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Question 15.1: THE EFFECT OF CONTROLLER TUNING FOR THE THREE WATER TANK SYS...

THE EFFECT OF CONTROLLER TUNING FOR THE THREE WATER TANK SYSTEM.

Let us recall the three water tank system of Section 11.5 which had the open-loop transfer function relating the level in tank 3 to the feed rate of tank 1 as:

g(s) = \frac{6}{(2s  +  1) (4s  +  1) (6s  +  1)}        (15.8)

If one uses a PID controller to control this system, the closed-loop set-point response is given by:

y(s) = \frac{6K_{c} \left( 1  +  \frac{1}{\tau_{I}s}  +  \tau_{D}s\right)}{6K_{c}  \left( 1  +  \frac{1}{\tau_{I}s}  +  \tau_{D}s\right)  +  (2s  +  1) (4s  +  1) (6s  +  1)}  y_{d}        (15.9)

For only PI action determine the effect of tuning parameters K_{c},  \tau_{I} on the closed loop response.

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