Chapter 4: Tuning Rules for PID Controllers

4.1 FOLPD Model

Table 44: PID controller tuning rules FOLPD model
Rule	K _c	T _i	T _d	Comment
	Process reaction
Callender et al. (1935/6). Model: Method 1	^[1]	1.418 ? _m	0.353 ? _m or 0.47 ? _m	=0.3
Ziegler and Nichols (1942). Model: Method 2	, a [1.2, 2]	2 ? _m	0.5 ? _m	Quarter decay ratio
Chien et al. (1952) regulator. Model: Method 2		2.38 ? _m	0.42 ? _m	0% overshoot;
	2 ? _m	0.42 ? _m	20% overshoot;
Chien et al. (1952) servo. Model: Method 2		T _m	0.5 ? _m	0% overshoot;
	1.36T _m	0.47 ? _m	20% overshoot;
Cohen and Coon (1953). Model: Method 2	^[1]K _c ⁽¹⁷⁸⁾	T _i ⁽¹⁷⁸⁾		Quarter decay ratio.
Three constraints method Murrill (1967) page 356. Model: Method 5			^[2]T _d ⁽¹⁷⁹⁾	;
Quarter decay ratio; minimum integral error (servo mode).
str m and H gglund (1988) pages 120 126.		T _90%	0.5 ? _m	Model: Method 23
T _90%=90% closed loop step response time (Leeds and Northrup Electromax V controller).
Parr (1989) page 194.		2.5 ? _m	0.4 ? _m	Model: Method 2
Borresen and Grindal (1990).		3 ? _m	0.5 ? _m	Model: Method 2
Sain and zgen (1992).	^[3]K _c ⁽¹⁸⁰⁾	T _i ⁽¹⁸⁰⁾	T _d ⁽¹⁸⁰⁾	Model: Method 24
Connell (1996) page 214. Model: Method 2		1.6667 ? _m	0.4 ? _m	Approximate quarter decay ratio
Hay (1998) pages 197, 198. Model: Method...