Chemical Process Control a First Course with Matlab

6 - 17
The ITAE, with about 14% overshoot, is more conservative. Ciancone and Marlin tuning relations
are ultra conservative; the system is slow and overdamped.
With the IMC tuning setting in Example 5.7B, the resulting time response plot is (very nicely)
slightly underdamped even though the derivation in Example 6.4 predicates on a system response
without oscillations. Part of the reason lies in the approximation of the dead time function, and
part of the reason is due to how the system time constant was chosen. Generally, it is important to
double check our IMC settings with simulations.
At this point, one may be sufficiently confused with respect to all the different controller
tuning methods. Use Table 6.3 as a guide to review and compare different techniques this chapter
and also Chapters 7 and 8.
Table 6.2. Summary of PID controller settings based on IMC or direct synthesis
Process model Controller K c τ I τ D
K p
τ p s+1
PI
τ p
K p τ c
τ p —
K p
(τ 1 s + 1) (τ 2 s+1)
PID
τ 1 + τ 2
K p τ c
τ 1 + τ 2
τ 1 τ 2
τ 1 + τ 2
PID with
τ 1 > τ 2
τ 1
K p τ c
τ 1 τ 2
PI
(underdamped)
τ 1
τ 1 —
4K p ζ 2 τ 2
K p
τ 2 s 2 +2ζτs+1
PID
2ζτ
K p τ c
2ζτ
τ
2ζ
K p
s(τ p s+1)
PD 1
K p τ c
— τ p
K p e – t d s
τ p s+1
PI
τ p
K p (τ c +t d )
τ p —
PID
1 2ττ p t d
+1
K p 2ττ c t d
+1
τ p
+ t d 2 τ p
2ττ p t d
+1
K p
s
P 1
K p τ c
— —