Voltage (V) 9 8 7 6 3 2 1 0 0 50 100 150 Open Loop Time (s) -Vq Vh 200 250 300 350 h qin dout Vm Va Vn A Cq Km Ка Kn Figure 4 - Open loop system is the height of the water in the tank is the flow rate into the tank (proportional to the voltage applied to the pump, Vm) is the flow rate out of the tank (dependent on the manual valve position) is the voltage delivered to the motorised variable speed pump is the voltage returned by the flow rate sensor (proportional to the flow rate in, qin) is the voltage returned by the water level sensor (proportional to the water height, h) is the cross sectional area of the tank = 9.35 × 10-³ m² -3 is the linearised flow constant of the manual valve (flow is assumed proportional to h and the characteristic of the valve is linearised) = ?? (cm³/min)/m is the constant of proportionality for the pump = 500 (cm³/min)/V is the constant of proportionality for the flow rate sensor = 0.00227 V/(cm³/min) is the constant of proportionality for the water level sensor = 40 V/m

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question

a)If the system has a transfer function of the form G_P (s)=H(s)/(V_m (s) )=μ/(1+Ts) where µ is the gain and T is the time constant, calculate values for µ and T for the case where the valve is at position 3.

Hints: Use the constants and information in table 1. The dynamics of the water tank can be found by applying the continuity equation: qin - qout = rate of change in water tank

Voltage (V)
9
8
7
6
3
2
1
0
0
50
100
150
Open Loop
Time (s)
-Vq
Vh
200
250
300
350
Transcribed Image Text:Voltage (V) 9 8 7 6 3 2 1 0 0 50 100 150 Open Loop Time (s) -Vq Vh 200 250 300 350
h
qin
dout
Vm
Va
Vn
A
Cq
Km
Ка
Kn
Figure 4 - Open loop system
is the height of the water in the tank
is the flow rate into the tank (proportional to the voltage applied to the pump, Vm)
is the flow rate out of the tank (dependent on the manual valve position)
is the voltage delivered to the motorised variable speed pump
is the voltage returned by the flow rate sensor (proportional to the flow rate in, qin)
is the voltage returned by the water level sensor (proportional to the water height, h)
is the cross sectional area of the tank = 9.35 × 10-³ m²
-3
is the linearised flow constant of the manual valve (flow is assumed proportional to h
and the characteristic of the valve is linearised) = ?? (cm³/min)/m
is the constant of proportionality for the pump = 500 (cm³/min)/V
is the constant of proportionality for the flow rate sensor = 0.00227 V/(cm³/min)
is the constant of proportionality for the water level sensor = 40 V/m
Transcribed Image Text:h qin dout Vm Va Vn A Cq Km Ка Kn Figure 4 - Open loop system is the height of the water in the tank is the flow rate into the tank (proportional to the voltage applied to the pump, Vm) is the flow rate out of the tank (dependent on the manual valve position) is the voltage delivered to the motorised variable speed pump is the voltage returned by the flow rate sensor (proportional to the flow rate in, qin) is the voltage returned by the water level sensor (proportional to the water height, h) is the cross sectional area of the tank = 9.35 × 10-³ m² -3 is the linearised flow constant of the manual valve (flow is assumed proportional to h and the characteristic of the valve is linearised) = ?? (cm³/min)/m is the constant of proportionality for the pump = 500 (cm³/min)/V is the constant of proportionality for the flow rate sensor = 0.00227 V/(cm³/min) is the constant of proportionality for the water level sensor = 40 V/m
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