Research Article 35 Tuning of a Cascade Control System in...

Journal of Applied and Industrial Sciences, 2014, 2 (1): 35-45, ISSN: 2328-4595 (PRINT), ISSN: 2328-4609 (ONLINE)

Research Article 35

Abstract-Two control strategies were undertaken for the system

water-Acetic acid- normal hexane in a rotating disc contactor

(R.D.C).The first cascade control system consists of a raffinate

composition variable transmitted to the primary controller that

transmits it’s output as the set point to the level controller of the

secondary loop. The second strategy takes the extract composition

transmitted to the primary controller which transmits its output

to the secondary level controller. The transfer functions for both

primary and secondary loops were identified, the overall transfer

functions were calculated for both primary and secondary loops

and consequently tuned by Routh, root locus and Bode methods.

The adjustable parameters for primary and secondary loops Kc’s ,

τi’s, τd’s were determined and optimized by Ziegler-Nichols

method. The offsets were determined and it was found that they

were reasonable for the secondary loop, but considerably high for

the primary loop. Therefore the gain Kc1 of the primary loop was

refined by trial and error to 3.5. This increase in the primary gain

reduced the offset to (- 0.239) which is a reasonable value and the

primary parameters were adjusted accordingly. The response of

each method of tuning was plotted and the characteristics of the

close loop responses were compared and found to be in agreement

as shown in figures 7,8,9,10,11,12,13,14,15,16,17,18.

Index Terms-Cascade control, Tuning, Offset, Responses

investigation.

I. INTRODUCTION

iquid-liquid extraction is a process that separates

components based upon solubility in solvents. The

liquid-liquid extraction is termed as solvent extraction,

extraction, or liquid extraction. The basic principle behind

extraction involves the contacting of a solution with another

solvent which is immiscible with the original; the solvent is

also soluble with specific solute contained in the solution. Two

phases are formed after the addition of the solvent, due to the

differences in densities. The solvent is chosen, so that the solute

in solution has more affinity toward the added solvent,

therefore mass transfer of the solute from the solution to the

solvent occurs, further separation of the extracted solute and the

solvent will be necessary. [1] The control of these units can

often be problematic, partially due to their multiphase nature,

and partially due to the difficulty of on-line measurements of

output variables. Thus, the reliable simulation of the transient

behaviour of these columns is extremely valuable. The column

hydrodynamics including flooding, entrainment, weeping, and

phase inversion will be controlled. [1]

Routh Criterion

The Routh criterion determines the number of the roots of the

characteristic equation that lie on the left-half plane, the right

-half plane or on the imaginary axis if the system is stable,

unstable or critically stable respectively.

The Root Locus Method

This method gives an approximate graphical representation of

the root as the gain is varied. This is very useful in the design of

a system since it gives the position of the poles of the system in

the S-plane for all values of the gain [ 2 and 3].

Bode plot

Bode plot is the graph on semi log paper of the amplitude ratio

and phase angle as the frequency is varied from zero to infinity.

From the plot the ultimate gain and period can be determined

and used for tuning[2-5].

Control systems with multiple loops

The feedback control configuration involves one measurement

(output) and one manipulated variable in a single loop. There

are other simple control configurations which may be used. If

there are more than one measurement and one manipulated

variable or one measurement and more than one manipulated

variables in such case the control systems with multiple loops

may arise, typical example is the cascade control. [6 and 7]

Cascade control

In a cascade control configuration one manipulated variable

and more than one measurement exist.

Industrial Controllers

These are a combination of two or three modes together. They

are usually in actions of P, PI and PID. [1, 2]

Tuning of a Cascade Control System in a Rotating Disk

Contactor (RDC) H.A. Khalil

*1, G .A. Gasmelseed

2, A.E Elhassan

3

(1, 2, 3)Department of Chemical Engineering, Faculty of Engineering, University of Science and Technology

Email:[email protected]

Telephone: +249919634134

Email:[email protected]

Telephone: +249999773300

(Received: December 10, 2013; Accepted: February 04, 2014)

L

*Corresponding author Email:[email protected]

Telephone: +249123896466


Objectives

1. To develop a control strategy of liquid-liquid extraction

process.

2. To identify the transfer functions.

3. To investigate the tuning stability analysis and response

simulation.

II. MATERIALS AND METHODS

Control strategy

This is based on paring the controlled variables with

the manipulated variables; these were specified first

as shown in Fig. 1 and Fig. 2.

Figure 1: Physical diagram of strategy1

36

Figure 2: Physical diagram of strategy 2

From the loops specified in the control strategy the

block diagrams were drawn as shown in Fig. 3 and

Fig. 4.

Figure 3: General block diagram of cascade systems

L.T

C.T.

T L.c

C.C

Extract Feed

PS.

PS.

organic phase Raffinate

L.T

C.C

C.T L.C

FeedExtract

PS.

PS.

Gm2

Gc1

Gm1

Gp2

Gc2

Gv Gp1

- -


37

Figure 4: General reduced block diagram of the cascade system

Figure 5: The response by each criterion

Procedure for stability analysis and tuning

The appropriate transfer functions were cited [4].

The overall transfer functions were determined and

the open loop and close loop characteristic equations

were derived.

The characteristic equations developed in the

previous step were used for tuning, stability analysis

and offset investigation.

The response by each criterion were graphically

determined and compared for the best performance

with regard to overshoot, decay ratio, rise time and

recovery time (Fig. 5).

1- Over shoot :

=A=

√

2- Decay ratio :

= =

√

3- Rise time: the time required for the

response to first reach its ultimate value.

4- Response time: TR: settling time or recovery

time, time for the response to be within

of its ultimate value, sec.

5- Period of oscillation, T : time for complete

cycle, in sec.

√

, frequency in rad/s

√ in seconds

The inner loop (Secondary loop)

G(s) =

Πf = Gc2 Gv Gp2 1+ ΠL = 1+ Gc2 Gv Gp2 Gm2

G(s) =

The characteristic equation of the inner loop:-

1 + Gc2 Gv Gp2 Gm2 = 0

III. RESULTS AND DISCUSSION

The responses for secondary loop are:-

Proportional controller (P controller)

1- Routh (Fig. 6)

Kc=11.9

Gc1

Gm1

Gp1

+

- y(t)

C(t)

Rt0

A

B

±5%

C

rt response

time sec,,t

T)(tC


Step Response

Time (sec)

Am

plitu

de

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

Step Response

Time (sec)

Am

plitu

de

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

Figure 6: The responses for secondary loop for Proportional controller using Routh criteria

2- Root locus (Fig. 7) Kc=11.8

Figure 7: The responses for secondary loop for Proportional controller using Root locus


Step Response

Time (sec)

Ampl

itude

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450-0.5

0

0.5

1

1.5

2

2.5

Step Response

Time (sec)

Am

plitu

de

3- Bode plot (Fig. 8)

39

Kc=12.07

Figure 8: The responses for secondary loop for Proportional controller using Bode plot

Proportional integral controller (PI)

1- Routh (Fig. 9)

Kc=10.71 ,τi=33.139

Figure 9: The responses for secondary loop for Proportional integral controller using Routh criteria


0 100 200 300 400 500 600 700-0.5

0

0.5

1

1.5

2

2.5

Step Response

Time (sec)

Am

plit

ude

0 100 200 300 400 500 600 700 800-0.5

0

0.5

1

1.5

2

2.5

3

Step Response

Time (sec)

Ampli

tude

2- Root locus(Fig. 10) 40

Kc= 10.62 ,τi = 24.017

Figure10: The responses for secondary loop for Proportional integral controller using Root locus

3- Bode plot(Fig. 11)

Kc=10.863, τi= 23.75

Figure 11: The responses for secondary loop for Proportional integral controller using Bode plot

Proportional, integral and derivative controller (PID)

1- Routh (Fig. 12)

Kc=14.28 ,τi= 19.8835 , τd= 4.97


Step Response

Time (sec)

Ampl

itude

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

Step Response

Time (sec)

Am

plitu

de

0 50 100 1500

0.5

1

1.5

2

2.5

41

Figure 12: The responses for secondary loop for Proportional integral and derivative controller using Routh criteria

2- Root locus (Fig. 13)

Kc=14.16 ,τi=14.41 ,τid=3.6025

Figure 13: The responses for secondary loop for Proportional integral and derivative controller using Root locus

3- Bode plot ((Fig. 14)

Kc=14.484, τi= 14.25 , τid= 3.5625


Step Response

Time (sec)

Am

plitu

de

0 50 100 1500

0.5

1

1.5

2

2.5

Step Response

Time (sec)

Ampl

itude

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

System: G2

Final Value: 0.993System: G2

Settling Time (sec): 0.387System: G2

Rise Time (sec): 0.218

42

Figure 14: The responses for secondary loop for Proportional integral and derivative controller using Bode plot

For the second strategy:

The responses for secondary loop are:

Proportional Controller (P-Controller Only)

Kc=376.25 (Routh ) (Fig. 15)

Figure 15: The responses for secondary loop for Proportional controller using Routh criteria

Proportional integral controller (PI)

Kc= 338.625, τi=3.68 sec (Fig. 16)


Step Response

Time (sec)

Am

plitu

de

0 0.5 1 1.5 2 2.5 3 3.50

0.2

0.4

0.6

0.8

1

1.2

1.4

System: G2

Final Value: 1

System: G2

Peak amplitude: 1.02

Overshoot (%): 1.9

At time (sec): 0.825System: G2

Settling Time (sec): 0.361

System: G2


Step Response

Time (sec)

Ampl

itude

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

System: G2

Final Value: 1

System: G2

Settling Time (sec): 0.835

System: G2

Peak amplitude: 1.14

Overshoot (%): 13.9

At time (sec): 0.394

System: G2


43

Figure 16: The responses for secondary loop for Proportional and integral controller using Routh criteria

Proportional, integral and derivative controller (PID)

Kc=451.5 , τi=0.22sec , τid= 0.055 sec (Fig. 17)

Figure 17: The responses for secondary loop for Proportional, integral and derivative controller using Routh criteria


Table 1 44

Comparison between the characteristic of the closed-loop responses using Different techniques for the secondary loop

Method Routh Root locus Bode plot

Type of

control

P PI PID P PI PID P PI PID

Kc 11.9 10.71 14.28 11.8 10.62 14.16 0.42385 0.381465 0.50862

τI(sec) ---- 33.139 19.8835 ---- 24.017 14.41 ---- 23.5855 14.1513

τD(sec) ---- ----- 4.97 ---- ---- 3.6025 ---- ------- 3.5378

overshoot 1.26 1.34 1.08 1.25 1.49 1.28 1.28 1.52 1.28

offset 0.05 0 0 0.01 0 0.005 0 0

Tr 3.91 4.26 1.49 3.93 4.24 1.99 3.87 4.17 1.96

Settling

timeTS

171 288 46.3 171 457 91.8 171 513 91.2

Period of

oscillation

38.1 40.5 17.01 38.7 40.7 38.8 38.2 40.9 38.49

Table 2

Comparison between the characteristic of the closed-loop responses using Different techniques for the primary loop

Method Routh Root locus Bode plot

Type of control P PI PID P PI PID P PI PID

Kc 0.9265 0.83385 1.1118 0.885 0.7965 1.062 0.42385 0.381465 0.50862

τI(sec) ---- 23.799 14.25 ---- 9.45125 5.67075 ---- 23.5855 14.1513

τD(sec) ---- ----- 3.56 ---- ---- 1.41768 ----- ----- 3.5378

overshoot 1.17 1.26 0.536 1.06 1.07 1.25 1.11 1.37 0.715

offset 0.009 0.005 0.003 0.005 0.001 0 0.001 0.001 0.002

Tr 1.9 2.94 1.78 2.98 3.05 2.4 3.4 3.42 2.21

Settling timeTR 220 82.1 23.8 457 59.5 97.7 83.9 136 >35

Period of

oscillation(Ps)

(sec)

11.69 22.9 24.02 21.94 22.9 21.69 28.4 30.1 19.11

A system of normal hexane- water – acetic acid – is

investigated with regard to controlling the efficiency of

separation and column hydrodynamics. A rotating Disc

Contactor column is used for a counter-current liquid-liquid

extraction of the above system.

A control strategy was developed using multi-loop cascade

control. In this study two strategies were undertaken. One

strategy takes the composition controller as a master controller

which transmits its output signal as a set point to the level slave

controller, which controls the input flow rate of the organic

phase as shown in figure 1. The second strategy uses the

composition controller of the extract that transmits its output

signal to the level secondary controller, in order to adjust the

feed rate as shown in figure 2.

The transfer function of each loop in each strategy were

identified and used to get the overall transfer functions and

characteristic equations. These transfer functions were use

through the method of Routh, Root locus and Bode plot to

determine the adjustable parameters (Kc , τi , τd) and the simple

performance parameters , overshoot, offset , settling time, Rise

time and period of oscillation.

These adjustable parameters were used to draw the response

using P,PI and PID controllers and it was found that the

responses give different performance as shown in figures

(6,7,8,9,10,11,12,13,14,15,16,17) and as stated in tables 1 and

2.

IV. CONCLUSIONS

It is concluded that cascade control tuning requires tuning the

secondary and primary loops separately, the adjustable

parameters calculated for the two loops are found to be

different and are not able to give a stable system when set to be

equal for both loops.

The method is to calculate the ultimate gain and ultimate period

for the secondary loop first and then calculating the same for

the primary loop and that the loop should be tuned separately.

ACKNOWLEDGEMENT

The authors wish to thank the College of Graduate Studies and

Scientific Research, Karary University for their help and

assistance to allow this partial research to accomplish. The

authors also wish to thank the technical staff of university of

Science and Technology, faculty of engineering-department of

chemical engineering for their help and permission to carry out

the experimental work.

REFERENCES [1]. http://vienna.che.uic.edu/teaching/che396/sepProj/Snrtem~1.pdf [2]. Seader,(1998). Principle of separation process –J. W,(I.N.C)-liquid-Liquid

extraction with ternary systems. pp ,419-449.

[3]. http://en.wikipedia.org/wiki/Concentration Last modified February 2008

[4]. Dale,E,Edgar, T.F and Duncan, A.M (1998). “Process Dynamic and

control. John Willey and Sons, New York.

[5]. Luyben, L.L (2007).” Process Modeling Simulation and Control for

chemical Engineering”. Mc Graw Hill Publishing Company, New York.

http://vienna.che.uic.edu/teaching/che396/sepProj/Snrtem~1.pdf


6]. Stephan Opoulus, G (1994). “Chemical process control An Introduction to Theory and Practice” Prentice Hall, India,.

45

[7]. Abu-Guok, M. E (2003). “Controlling Techniques and System Stability, University of Khartoum Press.

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