A Predictive hill climbing algorithm for real valued multi-variable optimization problem like PID tuning

Abstract

This paper proposes a novel method of applying Hill Climbing algorithm for optimizing a problem which has more than one dependent variable and a very large search space. Tuning of PID controller for complete Black-Box plant model is an example of one such problem, where the search algorithm is applied to find PID gains which satisfy the desired optimization criteria. The traditional Hill Climbing algorithm cannot be directly applied to tune PID since the PID controller has three parameters to be tuned and search space is a large collection of real numbers. Searching the entire 3D infinite space without knowing the step size is not easy for this search method. Hence, the traditional Hill Climbing algorithm is modified to adjust the step size and the direction of search dynamically to make the search faster. The algorithm maintains the direction of search as long as it is approaching the optimal point with increase in step size. When it fails in its prediction, the search is randomized in all directions with decrease in step size. This predictive search method reduces the search time and is effective for a very large search space. This paper explains how the algorithm is successful in tuning PID controller and the performance of the algorithm is analyzed.