in directly before the plant) then the steady state error for a step input would be step_input*(1/(1+3*k))

so if you made K infinitely large, the steady state error would approximately equal zero.

5. May 22, 2014

Thank you!