Control Systems
Control System Design
Practice questions from Control System Design.
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IncorrectA controller of the form is to be designed for the plant as shown in the figure. The value of that yields a phase margin of at the gain cross-over frequency of is ___________ (round off to one decimal place).
Given:
Gain cross-over frequency, .
Phase Margin at
Open-loop Transfer function of system, OLTF
…(i)
From equation (i),
Consider a unity-gain negative feedback system consisting of the plant (s) (given below) and a proportional-integral controller. Let the proportional gain and integral gain be 3 and 1, respectively. For a unit step reference input, the final values of the controller output and the plant output, respectively, are
Transfer function of PI controller
Given, &
Block Diagram of Control System is given by
Forward path transfer function
Overall transfer function
Final value of plant output,
Controller Output X(s) =
X(s) =
Final value of controller
Consider a lead compensator of the form
The frequency at which this compensator produces maximum phase lead is . At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of , is . The values of , respectively, are
1,16
2,4
3,5
Frequency of maximum phase shift
Corner frequencies = α, αβ
At frequency of maximum phase shift,
Asymptotic approximation of K(s) is,
