Optimal Tuning of Decentralized PI Controller of Nonlinear Multivariable Process Using Archival Based Multiobjective Particle Swarm Optimization

Table 6

(a) Summary of test output results—Maximum Absolute Error. (b) Summary of test output results—Integral of Absolute Error.

(a)

Test description	Outputs	Baseline PI	Cuckoo PI	Bat PI	Simm A	MOPSO PI
100% load,; step disturbance	CVGAS (KJ/kg)	4.8533	6.0736	6.5038	4.23649	1.0751
	MASS (kg)	6.9383	6.9382	6.9382	6.9407	7.4428
	PGAS (bar)	0.0499	0.040952	0.0410	0.05131	0.0561
	TGAS (K)	0.2395	0.27865	0.2941	0.22438	0.2698
50% load,; step disturbance	CVGAS (KJ/kg)	5.0310	6.7232	7.3247	4.45998	1.0659
	MASS (kg)	8.4548	8.4548	8.4548	8.4548	9.0476
	PGAS (bar)	0.0577	0.0496	0.0494	0.05918	0.0634
	TGAS (K)	0.2660	0.31869	0.3395	0.24766	0.2852
0% load,; step disturbance	CVGAS (KJ/kg)	5.8914	8.0184	9.8772	4.70603	1.0445
	MASS (kg)	11.053	11.053	11.053	11.0529	11.8115
	PGAS (bar)	0.0772	0.075986	0.0760	0.078547	0.0829
	TGAS (K)	0.3232	0.40339	0.4315	0.30182	0.3218
100% load, sinusoidal disturbance	CVGAS (KJ/kg)	4.1025	3.7562	3.7838	2.4006	0.3603
	MASS (kg)	10.858	10.756	10.799	10.173	9.9925
	PGAS (bar)	0.0496	0.029062	0.0258	0.04049	0.0401
	TGAS (K)	0.3784	0.35226	0.3566	0.280606	0.2491
50% load, sinusoidal disturbance	CVGAS (KJ/kg)	4.7122	4.3039	4.3730	2.7118	0.4094
	MASS (kg)	12.852	12.719	12.783	11.991	11.7817
	PGAS (bar)	0.0623	0.036325	0.0325	0.04949	0.0495
	TGAS (K)	0.4226	0.39123	0.3982	0.31069	0.2785
0% load, sinusoidal disturbance	CVGAS (KJ/kg)	5.8585	6.8594	7.9930	3.4857	0.7028
	MASS (kg)	16.346	16.296	16.365	15.532	15.2117
	PGAS (bar)	0.1196	0.099138	0.0991	0.09041	0.0879
	TGAS (K)	0.4791	0.51445	0.5699	0.36566	0.3573

(b)

Test description	Outputs	Baseline PI	Cuckoo PI	Bat PI	Simm A	MOPSO PI
100% load, step disturbance	CVGAS (KJ/kg)	30.492	34.956	37.035	21.4567	4.1192
	MASS (kg)	795.29	766.03	768.72	770.167	845.6540
	PGAS (bar)	0.3883	0.71104	0.6365	0.66801	0.4134
	TGAS (K)	32.449	31.668	31.812	25.3313	28.0122
50% load, step disturbance	CVGAS (KJ/kg)	32.224	37.329	38.920	23.588	4.3242
	MASS (kg)	421.53	442.03	437.36	905.62	1671.89
	PGAS (bar)	0.4669	0.96041	0.8552	0.8308	0.51978
	TGAS (K)	38.433	37.073	37.278	31.295	35.5484
0% load, step disturbance	CVGAS (KJ/kg)	43.864	46.585	49.858	30.7476	5.65885
	MASS (kg)	667.9	573.95	580.91	834.466	1754.91
	PGAS (bar)	0.59493	2.2373	1.9707	0.86776	0.56538
	TGAS (K)	38.388	35.714	36.169	29.5588	32.109
100% load, sinusoidal disturbance	CVGAS (KJ/kg)	773.94	703.34	709.01	450.358	68.077
	MASS (kg)	2076.5	2075	2073.8	2073.03	2191.29
	PGAS (bar)	9.2825	5.4295	4.8282	7.4122	7.452
	TGAS (K)	66.998	62.211	62.933	49.092	44.986
50% load, sinusoidal disturbance	CVGAS (KJ/kg)	879.66	802.54	812.64	506.179	76.7957
	MASS (kg)	2522.2	2517.3	2515.5	2515.83	2655.36
	PGAS (bar)	11.506	6.7252	6.0099	9.125	9.1915
	TGAS (K)	74.717	69.129	70.358	54.105	50.16
0% load, sinusoidal disturbance	CVGAS (KJ/kg)	1039.5	1061.7	1126.2	640.636	97.1409
	MASS (kg)	3007.2	3040.6	3018.1	3156.57	3336.64
	PGAS (bar)	19.145	13.123	12.702	14.4267	14.723
	TGAS (K)	79.541	82.098	85.674	64.371	60.749