Controller Design for Rotary Inverted Pendulum System Using Evolutionary Algorithms

Table 3

Best results of PID controllers with different 𝛽 values gained by PSO, GA, and ACO algorithms in 50 runs.

	β	𝐾𝑑𝑝	𝐾𝑝𝑝	𝐾𝑑𝑎	𝐾𝑝𝑎	𝑀𝑝%	𝑡𝑟(sec)	𝑡𝑠(sec)	𝑡𝑝(sec)	𝐸𝑠𝑠	𝐸𝑢	cost
GA	1	0.473	4.118	0.51	0.356	36.787	0.008	0.958	0.29	0.0008	18.213	20.908
	1.5	0.666	3.276	0.444	0.248	28.34	0.008	1.776	0.44	0.0046	22.624	22.519
PSO	1	0.551	3.989	0.398	0.153	22.243	0.008	1.301	0.38	0.001	17.839	16.189
	1.5	0.529	3.206	0.35	0.119	21.805	0.006	1.24	0.41	0.0008	18.242	17.728
ACO	1	0.35	4.091	0.281	0.125	16.528	0.035	1.864	0.32	0.0022	19.904	15.513
	1.5	0.539	2.821	0.441	0.23	17.57	0.008	1.721	0.28	0.0022	19.095	16.571