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The dynamic behavior of a piezo positioning system depends on factors including the system’s resonant frequency, the position sensor and the controller used. Simple controller designs limit the usable closed-loop tracking bandwidth of a piezoelectric system to 1/10 of the system"s resonant frequency. PI offers controllers that significantly increase piezo actuator system dynamics (see table). Two of the methods are described below; additional information is available on request.
InputShaping® Stops Structural Ringing Caused by High-Throughput Motion
A patented, real-time, feedforward technology called InputShaping® nullifies resonances both inside and outside the servo-loop and virtually eliminates the settling phase. The procedure requires determination of all critical resonant frequencies in the system. A non-contact instrument like a Polytec Laser Doppler Vibrometer is especially well-suited for such measurements. The values, most importantly the resonant frequency of the sample on the platform, are then fed into the InputShaping® Signal processor. There the sophisticated signal processing algorithms assure that none of the undesired resonances in the system or its auxillary components is excited. Because the processor is outside the servo-loop, it works in open-loop operation as well.
The result: the fastest possible motion, with settling within a time equal one period of the lowest resonant frequency. InputShaping® was developed based on research at the Massachusetts Institute of Technology and commercialized by Convolve, Inc. (www.Convolve.com). It is an option in several PI digital piezo controllers.
Signal Preshaping / Dynamic Digital Linearization (DDL)
Signal Preshaping, a patented technique, can reduce rolloff, phase error and hysteresis in applications with repetitive (periodic) inputs. The result is to improve the effective bandwidth, especially for tracking applications such as out-of-round turning of precision mechanical or optical parts. Signal Preshaping is implemented in object code, based on an analytical approach in which the complex transfer function of the system is calculated, then mathematically transformed and applied in a feedforward manner to reduce the tracking error.
Signal Preshaping is more effective than simple phase-shifting approaches and can improve the effective bandwidth by a factor of 10 and in multi-frequency applications.
Frequency response and harmonics (caused by nonlinearity of the piezo-effect) are determined in two steps using Fast Fourier Transformation (FFT), and the results are used to calculate the new control profile for the trajectory. The new control signal compensates for the system non-linearities.
For example, it is possible to increase the command rate from 20 Hz to 200 Hz for a piezo system with a resonant frequency of 400 Hz without compromising stability. At the same time, the tracking error is reduced by a factor of about 50.
Dynamic Digital Linearization (DDL)
DDL is similar in performance to Input Preshaping, but is simpler to use. In addition, it can optimize multi-axis motion such as a raster scan or tracing an ellipse. This method requires no external metrology or signal processing, but is fully integrated in E-710 and E-711 digital controllers. DDL uses the position information from capacitive sensors integrated in the piezo mechanics (requires direct metrology) to calculate the optimum control signal. As with preshaping, the result is an improvement in linearity and tracking accuracy of up to 3 orders of magnitude.
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