Updated, Op-Amp based control-loop, help with simulation

Look again at the transfer function-- wrt the reference input the transfer function with the feedback = 0 is 1 + k/s not k/s. If you do a longer simulation you'll see the integrator ramp up after the initial step to Vref. The time to reach Vref is indeed determined by op-amp parameters (slew rate mainly).

Best regards, Spehro Pefhany

The difference is because your spice does not model an ideal integrator. The step on the reference goes straight through with a gain of 1, rather than being integrated. Move the pulse input to the inverting input (with a 10k resistor to change the voltage to a current but maintain a gain of 1, well -1, anyway), and you will see something very much closer to what Matlab predicts (except inverting).

Yes, and ideal integrator controller subtracts the process measurement from the setpoint and integrates that difference to produce the control output.

Which way the subtraction takes place (which of the two terms being added has a negative sign preceding it, or which is subtracted from the other) depends on whether the process responds directly or reversely to the control output.

Direct response would mean that an increasing control output drives an increasing process measurement. A reverse acting process would mean that a greater control output produces a decreasing process measurement. Any general controller must handle either of those cases.

In this example, I think you have been assuming that the process is just a copy of the controller output (direct acting with a gain of 1), so you are really just feeding the controller output back as the process measurement.

There has to be one inversion in that feedback process, to make it a negative feedback controller. So either you subtract the process measurement from the setpoint and do a non inverting integration of that difference to produce the controller output, or you subtract the setpoint from the process measurement and use an inverting integrator to produce the controller output from that difference. Either way, you get one inversion from process measurement to controller output.

If you follow my directions it the last post, you will be using an inverting integrator, and subtracting the setpoint from the process measurement. You would need an additional opamp inverter to add the negative sign to the setpoint, to you to input a non inverted setpoint.

You could also use that additional opamp to make a subtractor (that takes 4 resistors) to produce an error voltage and integrate that output. This is the more obvious form and easier to generalize to other controllers.

Integrators are inherent low pass filters. Adding more filtering in the feedback loop from output back to process measurement input will produce phase delay that will make the controller less stable. If you want to slow the response to setpoint changes, you can add all the filtering to that input you like before producing the error term to be integrated. If you want lower controller bandwidth, I suggest you just increase the size of the integrator cap so that the integration proceeds with a lower gain factor.

They are assuming that Vref (the setpoint) is fixed, so the response to changes in it don't matter. Their Rbias resistor is essentially the variable setpoint input I have been describing.

I'll look around, and maybe, get back to you on that.

John, Spehro,

In article ,

I see your points now, thank you. A few things still confused me, maybe these are dumb questions but I would appreciate some help.

1. If I want to build the "ideal" integrator control-loop, can I do it using one op-amp, or do I need another to generate the error term and feed that output to the integrator op-amp? I guess for an ideal integrator, the second op-amp would have V+ grounded.
2. If I continue to use my existing circuit, if I wanted to "limit" the bandwidth would I be remiss for just putting in a low-pass after the op- amp output?
3. I was following
   formatting link
   for some guidance on implementing op-amp based control-loops, figure 5.

I assume the transfer function they give is wrong since their implementation is like mine?

1. Are there any good resources on practical control-loop implementation using op-amps? I'm OK with control-loop theory, and I've done a few closed-loop designs digitally, never fully in the analog world. I'm finding too many articles that are dumbed down introducing PID (which I'm OK with), neglecting some of the salient points in using op-amps for this kind of stuff.

Thanks Rob.