Iterative PID gain tuning using gradient estimate of variance cost criterion through regulatory control data

The paper proposes an iterative PID gain tunin method using a cost criterion representing the vairance of the process output for the oritinal control objective. The approach estimates the gradient vector of the original cost criterion using closed-loop regulatory data. The PID gains are iteratively updated based on the gradient descent algorithm. Unlike the conventional IFT(IterativeFeedback Tuning), the proposed approach firstly estimates the sensitivity function from the regulatory control data for deriving the gradient of the cost function. While the IFT that requires a special experiment that feeds the closed-loop response data as a reference signal, the proposed one estimates the gradient vector of the cost criterion without using a special experiment. Additionally, the proposed approach uses two sets of output data are collected from the closed-loop system, then each time series model is estimated from time-series analysis. The gradient of the output variance is estimated from the ratio of these derived time series models. The effectiveness of the proposed method is shown through a numerical example.