Poportional error squared example

[bubulescu]

Hello,

I have to admit that this is the first time I hear about a "proportional-error-squared" controller, with the basic transfer function like in the first attachement. I searched the net for a practical approach because, judging by its formula, the block level schematic that I could "translate" was ...ridiculous. But I could only find an old patent about a **broken link removed**.

So, I ask you, does anyone know more about them?

 

[Emanuel_hr]

From what i can see, the regulator described in the patent is different from this one, that is a linear regulator whereas this one is non-linear. You can consider it a kind-of adaptive algorithm, at high errors gives a greater command, this should improve response time, but it could be a problem though. A simulation should clear things up.

 

[bubulescu]

Yes, the difference is the problem. Well, I could implement two PI in parallel and multiply the outputs, as a brute force method, or I could stick to the barbaric way of implementation that I did in the first place, that is with abs() and multiplications and integrator.
Well, the lack of anything better means simulations, indeed. Thanks for the answer.

 

[bubulescu]

Right, I did a brute-force implementation and, after a bit of tampering with the values (I still don't know any way of calculating the components), thess are the results -- see the attachements. The red waveform, v(s), is the input signal, the blue one, v(i) is the reference and the green one, v(o), the output.
kw is "a weighting factor", but it seems to only have an effect on offset. kp is the DC gain and tau being the time constant. Now, if I wanted the response to be as symetrical as possible, looking like a brace, then tau would have to be something like 20s(!) for a 1s run time. The second screenshot shows this better. the large "S" form v(o) is for tau=20m, the almost symmetrical one (the thinnest) is for tau=20s.

As a practical thought I want to replace a classical PI controller in an inverter stage, voltage mode, with a DC capacitor needed to be regulated. Not that it doesn't work, after all, it's tried and tested over time, but the ripple (2x50Hz, as in the simulation) is superimposing on the rest of the signals, which yields slight distorsions in the output sinewave (3rd harmonics) -- unacceptable, since it's meant to be pure sine. So, if the ripple gets bigger as the load increases, the error wouldn't add up to the output proportionally. This thesis, found online, has some reference to the controller: "Juha Turunen - Series Active Power Filter in Power Conditioning".


So, rather than trying this in the most basic, crude, empyrical way, I'd still like to know if there is somewhere where I can find some explanations and, maybe, some ideas how to implement it practically. Does anyone know where? At this point, I know it's a nonlinear controller, PI-based, but the calculations are foreign to me now so, here I am, asking for some directions.