SOLUTIONS

ERT 321Process Control & Dynamics

Anis Atikah binti Ahmad

EXERCISE 3

In this question, a model is not given. Thus, we have to develop a process model from the experimental data.

Time (min) T2m(mA)

0 131 132 13.54 166 16.68 16.9

10 1712 1714 17

At time = 1 min, there is no change in temperature data. Thus, we know that time delay term should be included in our model.

From the reaction curve, we know that our process model is in the form of

first order plus time delay (FOPTD);

where

0 2 4 6 8 10 12 14 1613

13.5

14

14.5

15

15.5

16

16.5

17

17.5

T2m

Time

min6.1 min0.36.16.4

1~

sKeG

s

mpvIP KKKKK pmKKpsipsimApsi 9.075.0

You have to find K, τ and θ

given in the question You have to find

psimApsimAKK mp 2

16181317

mpvIP KKKKK mpKKpsipsimApsi 9.075.0

Process output (Temperature, ° C)

Process input (Pressure, psi)

pK mKTransmitter output (Temperature, mA)

Transmitter input (Temperature, °C)

mp KKProcess output (Temperature, ° C)

Process input (Pressure, psi)

Transmitter output (Temperature, mA)

Transmitter input (Temperature, °C)

Transmitter output (Temperature, mA)

Process input (Pressure, psi)

mpvIP KKKKK

psimApsipsimApsi

161813179.075.0

13

35.1 6.1

sesG

s

35.1

Thus,

12

cKK 916.0586.0

772.036.1586.035.11 916.0

cK

I 165.003.1

min18.336.1165.003.1

3

I

(a)ITAE (setpoint change)From ITAE Performance Index Table,

PI controller

(b) Direct Synthesis method with τc= τ/3From Table 12.1,

c

cKK min3 I

85.06.11

335.111

cc KK

PI controller

(c) Ziegler Nichols

01 GGc

13

35.1 6.1

sesG

s

013

35.116.1

seG

s

c

013

35.116.1

seK

s

c

01 OLG

1. Use characteristic equation.

2. Use proportional only controller, Gc= Kc

Using 1/1 Padé Approximation, substitute e-1.6s = into (1) s

s26.1126.11

(1)

013

35.116.1

seK

s

c

08.018.01

1335.11

ss

sKc

Substituting and

08.0135.18.0113 sKss c

008.135.18.014.23 2 sKKsss cc

035.1108.18.34.2 2 cc KsKs

cuc KK js u

0035.1108.18.34.2 2 jKjK cuucuu Equating imaginary and real coefficients;

008.18.3 ucuK 035.114.2 2 cuu K

52.3cK min548.1 radu

Direct substitution method

min06.42

uuP

584.152.345.045.0 cuc KK

min38.32.106.42.1 uI P