Computer-based Simulation Results for the Fuzzy Logic Controller

This section discusses some dynamic responses obtained from computer-based simulation work. All of the results shown in this section are based on the performance of the fuzzy logic controller with the modified pH model. This model is in actual fact the final version of the modified model (referring to information in Section 4.5.3), which includes the new set of dissociation constant values as well as the additional part for initialisation purposes. As mentioned earlier, the main goals for this exercise are to evaluate the reliability of the model as well as to investigate some benefits and limitations of the fuzzy logic approach.

Selected experimental data have been chosen to assist in this investigation such as the value of conductivity for both solutions, flowrates for acid as well as set point values in the reactor tank. There are four simulation results that represent the same four experiments which have been presented and discussed in the earlier section (i.e.

the experimental results).

The first simulation result, shown in Figure 6:17, is based on the configuration for the set point change experiment. The actual response from the pilot plant for this exercise is shown in Figure 6:11. As explained earlier, the idea of this experiment is to observe the control performance of the fuzzy controllers when a set point change has been introduced.

0 100 200 300 400 500 600 700 800 900

(b) Flowrate for alkaline and acid streams

Time (s)

Figure 6:17: Simulation of the set point change experiment

As shown in the figure, for the first step change, which is from pH value 7 to pH value 10, the simulation result shows a response that is similar to the experimental result. However, at the second step change (from pH value 10 to pH value 7) the dynamic response in the simulation shows a different transient behaviour, particularly from pH value 8 to pH value 7. This might be due to the variation of the process gain for different parts of the range of pH value. As explained in Section 4.4 (referring to the explanation for Figure 4:4), the process gain for the region from pH value 6 to pH value 8 is lower than the process gain for the region from pH value 8 to pH value 10. However, as shown in Figure 6:17, the transient takes a much longer time to reach the new set point at pH value 7 compared with the transient results obtained from the pilot plant. The result suggests that the acid-base reaction process from the modified pH neutralization process model is slightly slower than the actual reaction in the pilot plant in this part of the operating range.

Some modifications have been made in order to consider the above- mentioned problems in more detail. These changes are intended to improve the dynamic response of the model between pH value 6 and pH value 8. Figure 6:18 shows the new structure of the controller. As shown in the figure, there is an additional input to the pH fuzzy logic controller that represents the critical region (i.e. from pH value 6 to pH value 8). There is also an additional output from the controller that reacts to the additional input. The main idea of this new configuration is that whenever the set point of the pH value is set within the critical region the total value of the manipulated variable, MV will depend on the second output (i.e. the additional output) from the pH controller. The function of the additional control valve opening from the second output is to make the system more sensitive through more aggressive control valve movements. However, if the set point of the pH value occurs outside this region, the pH controller will only respond to the first input set, which is the pH error. For this condition the second output from the fuzzy logic controller will always be zero. This shows that outside the critical region the pH controller will utilise the same configuration as that used in the experimental work on at the pilot plant. For the fuzzy logic flow controllers, the configuration remains the same as that being used in the experiment on the pilot plant.

1

Figure 6:18: The new structure of the controller

Figure 6:19 shows the membership functions for the additional input while Figure 6:20 shows the membership functions for the additional output for the pH controller.

There is a single membership function for the additional input, which indicates the critical set point pH value. However there are six triangular shapes of membership functions for the additional output.

Figure 6:19: Membership function for the additional input set

Figure 6:20: Membership function for the additional output set

Table 6.9 provides the detailed description of the controller and the actual parameter values used for the membership functions for both the additional input and the output. The investigation of parameters values for the membership functions was mainly based on the performance of the modified pH model. Some titration curves from the modified model and also the performance of the pH controller shown in Figure 6:17 were used as guidelines. Once the structure of the new pH controller was identified the final choice of the parameters for the membership function was based on a trial and error approach.

7 7.2 7.4 7.6 7.8

6 6.2 6.4 6.6 6.8 8

1

0

CReg

0 20 40 60 80

-100 -80 -60 -40 -20 100

1

0

CNLpho CNMpho CNSpho CPSpho CPMpho CPLpho

Table 6.9: Membership function descriptions and parameters for the additional input and output sets

Additional Input

Symbol Descriptions Type Parameters

CReg Critical Region Trapezoid 6 6 7 8

Additional Output

Symbol Descriptions Type Parameters CNLpho

Critical Negative

Large Triangular -100 -95 -90

CNMpho

Critical Negative

Medium Triangular -60 -35 -15

CNSpho

Critical Negative

Small Triangular -30 -18 0

CPSpho

Critical Positive

Small Triangular 0 18 30

CPMph_o Critical Positive

Medium Triangular 15 35 60

CPLph_o Critical Positive

Large Triangular 80 90 100

Apart from the additional input and output there are also four additional membership function that have been added to the previous input set (i.e. pH error) of the pH controller. Table 6.10 provides the description of the new configuration of membership function for the input set. As given in the table, the additional membership functions are highlighted as CNSph, CNVSph, CPVSph, and CPSph.

The main purpose of the additional membership functions is to make the fuzzy logic controller more sensitive to the pH error (that is to the difference between the set point and the process variable).

Table 6.10: New configuration for the first input set for the pH controller Symbol Descriptions Type Parame ters

NVLph Negative Very

Large Trapezoid -5.0 -5.0 -4.0 -2.0 NLph Negative Large Triangular -3.0 -2.0 -1.0

NMph Negative Medium Triangular -2.0

-1.25 -0.5 NSph Negative Small Triangular -1.0 -0.5 0 CNSph Critical Negative

Small

Triangular

-0.6 -0.3 -0.1 CNVSph Critical Negative

Very Small

Triangular

-0.3 -0.1 0

Zph Zero Triangular -0.5 0 0.5

CPVSph Critical Positive Very Small

Triangular

0 0.1 0.3