Final Exam Control-system2014a

Department of Electrical Engineering MEEN 3392 (Mechanical Engineering design II)/ EEEN 4351 (Automatic Control System) Final Exam January 8, 2014 Instructor: Dr. Nizar Tayem Exam Time: 2 Hours

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Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6 Total

Problem # 1

(20 %)

Part 1 List all advantages and disadvantages of a closed-loop system

Part 2 True/False Questions: Circle the right answer 1) If an open-loop system is unstable, then applying feedback will always improve its stability. (T) (F) 2) When a row of Routh's tabulation contains all zeros before the tabulation ends, this means that the equation has roots on the imaginary axis of the .-plane.

(T) (F)

3) The following characteristic equation of a continuous-data system represents an unstable system because it contains a negative coefficient.

(T) (F)

4) Adding a pole to Q(s)/P(s) has the general effect of pushing the root loci to the right, whereas adding a zero pushes the loci to the left. (T) (F) 5) If a unity-feedback control system type is 2, then it is certain that the steady-state error of the system to a step input or a ramp input will be zero.

(T)

(F)

(T)

(F)

7) Increasing the undamped natural frequency will generally reduce the rise time of the step response.

(T)

(F)

8) Discrete-data control systems are more susceptible to noise due to the nature of their signals.

(T)

(F)

6) Adding a zero to the forward-path transfer function will generally improve the system damping and thus will always reduce the maximum overshoot of the system.

Problem #2 (20 %) Consider the speed control system in the block diagram below wherein the inner loop corresponds to motor back emf. The controller is the an integrator with gain K observe that the load is inertia only.





Determine the value of K for which steady state error to unit ramp input Vr s   1 / s 2 is less than 0.01 rad/sec.

Problem #3 (20 %) For the system shown below. a) Find the transfer function G(s)  X (s) / F (s). b) Calculate ζ, ωn , %OS, Ts , T p , Tr c) Comment on the results you obtained on (b)

Problem # 4 (20 %) Establish the state space equations describing the unit feedback system below.

Problem # 5 (20 %) Consider the following loop transfer function ( ) ( ) a) b) c) d)

( (

) )(

)

Find the range of K where the system is stable Find the asymptotes of root locus Determine the breakout point Sketch root locus of the closed-loop system when K varies from 0 to ∞.

Problem # 6 (20 %) The position control system of an object holder robot and its block diagram is shown below. a) Use the stability method of Ziegler- Nichols to determine the parameters of the PID controller b) Determine the actual position Y(s). Object Holder Robot PID Controller Actual Position Y(s)

Desired Position

G(s)

Gc ( s )  K P 

  KI 1  K D s  K P 1   TD s  s TI s  