Control de Procesos - Joyssy Ticona

8/2/2019 Control de Procesos - Joyssy Ticona

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UNIVERSIDAD NACIONALMAYOR DE SAN MARCOS

FACULTAD DE QUIMICA, ING.

QUIMICA E ING. AGROINDUSTRIAL

Curso: Control de ProcesosProfesor: Ing. Eder Vicua Galindo

Alumna: Joyssy Ticona Vilca

Lima, 2011


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Title:Temperature control at the bottom of an

aquarium by the variation of heat entering,ambient temperature and the partial pressure ofwater

One aquarium can be modeled bytwo perfectly mixed pools.

Be want derive an equations thatrepresent the response of the

temperature in bottom of anaquarium for the changes in heatinput, in the surroundingtemperature, and in thesurrounding water partial

pressure.


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The process is defined:There is a electric heater.

There are two perfectly mixed pools. The temperature at the bottom is T1(t),C . The temperature at the top is T2(t),C. The rate of vaporization of water from the tank: w = Ky*A*[p(T)-ps(t)] p[T(t)]= e A-B/T+C(Antoanie Equation )

OBJECTIVE:

Variable temperature control since this affects the stability of

operation of a tank which aims to maintain the life of the fishthat inhabit it.


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process scheme

f2 f1

f1

f2

VARIABLES:* Inputvariable: T1(t)* Disturbance

variable: ps(t)* Manipulationvariable: I(t)* State

variable: T2(t)

PARAMETROS:

f [m3/s]


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Assumptions:

Transfer of heat and mass to the surroundings isonly from the free surface of the water .

V1 = V2 = v

p[T2(t)]

The physical properties of water (Cp, Cv, and ) are constant.

Cp = Cv

1 = 2

The rate of vaporization is so small that the totalmass of water in the tank, M, kg, maybe assumedconstant.


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Mass balance1*f1 = 2*f2 1= 2 f1 = f2

Energy balance at the top:

1*f1*h1(t)- 2*f2*h2(t) - W(t)* = d[V**U(t)]dt

*f*Cp[T1(t)- T2(t)] - W(t)* = V**Cv*d[T2(t)] (1)dt

One equation with three unknows, T1, T2 and w

MATHEMATICAL MODELDEVELOPMENT


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Energy balance at the bottom2*f2*h2(t)- 1*f1*h1(t) + Fem = d[V**U(t)]

dt *f*Cp[T2(t)- T1(t)] + R*I(t)= V**Cv*d[T1(t)] (2)

dtTwo equations with four unknows, I

The rate of vaporization of waterw(t)= Ky*A*[p(T2(t))-p(t)]

Three equations with five unknows, p(T2)(3)

Antoanie equationP[T2(t)]= e A-B/T2+C

(4)


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4/17/12Establishing steady state equations

*f*Cp[ T1 T2] W* = 0 (6)

*f*Cp[ T2 - T1] + Fem*I = 0 (5)Linearizing and subtracting the aquations

corresponding to (1) and (2)*f*Cp[T1(t)- T2(t)] - W(t)* = V**Cv*d[T2(t)] (7)

dt*f*Cp[T2(t)- T1(t)] + R*I(t)= V**Cv*d[T1(t)] (8)

dt

Where:T2(t) = T2(t) T2T1(t) = T1(t) T1

I(t) = I(t) - IW(t)= w(t) w = Ky*A*[p(T2(t))-ps(t)]

= -


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4/17/12*Replacing (9) in (7)*f*Cp[T1(t)- T2(t)] - Ky*A*[a(T2(t))-ps(t)] * = v**cv*d[T2(t)](10)

dt

Using Laplace Transform and rearranging for equation (8) and(10)

T

1(s) = 1 T2(s) + K1 I(s)(11)

s 1+1 s 1+1

T2(s) = K2 T1s) + K3 Ps(s)(12)

s 2+1 s 2+1 Then:


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where

1= *V*Cv, = 20 segundos K1 = Fem= 0.98 K

*f*Cp *f*Cp

2= * V * Cv, = 60 segundos K2 = *f*Cp= 0.08 ,adimensional

Ky*A* *a+ fCp Ky*A* *a+ fCp

K3= Ky*A*, = 0.005 K/Pa


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Process transfer function:

Disturbance transfer function:

TRANSFER FUNCTION IN OPENLOOP


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block diagram for open loop system

K31s+1

K22s+1

K1

1 11s+1

I(s)

T1(s)

T2(s)

Ps(s)


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TT

TRC

T2

(t)

Tsp(t),K

m(t)

mA

outline of the process control system

Sensor

transmitter

Controller

Final

controlelement

T1(t)


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sensor transmitter:MBT 153

Static characteristics

Noise: 0,1mA p.p.

Sensor range : -10 50

Dynamic characteristics

Response Rate: 2 minPrecision: 0.1%

- Convert the millivolt output

current signal (typically 4-


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Transfer function of the sensor-transmitter

H(s) = Kt .ts+1

The transmitter can be represented by the

following linear relationship.

Gain:

Kt = 20 4 mA = 0.26750 (-10) C

Response time:t =2 min


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Is Tsp the set point:

e(t)= Tsp(t) Tm(t)

Mode of action: Reversible action

m(t)= m+ (Kc)e(t)

Mode of controller: Proportional

CONTROLLER


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4/17/12final control element:Electric actuator

Accion: fail closed (FC)

Linear valve characteristic.

Response time : 10 s


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Ky Kvp Kvqm(t)

mp(

t)

vp

(t)

K= 1 - 020 4

mA

Kvq=27.4

Kv= K*Kvq = 1* 27.416Kv= 1.712

Transfer function of thecontroller:

Gv (s)= 1.71210s + 1


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block diagram

0.98(20s+1)(s+0.016)(s+0.051)

0.005(s+0.016)(s+0.051)

1.712

10s+1

KcKsp

0.267

2s+1

Tsp(s)

Tm(s)

T1(s)I(t)

+

E(s)

M(s)

Ps(t)

+


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characteristic equation


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Stability analysis

1) ROUTH- HURWITZ TEST20 1.8196 0.0078+4.96Kc13.34 0.0764+29.7849Kc 0b1 b2c1 0

d1

For b1>0 :

b1= 1.896 44.65Kc >00.04>Kc Kcu= 0.04

For b2>0 :b2 = 0.00078 + 0.496Kc >0

Kc>-1.57*10^(-3)

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2) DIRECT SUBSTITUTION TEST

Grouping:

Is obtained:

Replacing: s = wcuiKc=Kcu

Then:

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Kc I D

PROPORTIONAL 0.175 - -

PROPORTIONAL-INTEGRAL

0.159 18.06 -

PROPOTIONALINTEGRAL

DERIVATIVO

0.206 10.83 2.71

controller tuning parameters

According to ZieglerNichols:

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RESPONSE TIMEAND

STABILITY

ANALYSIS

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PROPORTIONALCONTROLLER

Kc= 0.1749

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Response time

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Kc = 0.175rlocus(FTCA)

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Kc = 0.175Bode(FTCA)

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Kc = 0.175nyquist(FTCA)

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PROPORTIONALINTEGRAL

CONTROLLER

Kc = 0.159i= 18.06

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RESPONSETIME

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rlocus(FTCA)

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bode(FTCA)

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nyquist(FTCA)

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PROPORTIONAL

INTEGRALDERIVATIVE

CONTROLLER

Kc = 0.206i = 10.83D = 2.71

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RESPONSE TIME

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rlocus(FTCA)

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bode(FT

CA)

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nyquist(FTCA)

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ANALYSIS IN ACONTROLLER OFPROPORTIONAL

INTEGRALDERIVATIVE

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An increase of Kc in10%

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A decrease ofKc in 10%

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* Shows that the three response timegraphs for stability, but at the beginningintroduces instability. We conclude a

change in the controller (Kc) does notinfluence the search process stability

*The Kc Increase by 10% the amplitudedecreases and the same percentage

decrease in the amplitude increases,conclude that Kc varies the amplitude andincreasing its value the process will becloser to stability

ANALYSIS

Control de Procesos - Joyssy Ticona

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