Influence of the Selection of Reaction Curve’s Representative Points on the Accuracy of the Identified Fractional-Order Model

Table 10

Algorithm for determining FFOPDT model parameters θ_P = {K, T, L, α} when three symmetrical points {t_x, t₅₀, t_100‒x} on the reaction curve are specified.

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Algorithm: identification method for three symmetrical points

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Input: {t_x, t₅₀ and t_100‒x}, Δy, and Δu from the process reaction curve

Output: FFOPDT model parameters θ_P = {K, T, L, α}

1: Calculate the process gain K using (21).

2: Collect t_x, t₅₀, and t_100‒x from the process reaction curve.

3: Calculate the value of Δ using equation (32).

4: Calculate the value of α = f₁(Δ) using equation (34).

5: Calculate the value of functions f₂(α) and f₃(α) using equations (35) and (36), respectively.

6: Determine the value of T = f₂(α)·(t_100‒x – t_x)^α.

7: Determine the value of L = t_100‒x – f₃(α)·T^1/α.

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