c) Draw the block-diagram for the closed-loop system.
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 12.4P
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Question
help part c block diagram
![In this problem you will create and analyze a block-diagram for an HVAC system.
a) The room temperature dynamics are
mcT'(t) = –KT(t) +q(t)
where m is the mass of air in the room, C is the specific-heat of air, k is the heat-
transfer coefficient through the walls, and q(t) is the heat supplied by the HVAC
system. The control input is the supplied heat q(t) and the controlled output is
the room temperature T(t). Find the transfer function P(s) for the room from
supplied heat q(t) to room temperature T(t).
b) The room temperature is controlled by a proportional-integral controller
q(t) = K„(Tref – T(t)) + K; |
| Tref – T(7)dr
-
where Kp and K; are the proportional and integral gains, respectively, and Tref is
the desired room temperature. Find the transfer function K(s) for the controller
from tracking error e(t) = Tref – T(t) to supplied heat q(t).
Draw the block-diagram for the closed-loop system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9d1b16c-cad2-4bde-bee3-b0a69a125535%2F537553fd-14bc-4c99-b8ef-69fb819925d3%2Fpcrsjps_processed.png&w=3840&q=75)
Transcribed Image Text:In this problem you will create and analyze a block-diagram for an HVAC system.
a) The room temperature dynamics are
mcT'(t) = –KT(t) +q(t)
where m is the mass of air in the room, C is the specific-heat of air, k is the heat-
transfer coefficient through the walls, and q(t) is the heat supplied by the HVAC
system. The control input is the supplied heat q(t) and the controlled output is
the room temperature T(t). Find the transfer function P(s) for the room from
supplied heat q(t) to room temperature T(t).
b) The room temperature is controlled by a proportional-integral controller
q(t) = K„(Tref – T(t)) + K; |
| Tref – T(7)dr
-
where Kp and K; are the proportional and integral gains, respectively, and Tref is
the desired room temperature. Find the transfer function K(s) for the controller
from tracking error e(t) = Tref – T(t) to supplied heat q(t).
Draw the block-diagram for the closed-loop system.
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