# Designing a circuit from a transfer function [linear control]

1. Nov 17, 2007

### Ian_Brooks

1. The problem statement, all variables and given/known data

Linear Control Systems - 2006 past paper

If I wanted to design a controller with a transfer function of the form

$$\frac{5(s+0.5)(s+2)}{s(s+10)}$$

How would I go about doing so?

2. Relevant equations

A constant gain is given as a constant
A differentiator will have an S term in the numerator
An integrator will have an S term in the denominator

3. The attempt at a solution

From the transfer function I can see that a Gain of 5 is used, and an integrator is required

How would i choose discrete circuit components to satisfy the above?

Basicly $$\frac{V_{out}}{V_{in}}$$ = $$\frac{(s+0.5)(s+2)}{(s+10)}$$

So some resistor and capacitor network would be needed to realize the remaining transfer function. And an integrator would be needed with some capacitor fed back.

2. Nov 17, 2007

### wildman

This is probably not what you are looking for, but I can tell you how to implement it digitally.
(I am a software geek and I don't know how to map a s plane transfer function into analog components -- sorry).

The way I would map it into digital hardware or software is to use the Bilinear Transform to map the transfer function into the z plane and then the time domain expression can be read out directly and easily implemented in hardware or software as shift registers. Matlab provides the function bilinear to do this conversion. Just make sure your sampling time is fast enough (2 times the highest frequency component).

3. Nov 17, 2007

### Ian_Brooks

well i have implemented it with software before in a course called real time instrumentation where we made digital filters and represented our transfer functions as difference equations - however, sadly i can't draw from that to get the 4 marks for this question.

any other help?