Iterative PID Regulatory Control Design using Gradient Estimate of LQG evaluation

Iterative Feedback Tuning (IFT) is a kind of datadriven controller parameter tuning that estimate a gradient vector of a prescribed cost criterion. Using the estimated gradient vector controller parameters are updated by way of the steepest decent algorithm. The present work proposes an IFT for a discrete-time, velocity type of PID regulatory controller that optimizes a Linear Quadratic Gaussian (LQG) cost criterion. The main contribution of the present work is to extend our previous work to an LQG cost criterion from output variance evaluation. The proposed method inherits the feature from the previous work that avoids the second experiment where the first experimental data is fed to the closed-loop system as a reference signal and provides an estimation method for a gradient vector of the sum of output variance and input variance. In detail, the present work provides an estimate of sensitivity function for an estimate of a gradient vector of the variance of input signal while the previous work provided an estimate of complementary sensitivity function for an estimate of gradient vector of output signal. The effectiveness of the proposed method is shown through a numerical simulation result.