Optimal gain-scheduled proportional integral-derivative (PI-D) control of asymmetrical thermal processes

Asymmetrical systems are those which have two operating modes. In this paper, it is focused on optimal control of asymmetrical thermal (heating and cooling) processes. Although asymmetrical thermal processes are common in industry, studies on this subject are surprisingly very few. This situation has been a driving force to conduct this study. In this paper, First Order Plus Dead Time (FOPDT) transfer function model is used for each operating phase of asymmetrical thermal processes. For the control goal, two optimal Proportional Integral-Derivative (PI-D) controllers are designed and merged in a gain-scheduled manner. Optimal tuning rules for PI-D controller parameters are attained by minimizing time-weighted integral performance indices and utilizing curve fitting technique. Therefore, the study provides a novel method which allows calculation of optimal PI-D controller parameters by explicit formulas according to designated integral performance criterion. The derived formulas consist of only process transfer function parameters and are easy-to-use. Some simulation examples are provided to show the use and benefits of the proposed control method. Comparisons with a similar recent study are performed and it is demonstrated that proposed method has important advantages on the control performance.