1#. • Basis Weight Control System
'JH Ȟ Step response of the best FOPDT approaching P 3 using classical PSO, PSO-TVAC, MPSO, and SNPSO
Table 6 and Table 7 present the FOPDT and SOPDT model parameters for processes P 4 , respectively. To compare the identification capabilities of the four algorithms, the tables also include a measure of 'JH Ȟ Nyquist curve: primitive high-order function P 3 (black line), and approximation model using PSO (blue), PSO-TVAC, MPSO, and SNPSO 5BCMF Ȟ '01%5SFTVMUTGPS 1 VTJOHGPVS140 - CBTFEBMHPź SJUINT Methods Min Max Mean Std
SOPDT step responses approximating P 3 using classical PSO, PSO-TVAC, MPSO, and SNPSO. Black line represents the primitive high-order function P 3 . The identification method based on optimization algorithm can make the identification model approach the primary model well. The approximation performance of the SOPDT model is better than that of the FOPDT model. Nyquist curve further proves that the SOPDT model is more approximate to the primary model than the FOPDT model as illustrated in Fig. 16. 6.4 Ȟ Transfer function P 4 When the real process is assumed to be the transfer function (Eq. (14)), the estimation models are as follows: G F ( s ) = K F T F s + 1 e ϖ L F s (19) G S ( s ) = K S ( T S 1 s + 1) ( T S 2 s + 1) e ϖ L S s (20) 'JH Ȟ Step response of the best SOPDT approaching P 3 using classical PSO, PSO-TVAC, MPSO, and SNPSO
Best parameter K F =1.000, T F =0.919, L F =0.294 K F =1.000, T F =0.921, L F =0.318 K F =1.000, T F =0.873, L F =0.360 K F =1.000, T F =0.974, L F =0.243
22.3
2331.2
290.9
718.5
Classical PSO
22.2
4887.8
1119.0
1774.5
PSO-TVAC
23.0
236.7
53.0
66.1
MPSO
22.9
104.1
43.7
29.5
SNPSO
7PM /P
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