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# Consider the storage tank with sight glass in Figure. The parameter values are R1 = 05 min/ft2, R2 = 2min/ft2, A1 = 10 ft2, Kv = 2.5cfm/mA, A2 = 0.8ft2, Km = 1.5mA/ft, and tm = 0.5 min. (a) Suppose...

Consider the storage tank with sight glass in Figure. The parameter values are R1 = 05 min/ft2, R2 = 2min/ft2, A1 = 10 ft2, Kv = 2.5cfm/mA, A2 = 0.8ft2, Km = 1.5mA/ft, and tm = 0.5 min.
(a) Suppose that R2 is decreased to 0.5 min/ft2. Compare the old and new values of the ultimate gain and the critical frequency. Would you expect the control system performance to become better or worse, justify your answer.
(b) If PI controller settings arc calculated using the Ziegler-Nichols rules, what are the gain and phase margins? Assume R2 = 2 mm/ft.

## Solution

David answered on Dec 31 2021
Documentation
Gain margin, phase margin, and crossover frequencies
Syntax
[Gm,Pm,Wgm,Wpm] = margin(sys)
[Gm,Pm,Wgm,Wpm] = margin(mag,phase,w)
margin(sys)
Description
margin calculates the minimum gain margin, Gm, phase margin, Pm, and associated
frequencies Wgm and Wpm of SISO open-loop models.
The gain and phase margin of a system sys indicates the relative stability of the closed-
loop system formed by applying unit negative feedback to sys, as in the following
illustration.
The gain margin is the amount of gain increase or decrease required to make the loop
gain unity at the frequency Wgm where the phase angle is –180° (modulo 360°).
In other words, the gain margin is 1/g if g is the gain at the –180° phase frequency.
Similarly,
the phase margin is the difference between the phase of the response and –180° when
the loop gain is 1.0.
The frequency Wpm at which the magnitude is 1.0 is called the unity-gain
frequency or gain crossover frequency.
It is generally found that gain margins of three or more combined with phase margins...
SOLUTION.PDF