Question

The liquid level in the second tank for a noninteracting tank system is controlled by manipulating the inlet flow rate of the first tank. Fi hi R1 h2 R2 All of the resistances are linear and R1=0.05, R2=0.1 min.m/m³; the cross-sectional areas of the tanks are constant and A1=5, A2=3. a. Derive the transfer function between inlet volumetric flow rate and height of liquid level in second tank, find natural period and damping factor. b. The transfer function of measuring device with its transmitter and the transfer function control valve are 1, show the effect of P controller by considering i) order of response, ii) speed of response, iii) ultimate value iv) offset for the unit step change is set point. 

          The liquid level in the second tank for a noninteracting tank system is controlled by manipulating the inlet flow rate of the first tank.

Fi
hi
R1
h2
R2

All of the resistances are linear and R1=0.05, R2=0.1 min.m/m³; the cross-sectional areas of the tanks are constant and A1=5, A2=3.
a. Derive the transfer function between inlet volumetric flow rate and height of liquid level in second tank, find natural period and damping factor.
b. The transfer function of measuring device with its transmitter and the transfer function control valve are 1, show the effect of P controller by considering i) order of response, ii) speed of response, iii) ultimate value iv) offset for the unit step change is set point.
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The liquid level in the second tank for a noninteracting tank system is controlled by manipulating the inlet flow rate of the first tank. Fi hi R1 h2 R2 All of the resistances are linear and R1=0.05, R2=0.1 min.m/m³; the cross-sectional areas of the tanks are constant and A1=5, A2=3. a. Derive the transfer function between inlet volumetric flow rate and height of liquid level in second tank, find natural period and damping factor. b. The transfer function of measuring device with its transmitter and the transfer function control valve are 1, show the effect of P controller by considering i) order of response, ii) speed of response, iii) ultimate value iv) offset for the unit step change is set point.

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Chemistry: Structure and Properties
Chemistry: Structure and Properties
Nivaldo Tro 2nd Edition
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The liquid level in the second tank for a noninteracting tank system is controlled by manipulating the inlet flow rate of the first tank. Fi hi Ri h2 R2 All of the resistances are linear and R=0.05, R=0.1 min.m/m3; the cross-sectional areas of the tanks are constant and A=5.A2=3. a. Derive the transfer function between inlet volumetric flow rate and height of liquid level in second tank, find natural period and damping factor. b. The transfer function of measuring device with its transmitter and the transfer function control valve are 1, show the effect of P controller by considering i) order of response, ii) speed of response, iii) ultimate value iv) offset for the unit step change is set point.
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Transcript

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00:01 Hi, in this question we are given with a liquid level system where we have to find the transfer function.
00:06 So, here we can use the conservation of mass principle and the laplace transform.
00:11 So, here we have to do so in the part a we have to derive the transverse function.
00:15 So, we have the laplace transform of the variable.
00:19 So, laplace transform of variable q is given as q of s and laplace transform.
00:26 So, this is for inflow.
00:29 So, inflow rate and we have laplace transform of the liquid level is h which is represented by h of s.
00:40 Now, we can write the equation for tank 1.
00:44 So, we can have q plus q minus r into h of s is equal to c into h of s.
00:51 So, h dash of s and for tank 2.
00:55 So, for tank 2 we can write h of s minus r into h 2 of s.
01:00 So, h 2 of s is equal to c of 2.
01:03 So, c of 2 into h 2 of s dash.
01:07 Then we have the flow rate between the tank is 0.
01:11 So, the liquid level will be.
01:13 So, liquid level will be h 2 s is equal to.
01:18 So, h of s minus h of s since flow rate is 0.
01:23 Then for tank 2 we can write this equation.
01:27 So, taking this equation we have h of s minus r into h 2 of s can be replaced by this equation which is h of s minus h of s which is equal to c 2 into h of s minus h of s whole dash...
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