where
wi =
1 di k P i=1
1 di
. (10)
By these procedures, PID gains are adaptively-tuned at every step. The block diagram of the DD-PID controller is shown in Fig. 1. However, an initial database obtained by utilizing a fixed PID controller is not able to tune PID gains suitably in operation because all PID gains in a dataset are same. Thus learning these parameters in advance is required. In Section III, the data-driven fictitious reference iterative tuning (DDFRIT) method for learning an initial database is presented.