alt="Graph depicts the control action."/>
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.
2.6.2.2 Reference = 500
When the reference value is set as 500 and the Kp, Ki, and Kd values are taken by execution of iterations in GA, then the error is minimized and the displacement is settled at the reference value in the output as shown in Figures 2.14a, b and c.
The Kp, Ki, and Kd values obtained by GA are 0.221923828125,1.32339 6901967211, and 0.12735267270242523.
2.6.2.3 Reference = 1,500
When the reference value is set as 1,500 and the Kp, Ki, and Kd values are taken by execution of iterations in GA, then the error is minimized and the displacement is settled at the reference value in the output as shown in Figures 2.15 a, b and c.
The Kp, Ki, and Kd values obtained by GA are 0. 38281, 0.19672, and 0.24252.
Figure 2.14 (a) Control error for reference value 500.
Figure 2.14 (b) Control action for reference value 500.
Figure 2.14 (c) System output for reference value 500 (error).
Figure 2.15 (a) Control action for reference value 1,500.
Figure 2.15 (b) Control action for reference value 1,500.
Figure 2.15 (c) System output for reference value 1,500.
Table 2.1 Analysis report.
| Distance | Kp | Ki | Kd | Settling time |
| Error 500 | 10 | 0.5 | 5 | NIL |
| 500 | 0.22192 | 1.32339 | 0.12735 | 11 seconds |
| 1,000 | 0.93028 | 0.31099 | 0.75421 | 8 seconds |
| 1,500 | 0. 38281 | 0.19672 | 0.24252 | 9 seconds |
2.6.2.4 Analysis Report
The MATLAB software has been analyzed for different values of reference. Kp, Ki, and Kd and settling time have monitored across each references (Table 2.1).
2.7 Hardware Results
The displacement of the piston is measured and converted to digital signal and then given to the System. The FOPID using GA generates the most accurate value using successive iterations. This value is given to the controller, which moves the piston to that value. Thus, the position is controlled using FOPID controller. Figure 2.16 shows the hardware setup of the position servo system.
Figure 2.16 Hardware setup of position servo system.
