How to drive an actuator in its resonance frequency?

[mharaghi]

I can give the following description to the problem, but I don't specifically know what should be done to drive an actuator (specially a piezoeelctric one) in its resonance frequency using a feedback.

**The sensor consists of a piezoelectric transducer and a vibration pickup. When an alternating voltage is applied across its electrode the piezo element is able to vibrate freely in the direction of its length. The pickup detects a vibration that is generated in the PZT element. As the amplification is increased in this system, and since the pickup transducer detects this frequency and feeds a small alternating signal to a driving amplifier,
the feedback circuit system oscillates at the resonance frequency Hence, the driving amplifier
always drives the PZT element at its resonance frequency.

I'm very good with block diagrams, and formulas, and algorithms, in comparison to descriptions. Therefore, I would really appreciate it if you can give me your professional feedback.

 

[berkeman]

I can give the following description to the problem, but I don't specifically know what should be done to drive an actuator (specially a piezoeelctric one) in its resonance frequency using a feedback.

**The sensor consists of a piezoelectric transducer and a vibration pickup. When an alternating voltage is applied across its electrode the piezo element is able to vibrate freely in the direction of its length. The pickup detects a vibration that is generated in the PZT element. As the amplification is increased in this system, and since the pickup transducer detects this frequency and feeds a small alternating signal to a driving amplifier,
the feedback circuit system oscillates at the resonance frequency Hence, the driving amplifier
always drives the PZT element at its resonance frequency.

I'm very good with block diagrams, and formulas, and algorithms, in comparison to descriptions. Therefore, I would really appreciate it if you can give me your professional feedback.

Welcome to the PF. First, check out the "Similar Threads" listed at the bottom of this page. The PF forum software looks for similar threads to your original post (OP), and lists them in case they are of help.

Second, the paragraph you quote is incorrect, or at the very best, incomplete. Just connecting a sensor to an actuator does not in general cause oscillations. It takes several things to get an oscillation to build and to sustain at some level.

What have you learned about feedback and oscillations so far? Have you learned about Bode Plots, Phase Margin, Gain Margin, Positive and Negative Feedback, and similar subjects? What would you guess would have to happen in the feedback in relation to the driven signal, in order to produce stable oscillations?

 

[mharaghi]

I searched and found nothing of particular interest...

I didn't put the complete situation, anyway. there is the actuator, then some spring and proof mass, and tip mass, which causes it to have a res. freq. This is captured by a sensor, and fed back. Essentially a biological tissue is also in contact with the tip mass, which will not change the problem really (it causes a differnce in res. freq., which is the ultimate goal)

I am grad student of electrical engineering-majoring control systems. Unfortunately, my mechanical knowledge is not that good. good with control theory, though never worked with positive feedback.

 

[berkeman]

I am grad student of electrical engineering-majoring control systems. Unfortunately, my mechanical knowledge is not that good. good with control theory, though never worked with positive feedback.

I'm certainly no expert in mechanical systems either, but the principals of feedback and oscillation are similar. In an electrical system, what are the gain and phase margin at oscillation? What does that tell you about the nature of the feedback at oscillation?

 

[mharaghi]

n the top of my head, phase angle should be -180 (margin zero), so it is essentially a positive feedback (output in phase with input with a -360 lag). gain margin should be zero (logarithmic), right??

 

[mharaghi]

specifically, we have an input u1 (which is defined by me, idk what it should be to best fit the problem)

there is a plant, which essentially has a res. freq. and outputs a displacement...

the displacement is captured via a sensor, as signal, say f1

it is fed back, to u1...

I guess the input to plant needs to be amplified, right?

and there is a need to have a bandpass filter to work on the desired range of frequencies (idk where this filter should be mounted, isn't it going to make some undesired delay?? any specific filter recommendation?)

 

[berkeman]

n the top of my head, phase angle should be -180, so it is essentially a positive feedback (output in phase with input with a -360 lag). gain margin should be zero (logarithmic), right??

Right, phase margin zero (so right at 180 degrees for positive feedback) and a loop gain of around 1.

So in an electro-mechanical system, you need to figure out what the delay is from drive to feedback, and adjust the delay to give you the conditions for oscillation. If you do a Bode Plot of the gain and phase through your system (actuator electrical drive --> physical motion --> pickup voltage --> delay through feedback electronics), you will start to get some idea of what you have to do to tune the Bode Plot characteristics to get you the conditions for oscillation at the natural frequency of the mechanical system...

 

[mharaghi]

there are damping and hysteresis, dashpots, piezoelectric material resposne.