Integral Compensator Realization from Transfer Function

Question

I am trying to design a compensator based on the transfer function below

Gc(s)=(1.017E6s+4.969E9)/(s^2+4.884E5s)

The transfer function has a constant that is offsetting circuit gain, followed by a low frequency pole of (1+(wl/s)) and high frequency of (1/(1+(s/wh))), where wl is the low frequency and wh is the high frequency. I need to determine how to realize this with capacitors and resistors connected to an operational amplifier as in the included image. Please let me know if you have guidance/suggestions.

Answer 1

If you're asking for guidance then the circuit you posted is a 3rd order (it has three caps, three states), whereas your transfer function is a 2nd order (\$s^2\$ in the denominator). If you eliminate R2 and C1 from it you will have the circuit you need. Its transfer function is:

$$H(s):=\dfrac{\dfrac{1}{R_1C_2}s+\dfrac{1}{R_1R_3C_2C_3}}{s^2+\dfrac{C_2+C_3}{R_3C_2C_3}s} \tag{1}$$

I've written it compacted so you can see the similarity. All you have to do now is to equate all the terms in (1) with the numeric values in your transfer function, form a system of equations, then solve for the unknowns. Since you'll have 4 unknowns and 3 equations, you can impose one of them (e.g. R1).