Process Modeling: The main problem in setting up a signal flow diagram for a level controlled system in a SG can be found in the inhomogeneous contents of the SG.

The filling consists of water at boiling temperature, pervaded by steam bubbles.

Since the volume fraction of the steam bubbles is quite considerable, the mean specific weight of the contents is very strongly dependent on the proportion of steam.

This, of course, means that the steam content also strongly influences the level in the SG. The steam content itself depends, in turn, on the load factor, on the changes in feed-water flow, and on feed-water temperature.

The presence of steam below the liquid level in the SG causes the shrink-and-swell phenomenon that in spite of an increased supply of water, the water level initially falls. Figure 2 shows responses of the water level to steps in feed-water and steam flow-rates at different operating power levels (Irving et al., 1980).

Particularly it is difficult to control automatically a steam generator water level during transient period or at low power less than 15% of full power because of its dynamic characteristics.

The inverse response behavior of the water level is most severe at low power (5%).

The changing process dynamics and the inverse response behavior significantly complicate the design of an effective water level control system.

A solution to this problem is to design local linear controllers at different points in the operating regime and then applies gain-scheduling techniques to schedule these controllers to obtain a globally applicable controller.

Consider a step in feed-water flow rate at 5% operating power. For this system, a fuzzy convolution model consisting of four fuzzy implications is developed as follows:

For j=1 to 4:

R’ : if VDd (n) is A

200

then j (n +1) = y1od () +Xh_Ddu(n +1 -i)

i=1

(a) (b)

Figure 3. shows the response of water level at 5% operating power to a step in feed-water flow — rate. In Figure 4 the system is decomposed into 4 subsystems: yD, , Уг>1, yD t, yD, ■

Figure 5 shows the impulse response coefficients for yD (, yD t, yB yD ( subsystems and Figure 6 shows the definition of fuzzy sets A1, A2, A3 and A4. Consider a step in steam flow rate at 5% operating power.

For this system, a fuzzy convolution model consisting of four fuzzy implications is developed as follows:

For j=1 to 4:

Rj: if Vd0 (n)isAl

200

then yD (n +1) = yD0 (n) + Xh — Do’u (n +1 -1)

0 i=1

Figure 7 shows the response of water level at 5% operating power to a step in steam flow — rate.

In Figure 8 the system is decomposed into 4 subsystems: yD0 , yD0, yD0 , yD0 •

Figure 9 shows the impulse response coefficients for yD0, yD0, yD0, yD0 subsystems, Figure 10 shows the definition of fuzzy sets A1, A2, A3 and A4.

Fig. 8. The system is decomposed into 4 subsystems: yDo, yD0, Vd0 , Vd0 •

Fig. 9. The impulse response coefficients for yD0 , yD0, yD0, yD0 subsystems

Controller Design: The goal is to study the use of the feed-water flow-rate as a manipulated variable to maintain the SG water level within allowable limits, in the face of the changing steam demand resulting from a change in the electrical power demand.

The simulations are organized around two different power transients:

• a step-up in power from 5% to 10% (Figure 11);

• a ramp-up in power from 5% to 10% (Figure 12)

The model horizon is T=200. Increasing Ny results in a more conservative control action that has a stabilizing effect but also increases the computational effort.

The computational effort increases as Nu is increased. A small value of Nu leads to a robust controller.

For both power transients the controller responses are very satisfactory and not very sensitive to changes in tuning parameters.

We can see that the performance is not strongly affected by the presence of the feed-water inverse response, only a slight oscillation is visible in the water level response.

Step power increase from 5% to 10%
Power [%]
	L
	5 1	5 3 Time [sec]	5 55

Fig. 11. Water level response to a step power increase from 5% to 10% (Nu=2, Ny=3, W1=1)

(b) (c)

(d)