Optimal Fuzzy Proportional-Integral-Derivative Control for a Class of Fourth-Order Nonlinear Systems using Imperialist Competitive Algorithms

Table 7

Design variables determined by means of the ICA for three case studies.

Design variables	Values
	1^st case study	2^nd case study	3^rd case study
	−1.06	−1.08	−0.99
	0.9	1.1	0.9
	0.99	−1.07	−1.06
	0.91	1.02	0.92
	−0.9	−0.9	−1.01
	0.99	1.1	1.07
	−1	−0.95	−1.1
	0.97	1.09	1.1
	−0.96	−1.1	−0.99
	1.03	1.1	1.1
	−0.9	−1.06	−1.1
	1.01	0.9	0.9
	0.97	0.9	0.9
	0.46	0.55	0.55
	0.3	0.03	0.03
	−0.03	−0.03	−0.03
	1.08	1.04	1.04
	6.58	13.28	18.73
	11	12.1	12.1
	0.47	0.45	0.45
	0.58	0.64	0.64
	0.26	0.32	0.26
	0.98	1.1	0.9
	0.55	0.55	0.55
	0.12	0.12	0.12
	0.14	0.15	0.16
	0.50	0.55	0.55
	1	1.07	1.1
	2.9	3.17	3.17
	4.16	4.17	4.17
	0.53	0.45	0.45
	1.03	0.9	0.9
	2.57	2.87	2.87
	−1.35	−1.35	−1.35
	0.45	0.45	0.45
	0.9	0.9	0.9
	2.11	1.73	1.73
	4.70	4.50	4.50