This study presents online-tuning approach using the moth flame optimization (MFO) algorithm to optimize the parameters of PID and modified PID (I-PD) controllers used in the split-range scheme to control the temperature of the mixing process. The performance of these controllers is investigated for the individual temperature setpoints in terms of settling time and compared with performances obtained using offline-tuning approach with the MFO algorithm. The simulation results show a significant improvement with online-tuning approach as compared to offline approach. To further improve the performance, this study proposes modifications in the original MFO algorithm in three phases: by changing the spiral path, by changing the initial population based on the opposition theory, and by a change in the selection of the flames for the updating mechanism. A new version of MFO algorithm is obtained by combining the above-mentioned modifications and used to tune the PID and I-PD controllers in both offline and online modes. Further, the new algorithm is tested for both the controllers with respect to the effect of system dynamics and the effect of process disturbance. The results obtained after validation show that the use of the new version of the MFO algorithm further improves the online tuning of both the controllers. The simulation results also clearly establish the superior performance of the modified PID (I-PD) controller over the PID controller under all conditions.

这项研究提出了一种在线调节方法，该方法使用飞蛾火焰优化（MFO）算法来优化PID的参数，并在分段范围方案中使用改进的PID（I-PD）控制器来控制混合过程的温度。针对稳定时间，对各个控制器的性能进行了调查，并将其与使用MFO算法的离线调节方法获得的性能进行了比较。仿真结果表明，与离线方法相比，在线调整方法有显着改善。为了进一步提高性能，本研究提出了对原始MFO算法的三个阶段的修改：通过更改螺旋路径，基于对立理论更改初始填充量以及更改用于更新机制的火焰选择。通过组合上述修改获得了MFO算法的新版本，并用于离线和在线模式下对PID和I-PD控制器进行调节。此外，就系统动力学的影响和过程扰动的影响，对两个控制器都测试了新算法。验证后获得的结果表明，使用新版本的MFO算法可以进一步改善两个控制器的在线调整。仿真结果还清楚地表明，在所有条件下，改进型PID（I-PD）控制器都优于PID控制器。针对系统动态和过程扰动的影响，对两种控制器的新算法都进行了测试。验证后获得的结果表明，使用新版本的MFO算法可以进一步改善两个控制器的在线调整。仿真结果还清楚地表明，在所有条件下，改进型PID（I-PD）控制器都优于PID控制器。针对系统动态和过程扰动的影响，对两种控制器的新算法都进行了测试。验证后获得的结果表明，使用新版本的MFO算法可以进一步改善两个控制器的在线调整。仿真结果还清楚地表明，在所有条件下，改进型PID（I-PD）控制器都优于PID控制器。