Tuning digital PI controllers for minimal variance in manipulated input moves applied to imbalanced systems with delay

Determining the discrete‐time proportional plus integral (PI) controller tuning parameters to achieve the smallest possible variance in the manipulated input moves, for a given variance in the controlled output, is the subject of this article. Previous researchers have developed tuning rules for PI and PI permutated nonlinear controllers to achieve what is commonly referred to as “level‐flow smoothing”, or “averaging level control”, on imbalanced or integrating processes with delay, such as liquid level and gas pressure systems. The intent of this note is to demonstrate a new and simple technique of tuning digital PI controllers which utilizes either open or closed‐loop historical data to estimate the process gain, dead‐time and expected flow disturbance magnitude from which the digital PI tuning constants can be easily derived. By parameterizing the closed‐loop system as a function of the PI tuning constants, we can simultaneously minimize the expected variation in the process input move and output responses while at the same time ensuring nominal stability of the overall system. In order to demonstrate the technique, an illustrative example is included which highlights the new procedure on an oil refinery liquid surge drum level process.