Here, yr(t) is the output of Gm(z−1) which is the desired response model given by an operator and it is denoted as follows:
Gm(z−1) :=
z−1P(1) P(z−1)
, (13)
where
P(z−1) = 1 + p1z−1 + p2z−2, (14)
p1 = −2exp− ρ 2µcos√4µ−1 2µ ρ p2 = exp−ρ µ
ρ := Ts/σ
µ := 0.25(1 − δ) + 0.51δ
. (15)
In (15), Ts is the sampling interval. Moreover, σ denotes the rise time that the system output attains about 60% of a finale value of a step reference signal. The damping property δ is generally set within 0 ≤ δ ≤ 2.0. In particular, it reflects the binomial response when δ = 0 and the Butterworth model response when δ = 1.0.
B. Initial Database Offline Learning Method by Utilizing FRIT In this research, PID gains in the initial database are learned using the closed-loop data which composes the database. First, in order to calculate PID gains, the neighbor datasets around a query ¯ φ0(t) (which is a query at t[step] in the closed-loop data) are chosen by (8). Next, PID gains Kold(t) are calculated by (9). Furthermore, the calculated PID gains Kold(t) is learned based on the following modified law: