Advanced Fireworks Algorithm and Its Application Research in PID Parameters Tuning

Table 2

Statistical results.

Function	Pa.	Z-N		AFW		EFW		PSO
		ITAE	ITUE	ITAE	ITUE	ITAE	ITUE	ITAE	ITUE
()		5.225	0.4536	0.0174	0.3646	0.0814	0.3649	0.0814	0.3672
		13.3021		0.6771	0.2594	30	0.2873	30	0.2791
		1.2164		7.5184	2.9116	30	3.1724	30	3.31
		12.0285		7.5108	2.9064	22.2751	3.1694	22.275	3.2908
		—		0.489	1.31	0.735	1.2	0.735	1.16
		4.36%		0%	0%	4.74%	0%	4.74%	0.0649%
()		0.05974	0.1008		0.1046	0.0016	0.1043	0.0016	0.1223
		1.1504		23.1311	0.5909	8.6633	0.7817	8.7425	2.7446
		0.7772		0	0	30	0	30	9.2965
		0.0705		2.0809	0.052	0.36304	0.09986	0.3646	0.1514
		0.587		0.0643	0.288	0.155	0.342	0.154	0.375
		10.4%		49.7%	0%	25.2%	0%	25.3%	8.12%
()		23.29	7.8	0.0042	0.1211	0.0039	0.1190	0.0061	0.1226
		0.0271		21.6408	1.3742	30	1.1759	30	1.4559
		0.0043		2.1830	11.7829	24.2796	9.2061	30	13.6554
		0.0866		0.74008	0.12561	15.2678	0.105	3.1136	0.14221
		23.9		0.0938	0.67	0.0718	0.808	0.0697	0.59
		7.41%		43.5%	3.77%	75.7%	4.26%	57.3%	3.9%
()		13.19	2.938	0.1055	0.5265	0.4358	0.5265	0.4358	0.5265
		0.7484		5.2644	2.8763	30	2.8741	30	2.8886
		0.0020		0	0	0	0	0	0
		2.6791		29.9807	14.6236	30	14.623	30	14.6463
		21.1		2.4	1.07	2.85	2.41	2.85	2.39
		5.04%		0.784%	0.0349%	18.9%	0.778%	18.9%	0.804%
()		5.67	0.9095	0.1211	0.6971	1.1880	0.6974	1.1880	0.6985
		21.5801		1.7623	0.94238	30	0.95494	30	1.0341
		0.92192		2.508	1.2476	11.3251	1.2849	11.3253	1.3078
		30		29.5197	14.6483	30	15.0704	30	15.1394
		0.706		2.73	1.18	6.07	2.66	6.07	2.54
		10%		0%	0%	26.1%	0.0874%	26.1%	0.449%