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Transfer Function of a second order system

Electrical Engineering Asked by Jün on February 1, 2021

2nd order system

Given the system, how do you find its transfer function? It has more questions after but what i just really need is the transfer function. I’m confused as to how to deal ones with motors.

One Answer

from what I recall...

Input torque $T(t)=K_tI(t)$

Frictional torque is $T_f=b_m~dtheta(t)/dt$ for viscosity b times rotational velocity dθ(t)/dt , or sometimes Ω(t) by Mech Eng. and acceleration d²θ(t)/dt with rot. inertia, J

$J~frac{d^2θ(t)}{dt^2} = T(t) − T_f$

Spring Torque is $T_s=K_s*frac{dtheta}{dt}$

Back EMF, Vb is proportional to RPM

$V_{emf}=K_bfrac{dtheta}{dt}$

and Current is the difference between applied voltage and Vemf into the motor coil resistance, R at DC

$I(t)=frac{V(t)-V_{emf}}{R_{dc}}$

hope that gets you started to get $G(t)=frac{theta}{I(t)}$ .... oh and gear ratio Kg=N1/N2 reduces velocity and increases torque.

Hint: current is proportional to acceleration

Answered by Tony Stewart Sunnyskyguy EE75 on February 1, 2021

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