Table 3 Comparison of identification results under different fractional order \(\alpha\).

From: Fractional order system identification using a joint multi-innovation fractional gradient descent algorithm

Fractional order

\(a_{1}\)

\(a_{2}\)

\(b_{0}\)

\(\overline{\alpha }\)

\(\delta\)

Truth value

8

5

3

1.5

 

\(\alpha = 0.5\)

8.0083

4.9599

2.9877

1.5220

0.00487

\(\alpha = 0.8\)

8.0190

4.9863

3.0062

1.5075

0.00253

\(\alpha = 1.2\)

8.0183

4.9890

3.0135

1.4996

0.00252

\(\alpha = 1.5\)

7.9370

5.0092

2.9908

1.4463

0.00837

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