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Important calculations: step response

Charging time

For the generation of steps, it is not physically possible to charge a piezo actuator instantly. Instead, in most cases the waveform will be trapezoidal, with a given charging time. Charging time will depend mainly on the slew rate or current capability of the driver and the capacitance of the piezo element.

Oscillations and optimal step response

Depending on the charging time and the mechanical resonance frequency of the system f0, the system will oscillate more or less.

For a long charging time (tcharge >> 1/f0), the system is close to quasi-static conditions and there will be very little oscillation. 

For a short charging time (tcharge < 1/f0), the system will experience a shock that will lead to the largest oscillations.

Near the resonance period (tcharge ≈ 1/f0), the system can react fast with minimum oscillation. This is sometimes referred to as a “tuned step”. This method requires a precise knowledge or identification of the dynamic characteristics of the system, which is not always straightforward, in particular in the case of variable operating conditions (typically a changing mass load).

This can be illustrated on these simulation results based on a NAC2013-H10 in blocked-free configuration, acting on a mass load of 20g (damping is reduced to illustrate the oscillations). Such a system has an undamped resonance period of 1/f0=0.097ms. Relatively large oscillations are generated for tcharge = 0.07ms and tcharge = 0.12ms while a “tuned step” (tcharge = 0.097ms) provides a fast and stable positioning.

Fastest step response

For a very short charging time (tcharge << 1/f0) the actuator can reach the target position after 1/(3.f0). That is the fastest possible movement; however, it should be noted that it generates very large oscillations (illustration below without damping).

Furthermore, the current requirements are much higher than with a “tuned step”. For the two examples below, there is a factor 20 difference in peak current. Also, acceleration and therefore stress is higher (factor 6).

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