Asymmetric fluid-structure dynamics in nanoscale imprint lithography

65actuator height, micron432100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1time, sFigure 5.5 Ideal s-curve (solid line) and actual encoder data (squares)Figure 5.5 show the ideal s-curve and the actual encoder data duringsqueezing process. The encoder data was averaged from 10 sets of data with bothair and water as fluid. The 5 th order polynomial ideal s-curve in this case is5 4 3() t = −30t+ 75t− 50t+ 5z Awhere z A is in microns. To achieve this outputfrom the actuators, inputs into the s-curve profile generator for the C-842 motorcontroller were: velocity = 0.05 mm/s, acceleration = 0.015 mm/s 2 , and jerk =0.025 mm/s 2 . PID terms were 300, 50, and 1200, respectively. The PIDparameters were determined through experimental tuning using data from themotor encoders.5.3 NUMERICAL METHOD5.3.1 Fourth Order Accurate Runge-Kutta with Adaptive Time StepThe fourth order Runge-Kutta method was used to obtain the solutions tothe equations of motion, which are initial value ordinary differential equations66