Fundamentals ... (cont.)
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For applications with continuous, repetitive (periodic) inputs, a new preshaping technique can reduce the rolloff, phase error and hysteresis of the servo-system. The result is to improve the effective bandwidth and allow more accurate tracking. 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 improves the effective bandwidth by a factor of 10 and is more effective than classical phase-shifting approaches in reducing tracking error in multi-frequency applications.
Signal Preshaping is based on FFT (fast Fourier transformation) techniques. Frequency response and harmonics (caused by nonlinearity) are determined in two steps. The results are applied to the original control function and a new control function is calculated.
E. g. for a PZT positioning system with 400 Hz resonant frequency, the command transfer function (amplitude and phase) can be improved from 20 Hz to 200 Hz without affecting the system stability. At the same time, the tracking error is reduced by a factor of up to 50 compared to that using the uncorrected control input signal.
Fig. 36. No preshaping. A: Control input signal (expected motion). B: Actual motion of system. C: Tracking error
Fig. 34. Signal preshaping, phase 1
Fig. 35. Signal preshaping, phase 2
Fig. 37. Signal after preshaping, phase 2. A: Expected motion (old control signal); B: Actual motion; C: New, preshaped input signal; D: Tracking error.