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I am attempting to design a PR control feedback loop for a grid tie inverter. The math checks out but I can't seem to convert the transfer function and/or block diagram into an actual electrical circuit. Please find the block and transfer function attached. I would like to get an op amp circuit to implement this block diagram

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Normally you would find an op amp topology such as a sallen key:

enter image description here

which the transfer function would be

$$ H(s)=\frac{Z_3Z_4}{Z_1Z_2+Z_3(Z_1+Z_2)+Z_3Z_4}$$

And typically resistors \$ Z_x(s)=R\$ and capacitors \$ Z_x(s)=\frac{1}{Cs}\$ are used in these types of active filters.

There are also other realizable transfer functions that you can build with op amps:

enter image description here Source: slideplayer.com

However the transfer function you supplied is not realizable with general filters:

$$ H(s)=\frac{Ks}{s^2+w^2} \neq \frac{Z_3Z_4}{Z_1Z_2+Z_3(Z_1+Z_2)+Z_3Z_4}$$

because there is a middle term in the polynomial, no combination of high pass or low pass filters can used to construct your desired loop.

I will say this, an integrator is achieved this way with opamps:

enter image description here Source: electronics-tutorials.ws/opamp/opamp_6.html

$$ H(s)=\frac{1}{sRC}$$

So you could use that in your top and bottom portion of the loop.

If your looking to simply shift the frequency, then use a PLL, described here. Or a circuit such as an orthogonal signal generator

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That looks like a Second Order Generalized Integrator (SOGI). In LTspice, it would look like this:

sogi

Time domain response:

time

Frequency response:

freq

G1, R1 form the error amplifier, G2, C1 the first integrator, and G3, C2 the second. These are, usually, implemented in a DSP, since the control is done digitally, and since you'd normally need several stages of these, one for each harmonic.

There are several version of a SOGI, this one is the simplest, yours looks like it allows for correction with external \$\omega t\$ signal, others have a stabilized loop, other corrections, etc.

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    \$\begingroup\$ That's a strange looking op-amp. \$\endgroup\$ – Harry Svensson Apr 19 '18 at 11:57
  • \$\begingroup\$ @HarrySvensson It's a behavioural model, since I've mentioned that, usually, they're implemented in DSP software. But, yes, that's an integrator, and nobody says an integrator must be with an opamp. \$\endgroup\$ – a concerned citizen Apr 19 '18 at 12:16
  • \$\begingroup\$ By the way, this could be done with a single bv-source. Or if you really need the signals, three bv-sources. \$\endgroup\$ – Voltage Spike Apr 19 '18 at 18:48
  • \$\begingroup\$ @laptop2d I know, but the whole point is getting the signals, because it outputs a quadrature (the outputs of each integrator). \$\endgroup\$ – a concerned citizen Apr 19 '18 at 19:32

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