In diagram provided 3a shows an air conditioning system as an open-loop system. Figure 3b shows the system with closed-loop proportional control. Finally, Figure 3c shows the closed-loop system with PD control. Described image Figure 3 (a) Open-loop system; (b) Closed-loop system with proportional control; (c) Closed-loop system with PD control You are given the task as a control engineer to design a closed-loop controller for this air conditioning unit so that it has the following properties: Maximum overshoot: 10% Maximum time to reach 99% of steady state: 10 seconds Maximum steady-state error: 10% Please find the values of the gain, natural frequency and damping coefficient of the open-loop system to two places after the decimal point. Does the open-loop system conform to the design constraints?

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In diagram provided 3a shows an air conditioning system as an open-loop system. Figure 3b shows the system with closed-loop proportional control. Finally, Figure 3c shows the closed-loop system with PD control. Described image Figure 3 (a) Open-loop system; (b) Closed-loop system with proportional control; (c) Closed-loop system with PD control You are given the task as a control engineer to design a closed-loop controller for this air conditioning unit so that it has the following properties: Maximum overshoot: 10% Maximum time to reach 99% of steady state: 10 seconds Maximum steady-state error: 10% Please find the values of the gain, natural frequency and damping coefficient of the open-loop system to two places after the decimal point. Does the open-loop system conform to the design constraints?
(a)
X(s)
(b) Input in V
X(s)
X(S)
Input in V
Air Conditioning Unit
1
(1 + 4s)(1 + 0.8s)
(c) Input in V
E(S)
Error
E(S)
Error
Controller
K
Controller
Kp(1+SK D)
Y(s)
Output in °C
C(s)
Air Conditioning Unit
1
(1 + 4s)(1+0.8s)
Input in V
C(s)
Air Conditioning Unit
1
(1 + 4s)(1+0.8s)
Input in V
Y(s)
Output in °C
Y(s)
Output in °C
Transcribed Image Text:(a) X(s) (b) Input in V X(s) X(S) Input in V Air Conditioning Unit 1 (1 + 4s)(1 + 0.8s) (c) Input in V E(S) Error E(S) Error Controller K Controller Kp(1+SK D) Y(s) Output in °C C(s) Air Conditioning Unit 1 (1 + 4s)(1+0.8s) Input in V C(s) Air Conditioning Unit 1 (1 + 4s)(1+0.8s) Input in V Y(s) Output in °C Y(s) Output in °C
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