Project Draft Control of Stirred Tank Heater

8/11/2019 Project Draft Control of Stirred Tank Heater

http://slidepdf.com/reader/full/project-draft-control-of-stirred-tank-heater 1/28



CBE 4424 – Computer Process Control

Course Project

Submitted to: Professor s.Rohani

Dawood Al-Mosuli – 250715524



Abstract

In this course project, we tried to tune PID controllers to control the liquid level and temperature

in a stirred tank.

The method used is tuning the PID controllers using the tuning facility in the Simulink program.

Tuning parameters are got in time, S and discrete domain. Nose is added using “Band limited

White noise” to the feedback loop of the discrete mode. The effect of noise on the system is

monitored and the highest noise power which could be handled by the system without bringing

the system into instability is recorded. The effects of noise are reduced by adding a first order

filter.

The conclusions and reference are cited at the end and the datasheet of the tank is demonstratedin the appendix.



Introduction and Process description

One of the most applicable apparatuses in chemical plants, reservoirs, drums or tanks are

commonly used in industry. These tanks represent continuous stirred tank reactors or are

installed in the outlet of a reactors or distillation towers or may use to keep the material in a

certain situation for a specific period of time, before pumping them to other plant locations.

Often in each tank, the variables that should be controlled are temperature and the liquid level of

the tank in order to avoid overflow, leaking spoilage and other common problems.

In this process, there are 2 streams of liquids at different temperatures to be mixed together in the

tank and come out as a single stream with a flowrate equal to the summation of the input flow

rates and temperature should be kept between the input stream temperatures.

In order to control these variables we use two control valves installed at each of the inlet streams

to control the temperature and liquid level inside the tank.

Density and heat capacity of the streams are assumed to be the same of the tank. The tank

components are assumed to be well mixed.

The controllers used in this tank are PID controllers and all the loops are feedback loops.

First of all, the simulation is offered in time domain, then simulations are given s and discrete

domains. In the discrete domain, the effect of noise and noise filtration are studied.



P&ID of the process and Block diagram

Figure 1-a shows the simple P&ID of the process

I/P I/P

LC

h TC

LT TT

F(t) ,T(t)

Figure 1

Fh(t),T(t)Fc(t),Tc(t)



Mathematical modeling

Disturbances

Th Tc Fc

FC Process T(t) Control variables

Fh h(t)

Figur2

Manipulated variables

The system can be represented by the above figure. This system requires 8 individual transfer

functions relating h and T to input variables (4 for T and 4 for h) .

Step 1: Linearization of non-linear mass and energy balances.

Mass balance: ; dV/dt=Fh(t)+Fc(t)-F(t) ---------------------1

Energy balance: (dV(t) T(t))/dt=Fh(t)Th(t)+Fc(t)Tc(t)-Ft(t)-----2

Both above equations are nonlinear.

For the mass balance equation, using the linearization of the relationship between F(t) and

h(t)



I.e. F(t)= K*h^0.5

Taylor series y(t)=~ K*hi^0.5+(h-hi)K/(2h^0.5) --------------------3

This is ended by the following equation in the Laplace domain:

h(s) = Fc(s)/(As+B) +Fh(s)/(As+B) ------------------------------------4

Where A is the tank cross sectional area. K is the flow resistance. B =K/(2hi^0.5)

From the energy balance of the system, the following equation is got in the S domain:

T(s)={[(Thi-Ti)/Fi]/(tp *s +1)}* Fh(s) + {[(Tci-Ti)/Fi]/(tp *s + 1)}*Fc(s) + {[(Fhi/Fi]/(tp *s +1)}

*Th(s) + {[(Fci/Fi]/(tp *s +1)} *Tc(s) -------------------------------------------------5

tp is the time constant = A*hi^0.5/K

Fi=K*hi^0.5

The symbol Indicates the initial conditions for the system .

By assuming that the steady state level is 16 meter at outlet flowrate =200 M3/min.

The value of K=50 is got. Cross sectional area is assumed to be 20 m^2. Steady state outlet

temperature is choose to be 30o

C.



Block diagram for the system in S domain

Th(s) (Fhi/Fi)/(tp s +1)

Tc(S) (Fci/F1)/(tp s +1)

+

Fc(s) 1/(A S +B) h(s)

+

((Tci-Ti)/Fi)/(tp s+1)

Fh (s) 1/(A S +B)

+ + +

((Thi-Ti)/Fi)/(tp s+1)

+ T(s)



Figure 3

Time domain simulation and results.

Figure 4 Simulation of the system in time domain simplified by a subsystem.



Figure 5 Details of the subsystem; hot water flow is used to control the tank level while cold

water flow is used to control the tank temperature.



Figure 6 Whole system with its details.



Results in time domain

Time

Figure 7. Response of the system in time domain using PID controller. Temperature in green, level in

blue. 30 is the set point for temperature, 16 is the set point for level



S domain simulation

Figure 8. Simulation of the S in time domain.



S domain results

Time

Figure 9. Response of liquid level with time (solution in S domain)

Time

Figure 10. Response of output temperature with time (solution in s domain)

30 is the set point for temperature, 16 is the set point for level.

evel

evel



Simulation in discrete domain

Figure 11. Simulation of the system in discrete domain simplified by a subsystem.



Figure 12.Details of the discrete subsystem (Zero order hold is added)



Results in discrete mode

Time

Figure 13.Response of liquid level with time.

Time

Figure 14.Response of outlet temperature with time.

30 is the set point for temperature, 16 is the set point for level

Level

mperature



Discrete mode simulation after adding noise

Band limited white noise is added to the system. It is found that the system can handle a

maximum noise power of till reaching 15.0. The temperature doesn’t affect in a significant

manner, but the level suffers from a fluctuation around 25% around its original value. The

effect of adding first order filter is noticed. The discrete transfer function of this filter is a/(1-(1-

a)*z-1

). The values of a range from 1 for no filtration to 0 for complete blocking of noisy signal.

Figure 15.Simulation of the process after adding noise without filtration. Filter is tuned to be

inactive.



Results of adding noise without filtration.

Time

Figure 16.Response of tank level after adding noise(magnitude=15) with time

Level



Time

Figure 17.Response of outlet temperature after adding noise (magnitude =15) with time.


Noise filtration.

Due to the strong effect of noise, a strong filter with (a) factor=0.1 is added to the level control

loop. Another filter with (a) factor of 0.9 (weaker than that used for the level)is added to the

temperature control loop since the temperature doesn’t affect a lot by the noise level . The

simulation is as follows:

m erature



Figure 18.Simulation of the system after adding Filter.



Results of adding filter

Time

Figure 19.Response of liquid level after adding filters with (a)=0.1 for level ,0.9 for

temperature.

Time

Figure 20.Response of outlet temperature after adding filters with (a)=0.1 for level, 0.9 for

temperature.

Level

emperature



30 is the set point for temperature, 16 is the set point for level.

If the (a) factor for the temperature controller increased to be 0.9 as in the level controller,

then this will cause over shooting for both temperature and level to an unacceptable values as

in the Figures below.

Time

Figure 21.Response of liquid level after changing the filtration factor (a) of the temperature

controller from 0.9 to 0.1. High over shooting of 37 is noticed. Noise level is still 15.

vel



Time

Figure 22.Response of outlet temperature after changing the filtration factor of the

temperature controller (a) from 0.1 to 0.9. Significant over shooting is noticed. Noise level is

still 15.


Effect of deleting the differential action from the controller.

In order to avoid increasing noise effects, the differential action is deleted and PI controller is

used instead. Noise level is kept 15. The following results are noticed without filtration.

mperature



Time

Figure 23.Level response when using PI controller at noise level 15 without using filter.

vel



Time

Figure 24.Temperature response when using PI controller at noise level 15 without using filter.

(smoother response than in the case of PID controller).

Time

Effect of adding filters on level response { (a)=0.1 for level, and 0.9 for temperature} to the PI

controller at noise amplitude=15

Level



Time

Effect of adding filters on temperature response { (a)=0.1 for level, and 0.9 for temperature} to

the PI controller at noise amplitude=15

Conclusions and discussion of results

1- It could be seen that in continuous time or s domain, the responses of both level and

temperature with time reach the set-points without offset. This is due to the use of PID

controller. The time domain solution reaches the steady state value in a longer time.

The difference in the solution shapes is due to the approximation of Laplace domain.

2- The solution in discrete mode is stable and reaches set-points without offset for both of

PID and PI controllers.

3- Adding noise causes a lot of instability to the system as seen in the Figures given. When

adding a noise of magnitude of 15, the response is still stable but oscillates with a

magnitude of -+30% around the set point for the level and -+15 for temperature. When

Temperature



the controller is changed into PI, the level response is still oscillating, but the

temperature response is smoother than in the case of PID controller.

4- When adding first order filter to minimize the effect of noise, there is a smoothing of the

curve when strong (a) of first order filter is added. But overshooting of the response

especially with the level is noticed. It causes the level to jump to 25 if filter with (a)=0.1is used for the level control loop and of 0.9 is used for the temperature control loop at

all noise magnitudes from 1 to 15. If filters of (a) = 0.1 are used for both temperature

and level control loops then an over shooting of magnitude of 37 . If the tank height was

in meter. Then when designing a tank with a level set-point of 16 meter, the tank height

should be around 18 meter. With overshooting of 37 meter, the tank will flood. Similar

results are got with PI controller. Decreasing the filtration power to (a)= 0.9 for both

level and temperature will have similar overshooting in level and larger amount of

oscillation. It is concluded that using filter as a mean for smoothing the response can

cause larger problem of overshooting, and it is better to avoid the noise sources. Tuning

the controller with the existence of filter increase the overshooting, and make the

condition even worse.

5- Noise level of magnitude of 10 is acceptable, since it causes oscillation which reaches

amount of 12.5% in level which could be handled by increasing tank safety height. It has

no significant effect on temperature

Reference

Dr.s.Rohani 2013 advanced process control course notes.

Documents

Project Draft Control of Stirred Tank Heater