EE 401 Control Systems Analysis and Design

Modeling an Electromechanical SystemThe DC Servomotor

Friday, Sept. 06, 2013 EE 401: Control Systems Analysis and Design Slide 1 of 4

The DC Servomotor

Friday, Sept. 06, 2013

• Modeling a DC Servomotor: Commutation results in a change in polarity

S

N

S N S N

V+

V-

S N

S N S N

V+

V-

EE 401: Control Systems Analysis and Design Slide 2 of 4

The DC Servomotor

Friday, Sept. 06, 2013

• An electromechanical system The torque is armature current

The back-EMF is shaft speed

Armature circuit suggests

Summing the angular forces

Assume a permanent magnet constant field

• Rm = armature resistance• Lm = armature inductance• ia = armature current• ea = armature input voltage• = torque constant• em = back-EMF voltage• Km = back-EMF constant• J = Motor inertia• B = viscous damping coeff• = torque• = shaft angle

( ) ( )aT s K I s

( ) ( )m mE s K s s

( ) ( ) ( )a m m a mE s L s R I s E s

2( ) ( )T s J s Bs s

EE 401: Control Systems Analysis and Design Slide 3 of 4

The DC Servomotor

Friday, Sept. 06, 2013

• An electromechanical system The torque is armature current The back-EMF is shaft speed Armature input voltage Motor torque

( ) ( )aT s K I s( ) ( )m mE s K s s

( ) ( ) ( )a m m a mE s L s R I s E s

( ) ( )T s J s B s s

+

-

( )aE s

( )mE s

( )aI s1

m mL s R

( )T s ( )s s

mK

( ) ( ) ( )a m m m aE s E s L s R I s

K1s

( )s1J s B

EE 401: Control Systems Analysis and Design Slide 4 of 4