Find the expressions of the static position and velocity error constants, Kep and Kev, respectively. Use these error constants to deduce the steady- state error for: (i) a step input Vr, and (ii) a ramp input Vrt. Do not substitute the parameters with their values yet.
Find the expressions of the static position and velocity error constants, Kep and Kev, respectively. Use these error constants to deduce the steady- state error for: (i) a step input Vr, and (ii) a ramp input Vrt. Do not substitute the parameters with their values yet.
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.2P
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Transcribed Image Text:Find the expressions of the static position and velocity error constants,
Kep and Kev, respectively. Use these error constants to deduce the steady-
state error for: (i) a step input V₁, and (ii) a ramp input Vrt. Do not
substitute the parameters with their values yet.
![64
Vr +
[-5..5] V
Vr +
[-5..5] V
Controller
Motor
Speed (V)
Wm
Ge(s)
Figure II-4.1: Block diagram of a speed feedback control for the motor system
As we did previously, the motor (plant) will be modeled by its first-order approximation,
Controller
Ge(s)
Motor
Position (V)
Om
Gp(s)
where K and 7 are process' DC gain and time constant, respectively.
=
Vm
Speed
Sensor
He(s)
63
K
TS+1
Vm
CHAPTER II-4. CONTROL OF MOTOR SPEED ERROR
Motor
System
Gp(s)
Motor
System
Gp(s)
Motor
Speed (rad/s)
Wm
Position
Sensor
Hp(s)
Motor
Speed (rad/s)
Wm
1
8
Motor
Position (rad)
Om
Figure II-4.2: Block diagram of a position feedback control for the motor system](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F875c2668-6917-4399-ac39-06da181475d5%2F56a83312-3be7-406a-8f81-cb70c3c544ab%2Fwkic87a_processed.png&w=3840&q=75)
Transcribed Image Text:64
Vr +
[-5..5] V
Vr +
[-5..5] V
Controller
Motor
Speed (V)
Wm
Ge(s)
Figure II-4.1: Block diagram of a speed feedback control for the motor system
As we did previously, the motor (plant) will be modeled by its first-order approximation,
Controller
Ge(s)
Motor
Position (V)
Om
Gp(s)
where K and 7 are process' DC gain and time constant, respectively.
=
Vm
Speed
Sensor
He(s)
63
K
TS+1
Vm
CHAPTER II-4. CONTROL OF MOTOR SPEED ERROR
Motor
System
Gp(s)
Motor
System
Gp(s)
Motor
Speed (rad/s)
Wm
Position
Sensor
Hp(s)
Motor
Speed (rad/s)
Wm
1
8
Motor
Position (rad)
Om
Figure II-4.2: Block diagram of a position feedback control for the motor system
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