An exponential based simulated Kalman filter algorithm for data-driven PID tuning in liquid slosh controller

This paper presents an Exponent-based Simulated Kalman Filter (EbSKF) algorithm. SKF is a random based optimization algorithm inspired from a Kalman Filter theory. A Kalman gain is formulated following the prediction, measurement and estimation steps of the Kalman filter design. The Kalman gain is utilized to introduce a dynamic step size of a search agent in the SKF algorithm. The proposed EbSKF is strategized such that the Kalman gain is formulated based on an exponential function with respect to number of cost function evaluation (NFE). The Kalman gain is exponentially reduced when the NFE increases in which happens when the search operation is progress forward. The algorithm is tested to PID tuning for liquid slosh control application. The EbSKF is compared with the original SKF algorithm. In this study, 30 independent runs are performed to record different values of the best solutions generated by the algorithms of interest. The average of the minimum value is compared. It determines significant difference of the generated solution and it reflected the accuracy of the solution. Result of the statistical analysis on the accuracy, which is tested on the function of slosh control application is presented in a table form. The result shows that the proposed algorithm outperforms SKF significantly. The convergence plot for both EbSKF and original SKF is also presented and it confirms the statistical result.