Piezoelectric actuators (benders, stacks, chips, etc.) are excellent fast and precise means for generation and control of micro, nano, and even atomic scale movement on millisecond and faster timescales. Unfortunately, they are also excellent high-Q resonators. Figure 1 shows what you can expect if you’re in a hurry to move a piezo and simply hit it with a unit step. Result: a massive (nearly 100%) overshoot with prolonged follow-on ringing.
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| Figure 1. | Typical piezo actuator response to squarewave drive with ringing and ~100% overshoot. |
Don’t worry. It’ll get there. Eventually. But don’t hold your breath. Clearly something has to be done to modify the drive waveshape if we’re at all interested in speed and settling time. Many possibilities exist, but Figure 2 illustrates a remarkably simple yet effective trick that actually takes advantage of the piezo’s natural 2x overshoot: Half and Half step drive.
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| Figure 2. | Half &Half drive step with half amplitude and half resonance period kills overshoot and ringing. |
The surprisingly simple trick is to split the drive step into an initial step with half the desired movement amplitude and a duration of exactly half the piezo resonance period. Hence: “Half & Half”(H&H) drive. The half-step is then followed by application of the full step amplitude to hold the actuator in its new position.
The physics underlying H&H rely on kinetic energy imparted to the mass of the actuator during the first quarter cycle to be just sufficient to overcome actuator elasticity during the second quarter, this bringing the actuator to a graceful stop at half cycle’s end. The drive voltage is then stepped to the full value, holding the actuator stationary at the final position.
Shown in Figure 3 is H&H would work for a sequence of arbitrary piezo moves.
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| Figure 3. | Example of three arbitrary H&H moves: (T2 – T1) = (T4 – T3) = (T6 – T5) = ½ piezo resonance period. |
If implemented in software, the H&H algorithm would be simplicity itself and look something like this:
Let DAC = current contents of DAC output register
N = new content for DAC required to produce desired piezo motion
Step 1: replace DAC = (DAC + N) / 2
Step 2: wait one piezo resonance half-period
Step 3: replace DAC = N
Done.
If implemented in analog circuitry, H&H might look like Figure 4. Here’s how it works.
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| Figure 4. | The analog implementation of H&H. |
The C1, R1, C2, R2||R3 voltage divider performs the half-amplitude division function of the H&H algorithm, while dual-polarity comparators U2 detect the leading edge of each voltage step. Step detection triggers U3a, which is adjusted via the TUNE pot to have a timeout equal to half the piezo resonance period, giving us the other “half”.
U3a timeout triggers U3b, which turns on U1, outputting the full step amplitude, completing the move. The older metal gate CMOS 4066 is used due to its superior low-leakage ROFF spec’ while the parallel connection of all four of its internal switches yields an adequately low RON.
U4 is just a place keeper for a suitable piezo drive amplifier to translate from the 5-V logic of the H&H circuitry to piezo drive voltage and power levels.
