Design of Positive Position Feedback Compensator(filter)

Design of Positive Position Feedback Compensator(filter)
Plant transfer function,P(s) = (-as-b)/(s^2 + 2*zeta*w + w^2)
PPF filter transfer function has the form,G(s) = g*wf^2/(s^2 + 2*zetaf*wf + wf^2)
The closed loop transfer function is T(s) = P(s)/(1-P(s)*G(s))
With the knowledge of P(s), can u suggest any method to determine the filter parameters : gain,g; damping ratio, zetaf; filter frequency, wf ?
I tried the pole placement technique, by equating the characteristic equation of T(s) to (s^2 + 2*zetac*w1 + w1^2)*(s^2 + 2*zeta*alpha*w1 + (alpha* w1)^2) and arrived at a set of non-linear equations.
Thank you
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Why must the controller have this form? This is a problem. There should be some zeros to help place the poles.

What do you want T(s) to be? This is important.

I have shown how to solve similar problems in previous posts this year. The format of the controller was much different.
Peter Nachtwey
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Are you there? You aren't here. You must be lost. Two more things: 1. The feed back is not positive. You just have a negative gain. Your plant doesn't look that much different from one of my hydraulic systems. In your case if the controller outputs a positive voltage the cylinder retracts instead of extends. 2. The feed back is not a position. It must be a velocity. Position feedback would have a pure integrator and be a type 1 system instead of a type 0 system. A position transfer function would look like:
P(s) = (-as-b)/(s*(s^2 + 2*zeta*w + w^2))
notice the extra s, integrator, in the denominator. What is wrong with this news group? I can tell no one else is paying attention or they would have pointed this out. Google claims there are 900+ people subscribed to this newsgroup. So is everyone clueless? Is this newsgroup dead? Is there intelligent life here?
Peter Nachtwey
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snipped-for-privacy@gmail.com wrote:
...

When I read about a controller whose primary feedback is positive, I move on. I've had more than my share of trying to converse with space aliens lately.
Jerry
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The aliens 'students' are every where. Actually, in these types of systems the derivative gain and/or second derivative gain can be negative or have postive feedback and yet be very stable and controllable. The characteristic equation can have all its pole on the negative real axis. Using the negative gains in the forward path causes the systems to have non-minium phase response which normally isn't desired. I have Mathcad examples of this too.
Peter Nachtwey
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On Aug 28, 9:12 pm, snipped-for-privacy@gmail.com wrote:

I don't mind the tag(alien) as long as i can learn something:-) . My plant is a thin aluminium cantilever beam with piezo electric sensors & actuators glued to it.The objective is vibration control. There's some research papers which show that 'Positive' Position feedback is stable:Fanson & Caughey1982. PPF filters are used in the control of flexible structures.A 2nd order PPF filter damps out the vibratory mode to which it is tuned. So I set out to see if the PPF technique would work for my plant...
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OK. you probably have a position system. This doesn't sound like a student question so why must the controller have the form you suggest. A PID should. A PID with a low pass filter may be better to cancel out the zero. If you are just interested in canceling out the vibration then a I-PD form will do. This mean the integrator is in the forward path and the P and D terms are in the feedback path only. This means the proportional and derivative gains are mulitplied by the changes in the actual postion. See this .pdf file from a previous thread ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20T0C1%20I-PD%20JCH.pdf I didn't show how I calculated the gains in this example all you need is the plant model, the desired response and formulas for placing the poles of the characteristic equations. The difference between your plant and JCH's plant is that yours has a zero and the gain is negative. If you solve for Ki, Kp and Kd symbollically then you can see that Kd can be negative if the location of the poles for the characteristic equation are close to 0. This is OK but if it is negative then Kd can only be used in the feedback path. The Ki and Kp gain should always be postive.
Do you have values for your plant? What kind of response to you require?
Peter Nachtwey
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snipped-for-privacy@gmail.com says...

Hello Peter! I'm back again In your above work You've writtne sth like this K ? (Kp Kd Kdd ) .................... u ? max[min[u + KiTe - K(x - xLast) , 10] , -10]
is it, that only Ki is in feedback path ?
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NO, just the opposite. The Ki gain is in the forward path because it is dependent on the error. The Kp and Kd are only in the feedback path because they are only dependent on the feed back or PV. Gains that are multiplied by the error are in the forward path. Gain multiplied by the PV or feedback are in the feedback path.
I still would like to have values for snovite's plants. I can assumed some values and show how to calculate the gains. Calculating gains is easy. The trick is to calculate the plant model.
Peter Nachtwey
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This is my plant (-0.0708s-2.687)/(s^2 + 0.5982s+ 1011) The sensor & actuator send/pick-up signals from a PC(MATLAB & dSPACE control desk) via a signal conditioning box. I m using 2 Piezo electric strips for sensing & actuating. external excitation: tap the free end of the beam lightly with a pencil(once)..the vibration is picked by the sensor.The control is such that the actuator induces vibrations in the opposite direction to the original- this results in destructive interference & hence vib suppression.
The first natural frequency of the plant is between 4.89 Hz - 5.1Hz:I want to damp the first mode vibrations.
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The basic problem is that you plant doesn't doesn't have enough gain. The controller gain must be cranked up high so the system goes into saturation with little error. If I knew what the position units or angle units were I could sanity check the results. Otherwise this is the best I could do. ftp://ftp.deltamotion.com/public/NG/Mathcad%20-%20T0C1%20snovite%20leadlag.pdf Notice the system will oscillate until the controller can control without going int saturation.
A simple derivative gain of -12 will also work nicely but it too suffers from the same saturation problem.
I haven't tried tuning to many plants with zeros so I learned a bit too.
Peter Nachtwey
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snipped-for-privacy@yahoo.com says...

Will it work if You make feed-forward control which send CV in natural frequency (initally, then in ratio to PV acceleration) and advanced in phase
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Feed forwards are gain mulitplied by the set point and its derivatives and added to the output. Since this is a damping system or regulator, the set point and its dervatives are 0. The questions I have is how big will the distrubances or initial value of x be? If the initial distrubance is too big the controller will saturate so its ability to dampen oscillations is limited.
Peter Nachtwey
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snipped-for-privacy@gmail.com says...

By feedforward I ment generating dumping signal, which is approximately inverse of transfer function.The signal could consist of natural frequency signal=f(phase(t),natfreq,Amplitude(t)) Then we need to create few fuzzy rules regarding dumping quality = f (phase) and f(amplitude) with this knowledge the system would know which direction to go in case of excessive error. The intersting part would be max system decceleration,phase shift betwen control signal and final steady error if applies. This method could distinquish between various environment changes. It has a kind of memory
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I told you what a feed forward is. Since the SP is always the steady state position then SP's derivatives are all 0. There is no feed forward term.
The signal could consist of natural

???? This sound like a lot of tweaking and coffee drinking to me. I can't think of any place where fuzzy logic should be used on a SISO system with a good transfer function available.
You and snovite are making this too difficult. If you thoroughly understand the basics of control then neither of you would be suggesting complicated control scheme for simple problems.

In my saturated example, the control output was doing all it could to stop the vibrations. What more can a control algorithm do? BTW, I did try changing the control output to +/- 1000 and saw that it works and then changed it back just to see what kind of response I would get...... from the newsgroup. Not much.

Yes, it is called state. That is the x array in my .pdf files.
I am waiting for snovite to tells us what the units are of his transfer function, what the control output limits are and what the desired response is.
I updated the .pdf files so the control output limit is +/-1000. You can see it dampens nicely if the starting amplitude is 1 or less. I placed the closed loop poles on the negative real axis to provide a crititcally damped response. Note, the lead lag has a closed loop transfer funciton with three poles at -2*PI*50 and the PD feedback example has only two poles at -2*PI*50. All the calculations necessary are shown for the PD feedback example. It uses Ackermann's equation to calculate the P and D gains given the desired pole location. I referenced the text book where I got the information to do this. ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20T0C1%20snovite%20leadlag.pdf ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20T0C1%20snovite%20Ack.pdf
This is easy, snovite did the hard part when he calculated the transfer function.
Peter Nachtwey
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BTW, if you are just damping vibrations you don't need an integrator term. I bet a simple PD controller with a low pass filter or lead/lag filter will do the trick depending on where the zero is. I don't think you need anything exotic for your vibration control. You provide values for your plant it would help. Were does the zero come from? How does the controller connect the beam to dampen the vibration?
Peter Nachtwey
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