A Hybrid PID-Fuzzy Control for Linear SISO Systems with Variant Communication Delays

Table 1

Simulation study analysis.

	Settling time(s)	Overshoot (%)	Steady state error (%)
	Oy	Oy	Oy
PID (fixed delay)
τ = 0.0 sec (S)	4.4	1.3	0
τ = 0.4 sec (S)	6.2	6.2	0
τ = 0.6 sec (S)	7.0	11.0	0
τ = 1.0 sec (S)	18.6	21.3	0
τ = 1.4 sec (S)	unstable
τ = 1.8 sec (S)	unstable
τ = 2.0 sec (S)	unstable
PID and fuzzy (fixed delay)
τ = 0.0 sec (S)	4.8	1.3	0
τ = 0.4 sec (S)	4.8	1.9	0
τ = 0.6 sec (S)	5.0	3.7	0
τ = 1.0 sec (S)	8.6	8.6	0
τ = 1.4 sec (S)	10.2	12.4	0
τ = 1.8 sec (S)	12.0	12.2	0
τ = 2.0 sec (S)	13.2	9.3	0
PID (variant delay)
S1 (τ max = 2.0 sec)	24.2	23.8	0
S2 (τ max = 2.0 sec)	31.2	26.8	0
S3 (τ max = 2.0 sec)	8.8	17.1	0
S4 (τ max = 2.0 sec)	16.0	27.2	0
S5 (τ max = 2.0 sec)	10.0	42.9	0
S6 (τ max = 2.0 sec)	9.2	25.3	0
S7 (τ max = 2.0 sec)	14.2	41.0	0
PID and fuzzy (variant delay)
S1 (τ max = 2.0 sec)	10.8	16.5	0
S2 (τ max = 2.0 sec)	9.8	9.0	0
S3 (τ max = 2.0 sec)	9.4	7.4	0
S4 (τ max = 2.0 sec)	9.2	12.3	0
S5 (τ max = 2.0 sec)	11.2	24.7	0
S6 (τ max = 2.0 sec)	6.8	2.5	0
S7 (τ max = 2.0 sec)	9.4	9.9	0