Process control, PID and adaptive control - Intelligent Buildings and Building Automation - page 127

Table 7.1 Ziegler and Nichols settings ( A=X/Y, B=T/L ; see Figure 7.11)

Type of Controller K p T i T d

P A*B - -

P+I 0.9*A*B 3.3*L -

P+I+D 1.2*A*B 2*L 0.5*L

Table 7.2 Cohen and Coon settings ( A, B as before, R=L/T ; see Figure 7.11)

Type of controller K p T i T d

P AB(1+R/3) - -

P+I AB(1.1+R/12) L(30+3R)

(9+20R)

-

P+D AB(1.25+R/6) - L(6-2R)

(22+3R)

P+I+D AB(1.33+R/4) L(32+6R)

(13+8R)

4L/(11+2R)

7.6.2 Closed-loop test method

An alternative empirical test which has been suggested is to allow the
controller to remain connected in the control loop but to decrease the
proportional band progressively (corresponding to increasing the gain K p )
until the system just sustains steady oscillations of constant amplitude as
shown in Figure 7.12. The test procedure is as follows. First, the integral
and derivative functions must be disabled in the controller or their effects
should be reduced to a minimum by setting T i to its maximum value and T d
to its minimum value. Then the proportional gain is increased progressively
while observing the response of the control loop. The smallest value of K p

Y

T'

Figure 7.12 Process response in closed-loop test method.