Chapter 6, Problem 6.18MCQ

4. Consider a unity (negative) feedback control system whose open-loop transfer function is given by the following. 2 G(s) = s³ (s + 2) Find the steady-state error of the system for each of the following inputs. = a) u(t) (t²+8t+5) 1(t) b) u(t) = 3t³ 1(t) c) u(t) (t+5t² - 1) 1(t) =

1 2. For the following closed-loop system, G(s) = and H(s) = ½ (s+4)(s+6) a. Please draw the root locus by hand and mark the root locus with arrows. Calculate the origin and angle for asymptotes. b. Use Matlab to draw the root locus to verify your sketch. Input R(s) Output C(s) KG(s) H(s)

5. Consider following feedback system. R(s) + 100 S+4 +1 Find the steady-state error for (i) step input and (ii) ramp input.

6. Find (i) settling time (Ts), (ii) rise time (Tr), (iii) peak time (Tp), and (iv) percent overshoot (% OS) for each of the following systems whose transfer functions are given by: a) H(s) = 5 s²+12s+20 5 b) H(s) = s²+6s+25 c) H(s) = (s+2) (s²+12s+20) (s²+4s+13) Use dominant pole approximation if needed.

7. Answer the following questions. Take help from ChatGPT to answer these questions (if you need). But write the answers briefly using your own words with no more than two sentences and make sure you check whether ChatGPT is giving you the appropriate answers in the context of class. a) Why do we need transient performance metrics? Name a few of such metrics. b) Define (i) settling time, (ii) rise time, (iii) peak time and (iv) percent overshoot. c) What is damping ratio? How does overshoot change with the change of damping ratio? When do we have zero overshoot? d) What is the criterion for selecting dominant pole in higher order systems? When dominant pole approximation is not valid? How will you calculate the transient performance metrics for the case when dominant pole approximation does not hold?

The transformer rating is 1200:2400 V @ 120 kVA. What is the apparent power provided by the source? What does this mean for the operation of the transformer?  Draw the power triangle at the source and calculate the power factor. The magnitude of the voltage source is given in VRMS.

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a) Find the Real and Imaginary Voltage across the inductor to 3 decimal points. b) Find the current and phase angle (phasor) magnitude from the Vs source to 3 decimal points. c) Find the magnitude and phase angle of the complex power(phasor) delivered by the Vs source to 3 decimal points.

Consider the circuit diagram below. If four identical capacitors, each with a capacitance of 0.07 F, are used to smooth the output, what will the ripple voltage VR be? The diode forward bias voltage, VF, is found to be 0.5 V.  Note that the amplitude of v(t) is given in VRMS.