Achieving Optimal Response for Nanopositioning Systems with nPoint DSP Controllers

By AZoNano Staff Writers

Topics Covered

Introduction
Settling Time, Rise Time and Bandwidth
System Measurements
Results and Discussion
Conclusion
About nPoint | nanopositioning and motion control

Introduction

With nPoint’s DSP controllers, users can modify the control parameters to obtain optimal response for a nanopositioning system. This article demonstrates the effect on bandwidth, rise time, and settling time of a nanopositioning system when control parameters are varied. Here, a stage with a resonance frequency of 630Hz and a C.300 DSP controller is used as the nanopositioning system.

Settling Time, Rise Time and Bandwidth

The settling time is the time taken by the nanopositioner to travel to a commanded position and settle to within 2% of the step size value. The settling time reveals the dynamic characteristics of the nanopositioner in detail when a small step size is employed. The rise time is the time taken by the nanopositoning system to travel from 10% of the commanded position to 90% of the commanded position.

Figure 1. 2μm step response of a nanopositioning system. The red lined define the rise time (2.5ms) while the black line defines the settling time (20ms).

Figure 1 illustrates the settling time and rise time for a nanopositioner with reasonably high control gains where oscillations are seen. The system is commanded to carry out a 2μm step. The rise time in this case is roughly 2.5ms (red lines), while the settling time is roughly 20ms (black line). The bandwidth is the frequency wherein the system response has reduced to 3db from its initial value at low frequencies. The bandwidth assesses the ability of a system to reliably reproduce/respond to an input signal. Here, the bandwidth is computed using Bode plots.

System Measurements

Figure 2 shows the open-loop step response of the nanopositioning system. Here, the resonance frequency is excited (roughly 600Hz) without using the control mode. The control mode used initially is typical PID control (Proportional, Integral, Differential). The system bandwidth can be increased or decreased by varying the PID values.

Figure 2. The open-loop step response of a nanopositioning system with a resonance frequency of ~630 Hz

A ‘high’ bandwidth system will have faster response, while a low bandwidth system will have slower response and may take more time to settle. Hence, optimal control is achievable with systems that have short settling time and high bandwidth. This represents the absence of oscillations. Since the I gain largely affects the system response, its value is varied from low to high. Figure 3 depicts the step response of the nanopositioning system and the Bode plot with I = 200.

Figure 3. 2μm step response and Bode plot of a nanopositioning system in PID with I = 200.

Figure 4 illustrates the step response of the system and the Bode plot with I = 500 and Figure 5 depicts the step response of the system and the Bode plot with I = 1000.

Figure 4. 2μm step response and Bode plot of a nanopositioning system in PID with I = 500.

Figure 5. 2μm step response and Bode plot of a nanopositioning system in PID with I = 1000.

Results and Discussion

The bandwidth of the nanopositioning system increases when the I gain raises, but its settling time and rise time decline. Nevertheless, after reaching a certain value of the I gain, significant oscillations can be observed in the system. The occurrence of oscillations may cause a considerable increase in the settling time albeit the rise time may remain short.

The use of notch filters can hinder the effects of the resonance frequency, while maintaining high bandwidth. This application uses two notch filters, with a central frequency of 630Hz and 1150Hz and width of 200Hz and 300Hz, respectively. Figure 6 delineates the response with the same I gain = 1000.

Figure 6. 2μm step response and Bode plot of a nanopositioning system with I=1000 and two notch filters.

Conclusion

As can be seen in Figure 6, the use of notch filters has considerably reduced the oscillations in the step response of the nanopositioning system. The increase in bandwidth is also clearly visible as marked by the frequency response (in the Bode plot) still ‘being flat’ at higher frequencies. The resonance peak is absent on the Bode plot.

About nPoint | nanopositioning and motion control

nPoint, Inc. specializes in piezo actuator driven flexure stages available in one, two or three axes of motion. Our ultra-precision motion control scanners and controllers provide users with the highest level of performance available in the marketplace.

With design and production facilities located in Middleton, WI and distribution channels throughout the world, nPoint provides each of our customers the same outstanding service regardless of the application.

Our product lines include standard products consisting of upgrade kits for your AFM and stand alone research instruments, a growing list of OEM applications and custom design for your unique research application. Let nPoint be your complete nanopositioning solution provider.

This information has been sourced, reviewed and adapted from materials provided by nPoint | nanopositioning and motion control.

For more information on this source, please visit nPoint | nanopositioning and motion control.

Date Added: Feb 25, 2014 | Updated: Feb 27, 2014
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