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When the reference value is set as 500 and the Kp, Ki, and Kd values are taken manually (10, 0.5, and 3) without using GA, then the output will be coming as follows. Figures 2.10, 2.11 and 2.12 shows the control error, control action and system output.

Figure 2.9 Genetic algorithm tool box.

Figure 2.10 Control error.

Figure 2.11 Control action.

Figure 2.12 System output.

Figures 2.13 a, b and c shows the piston displacement at a reference = 500 (error) using Kp = 10, Ki = 0.5 and Kd = 3 without GA.

Figure 2.13 (a) Control error for reference value 500 (error).

Figure 2.13 (b) Control action for reference value 500 (error).

Figure 2.13 (c) System output for reference value 500 (error).

Here, the displacement of the piston is not settled at a reference value. Hence, this output is considered as error. To rectify this, we use GA.