Handbook of PI and PID Controller Tuning Rules, 2nd Edition

4.10: Third Order System plus Time Delay Model

4.10 Third Order System plus Time Delay Model or

4.10.1 Ideal controller

Table 152: PID controller tuning rules third order system plus time delay model

Rule

K c

T i

T d

Comment

Minimum performance index

Standard form optimisation binomial Polonyi (1989).

[1]K c (582)

T i (582)

? m

Model: Method 1

T m1>10(T m2+ ? m)

Standard form optimisation minimum ITAE Polonyi (1989).

[2]K c (583)

T i (583)

? m

[1]


[2]


4.10.2 Ideal controller in series with a first order lag

Table 153: PID controller tuning rules Third order system plus time delay model

Rule

K c

T i

T d

Comment

Direct synthesis: frequency domain criteria

Schaedel (1997).

Model: Method 1

[3]K c (584)

T i (584)

T d (584)

T f=T d (584)/N;

5 ?N ?20

[3]


4.10.3 Controller with filtered derivative

Table 154: PID controller tuning rules Third order system plus time delay model

Rule

K c

T i

T d

Comment

Direct synthesis: frequency domain criteria

Schaedel (1997).

[4]K c (585)

T i (585)

T d (585)

Model: Method 1

[4]


0.05 ?a ?0.2, K v=prescribed overshoot in the manipulated variable for a step response in the command variable.

4.10.4 Non-interacting controller based on the two degree of freedom structure 1

Table 155: PID controller tuning rules third order system plus time delay model

Rule

K c

T i

T d

Comment

Minimum performance index: servo/regulator tuning

Taguchi and Araki (2000).

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