4.5: SOSPD Model

4.5 SOSPD Model or

Table 115: PID tuning rules SOSPD model or
Rule	K _c	T _i	T _d	Comment
	Process reaction
Auslander et al. (1975).	^[1]K _c ⁽⁴⁶³⁾	T _i ⁽⁴⁶³⁾	0.25T _i ⁽⁴⁶³⁾	Model: Method 3
	Minimum performance index: regulator tuning
Minimum IAE Wills (1962b) deduced from graph. Model: Method 1		0.36T _u	0.21T _u	Representative tuning values; T _m2= ? _m=0.1T _m1
	0.29T _u	0.29T _u
Minimum IAE Shinskey (1988) page 151. Model: Method 2	0.62K _u	0.38T _u	0.15T _u	=0.25
0.68K _u	0.33T _u	0.19T _u	=0.5
0.79K _u	0.26T _u	0.21T _u	=0.75
Minimum ITAE Lopez et al. (1969). Model: Method 17	x ₁/K _m	x ₂T _m1	x ₃T _m1
Representative coefficient values (from graphs)
x ₁	x ₂	x ₃	? _m	? _m/T _m1
25	0.5	0.25	0.5	0.1
0.7	1.3	1.2	0.5	1
0.35	5	1.0	0.5	10
25	0.5	0.2	1.0	0.1
1.8	1.7	0.7	1.0	1
9.0	2	0.45	4.0	1
Minimum ITAE Bohl and McAvoy (1976b).	^[2]K _c ⁽⁴⁶⁴⁾	T _i ⁽⁴⁶⁴⁾	T _d ⁽⁴⁶⁴⁾	Model: Method 1
Minimum ITAE Hassan (1993).	^[3]K _c ⁽⁴⁶⁵⁾	T _i ⁽⁴⁶⁵⁾	T _d ⁽⁴⁶⁵⁾	Model: Method 7
Minimum ITAE Sung et al. (1996). Model: Method 9	^[4]K _c ⁽⁴⁶⁶⁾	T _i ⁽⁴⁶⁶⁾	T _d ⁽⁴⁶⁶⁾
Nearly minimum IAE, ISE, ITAE Hwang (1995). Model: Method 10	^[5]K _c ⁽⁴⁶⁷⁾	T _i ⁽⁴⁶⁷⁾	T _d ⁽⁴⁶⁷⁾