A 8 pts b 8 pts 3 ece308 exam 2 name problem 3 15 pts

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(a) [8 pts] (b) [8 pts]
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3 ECE308: Exam 2 Name: [Problem 3 – 15 pts] Answer the following questions about the root locus shown below for a unity feedback system with gain 𝐾𝐾 . (a) Draw in the plot above the line associated with a damping ratio of 0.7( ~135 ) and find (approximately) the values of gain K which yields this damping ratio. [5 pts] (b) Where (approximately) are ALL the poles of the equivalent transfer function for the choice of 𝐾𝐾 in part (a)? [5 pts] (c) Can we make an argument for a good 2 nd order approximation for this system? Why? [5 pts]
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4 ECE308: Exam 2 Name: [Problem 4 – 20 pts] Assume a unity feedback system with transfer function 𝐺𝐺 ( 𝑠𝑠 ) and forward gain 𝐾𝐾 . Answer the following about the design of a PID controller for such system: (a) Which one do you design first the PD or the PI component? [3 pts] (b) What is the general form for the transfer function of a PI controller? [3 pts] (c) Why is it called a PI controllers? [3 pts] (d) What is the general form for the transfer function of a PD controller? [3 pts] (e) Why is it called a PD controller? [3 pts] (f) We have a choice on the location of the zero for the PI controller. How do we pick the location? What are the trade-offs that we have? [5 pts]
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5 ECE308: Exam 2 Name: [Problem 5 – 17 pts] Answer the following questions about the system below. Sketch in the plot provided below the Phase Bode plot of the forward gain 𝐺𝐺 ( 𝑠𝑠 ) for K = 100.
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6 ECE308: Exam 2 Name: [Problem 6 – 16 pts] Answer the following questions about the system below with the shown Nyquist diagram (for K = 1). Nyquist Diagram for 𝐺𝐺 ( 𝑠𝑠 ) 𝐻𝐻 ( 𝑠𝑠 ) with 𝐾𝐾 = 1 : (a) Determine if the system is stable for K = 1 using the Nyquist criterion. Show your work. [8 pts] (b) What is the range of values of K that will yield a stable system? [8 pts]
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