Step Response of 1 DOF System - ece.northeastern.edu

Step Response of 1 DOF System - ece.northeastern.edu

Schematic of a MEMS Gyroscope For constrained motion acor 2 vrel xrel x0 sin dr t vrel x0dr cos dr t acor 2dr x0 cos dr t Force-Feedback Fcor = macor Unconstrained motion acor x0 1m, 10 / s, dr 2 20 kHz acor 4.4 mm/s 2 , arel 15,800 m / s 2 MEMS Mechanical Sensors, Beeby, Ensell, Kraft and White MEMS Mechanical Sensors, Beeby, Ensell, Kraft and White MEMS Mechanical Sensors, Beeby, Ensell, Kraft and White Step Response of 1 DOF System 0, t 0 F (t ) F0 , t 0

=0.05 =0.2 F(t) =0.5 F0 exp( n t ) x(t ) 1 cos( d t ) 2 k 1 t 0, tan 1 2 1 x(t)/(F0/k) 1.5 t/n

for Step Response 2 1 0.5 0 0 , 1 2 d n 1 2 t/n 3

4 5 Step Response With Rise-Time Step With Rise-Time Response 1.4 1.2 =0 1 x(t)/(F0/k) 0, t 0 F (t ) ( F0 / n )t , 0 t n F0 , t n 0.8 F(t) =0.5 0.6

F0 =0.2 0.4 0.2 1 t/n 0 0 1 2 t/n 3 4 5

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