# compensator/actuator relationship

#### suzuki

Joined Aug 10, 2011
119
hi,

i am designing a control loop that uses a VCO (voltage controlled oscillator) as the actuator to control the plant. the vco is already a pre-designed product and for the frequency range i am interested in, i know that i need to input some number (not necessarily an integer) to the VCO input, to get the desired frequency. for those curious, the range is between 3V and 11V.

my question is, how can i generate these "numbers" so that i can get the appropriate frequency for my plant? i have a control loop which is calculating an error voltage, but this number is in the range of mV. I don't think the solution is as simple as scaling this value either.

So, i'd like to know of there is there a way i can get my compensator to output the "correct" voltage for me? Im not sure if this is possible (and what parameters in a compensator would actually affect this) and how this would affect the stability of my closed loop system.

tia

#### SgtWookie

Joined Jul 17, 2007
22,221
Is there no relationship between the control loop error voltage output, and the required input voltage range?

If there IS a definite relationship, then some form of circuit could be designed to adapt your mV output to the several-volts input.

However, you need to tell us what the range of the error voltage output is, and how that corresponds to what is needed in the way of the input voltage.

If there is no correlation between the two, I don't know how you're going to use the control loop.

#### steveb

Joined Jul 3, 2008
2,436

One posible solution is to use a very high gain with a roll-off at higher frequency, such as from an opamp. The small mv error would then get amplified to produce a voltage in the range of 3 to 11 V. However, instability is the more likely outcome, althought we need the details to be sure.

Another solution could be a smaller gain with an offset that puts the output in the center of the 3 to 11 V range. This might give better stability, but might also give poor control if the gain is too low. Again, we need to know the details to be sure.

Another solution could be to use a proportional-integral control (or similar variant; PI, IP PID etc.) to give stability and zero DC error. The integrator will automatically wind up to give the offset you need to be in the 3 to 11 V range, but deliberately introduced offset can also help to speed up the transient response at startup.

There may be other compensation options as well, depending on the details.

#### suzuki

Joined Aug 10, 2011
119
for the time being, i cannot think of a direct/obvious relationship between the error and the 3 to 11V value.

I actually have a PID controller in place, but the output value it produces seems to be meaningless to me. (it is in the range of 0.03mV) i suppose you could say that the problem is that i cannot find a set of gains that will produce the required input (3 to 11V) i need for the VCO.

At the same time, this vco controls what my output voltage is, but it keeps getting the wrong values, so it seems to me that its having a perpetual error. i.e wrong vco input ---> wrong vco output ---> wrong output voltage ---> wrong vco input again

#### mcasale

Joined Jul 18, 2011
210
There's lots of details missing here. What is the "plant"? What is its time constant(s)? Your compensator can only be chosen after you know the frequency response of the "plant". It should attempt to cancel out its dominant pole (ie time constant). Also, what is your feedback sensor? Does it have a delay or pole, too?

You can amplify the sensor signal to match whatever the setpoint signal is, or you can do the amplifying in the error (PID) amplifier.

Control systems can get tricky. Good luck.

#### crutschow

Joined Mar 14, 2008
27,718
Your PID controller is obviously not generating an error signal. What is the input signal level to the controller?

#### suzuki

Joined Aug 10, 2011
119
There's lots of details missing here. What is the "plant"? What is its time constant(s)? Your compensator can only be chosen after you know the frequency response of the "plant". It should attempt to cancel out its dominant pole (ie time constant). Also, what is your feedback sensor? Does it have a delay or pole, too?

You can amplify the sensor signal to match whatever the setpoint signal is, or you can do the amplifying in the error (PID) amplifier.

Control systems can get tricky. Good luck.
I have the FR of the plant already, and it is in the shape of a low pass filter FR.

what does it mean to cancel out the dominant pole? since my last post (i forgot i had made this thread), i have done some research on regulator/compensator design and what i understand is that i need to find a crossover frequency and then find gain and phase margins that are satisfactory (approx 45-60 degrees for PM and >10dB for GM)

ive read numerous times that the suggested "practical" choice for the crossover frequency is 1/10 (or less) of the switching frequency, but im not sure if this applies to all cases. For example, i plan to operate at 100-120Hz, but if my crossover is at 10Hz, it is not necessarily guaranteed that i will have enough phase margin in my operating region. My gut feeling is that it is more important to have stability in your operating region than at other points, so i have chosen my fc value to at around 100Hz instead. I'm not sure if this is the correct choice, so if anyone can confirm, that would be great.

My other question is about gain margin. i am still playing around with this, but after satisfying my phase margin requirement, i find that the corresponding gain margin is quite large (around 80dB). I looked at my impulse response, and there is a huge overshoot, and i think it is caused by the gain margin, but i'm not quite sure how to reduce the gain margin as it would affect my phase margin and i think the crossover frequency as well. i played around with a "derivative" term, but was not getting exactly what i was looking for.

thanks again for all the replies.

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#### suzuki

Joined Aug 10, 2011
119
i played around with the parameters, again, but as you can see, the step response is still kind of strange. In the bode, what i tried to do was put a lead compensator in my desired operating range so that it will have 45 degree PM during operation. Again, to achieve this, i could not use the "typical" switching frequency/10 rule. (the phase lead would not cover that portion of the spectrum) And as can be seen, as the plot reaches -180 as frequency goes to infinity, the gain margin of the becomes really high, and i think this is affecting my step response.

#### crutschow

Joined Mar 14, 2008
27,718
I see no posted plots from your latest simulations.

#### suzuki

Joined Aug 10, 2011
119
edit: and i suppose just to clarify my question (for my own sake), i guess what i want to know is how can i adjust the output of my compensator circuit (which IMO, is no longer the error voltage, or anything meaningful for that matter) to be a useful input for an actuator? i.e. how can i map 1e-3 to be equal to 4.7V or 1.3e-3 to be equal to 5V?

i suppose there is the possibility of increasing the gain with the risk of losing stability as steveb mentioned, but i am wondering if there is some more "elegant" solutions to this problem?

btw ,i hope the above plots answer some of the questions of the other posters.

thanks again

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