Metho d s to I mp rove Piezo Dyna m ics
Signal Preshaping / DynamicDigital Linearization (DDL) For example, it is possible toincrease the command rate from 20 Hz to 200 Hz for a piezo system with a resonant fre- quency of 400 Hz without com- promising stability. At the same time, the tracking error is reduced by a factor of about 50. Signal Preshaping, a patentedtechnique, can reduce rolloff, phase error and hysteresis in applications with repetitive (periodic) inputs. The result isto improve the effective band-width, especially for tracking applications such as out-of- round turning of precision mechanical or optical parts. Signal Preshaping is imple- mented in object code, based on an analytical approach inwhich the complex transferfunction of the system is calcu- lated, then mathematically transformed and applied in a feedforward manner to reduce the tracking error.Signal Preshaping is moreeffective than simple phase- shifting approaches and canimprove the effective band-width by a factor of 10 and in multi-frequency applications.Frequency response and har-monics (caused by nonlinearity of the piezo-effect) are deter- mined in two steps using Fast Fourier Transformation (FFT),and the results are used to cal-culate the new control profile for the trajectory. The new con- trol signal compensates for the system non-linearities. Fig. 34 a. Signal preshaping, phase 1. Fig. 34 b. Signal preshaping, phase 2. Fig. 36. Signal after preshaping phase 2. A: Expected Motion (old control signal). B: Actual motion of system. C: New control input (producted by preshaping). D: Tracking error. Fig. 35. No preshaping. A: Control input signal (expected motion). B: Actual motion of system. C: Tracking error. © PI 1998-2005. Subject to change w/o notice. Cat 118 05/09.17 4-34