Automatic Control Exam

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  • Topic: Control theory, Complex number, Laplace transform
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  • Published : May 27, 2013
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First name ........................

Surname ................................................ University (home) ................................. A (solid line) 2 a) U ( s)  e1s s 1 b) U ( s)  s c) U (s)  s B) (dotted line) 1 d) U ( s)  e5 s s 3 e) U ( s)  e 1s 2s 1 e 5 s f) U ( s)   s s

Laplace transforms of the functions depicted in Fig 1 are: u(t) 2 1

0
Fig 1

5

10

15

20

25

t [s] a) X1 is the set-point usually labeled w. b) X2 is the control error usually labeled d. c) X3 is input d) X4 is input e) X5 is input f) X3 is output a) G( s)  b) c) 1 1  GR GS G R GS G( s)  1  GR GS  GR G( s)  1  GR GS   0,5 y  y  u  4u   4 y  0,5u  u  y s1, 2  2 j

Which statements about the control loop depicted in Fig 2 are true?

X1

X2 GR

X3
GS

X4 X5

Figure 2

Make the correct assignment of the control circuit transfer function descriptions and their equations A) relation between the set-point and the control error B) relation between the disturbance variable and the manipulated variable C) relation between the set-point and controlled variable

Which equation do you get by using basic correspondence and rules of Laplace transform to derive the original differential equation from transfer function

a) b) c)

Y ( s) 0,5s  1 .  X ( s) s 2  4

What are the values of characteristic equation roots? Is system described by this transfer function stable?

d) s1, 2  2 e) The system is stable. f) The system is on border of stability or unstable.

The system is described by transfer function 0,5/(1s+0,5). What are values of time constant T and system gain K? The control loop consists from the controller and the plant. Transfer function of the controller

a) T = 1 [s] and K =0,5 d) T = 2 [s] and K = 1 b) T = 0,5 [s] and K =0,5 e) T = 1 [s] and K = 2 c) T = 1 [s] and K = 1 f) T = 2 [s] and K = 2 a) The controller is P. b) The controller is PI. Q( s ) s  1 is GC ( s)  and transfer function of c) The controller is PID.  e) The control loop characteristic polynomial is P( s ) s A(s) P(s)  B(s)Q(s) . B( s ) 5 the plant is GS ( s)  .  f) The control loop characteristic polynomial is A( s) (10s  1) A(s) B(s)  P(s)Q(s) . Which claims about the control loop are true? g) The steady-state error will be zero. h) The steady-state error will be nonzero. Which one from offered equation is overall transfer G1 1 a) G( s)  d) G ( s)  function of the system defined by block diagram 1  G2 1  G2G1 G1  G2 U(s) + Y(s) b) G( s)  e) G( s)  G2(s) G1(s) 1  G1G2 1  G2G1 + GG GG c) G ( s)  1 2 f) G ( s)  1 2 1  G2 1  G2

First name ........................

Surname ................................................ University (home) ................................. a) The model is stable. b) The model is unstable. c) Step response of the model is monotonic without oscillation. d) Step response of the model is oscillating. e) Characteristic equation of the model is first order. f) Characteristic equation of the model is second order. a) Roots of the system are two real numbers. b) Step response of the system is monotonic without oscillation. c) Step response of the system is bounded harmonic signal. d) Characteristic equation of the system is third order. e) Roots of the system are pair of conjugate complex numbers. f) The system is stable. g) The system is unstable. h) The system is on border of stability. a) The output will be oscillating with decreasing amplitude. b) The output will be oscillating with increasing amplitude. c) The output will be the same. The origin of complex plane will be lying d) on the right from Mikhalov curve e) on the left from Mikhalov curve f) on the Mikhailov curve if Mikhailov curve of the closed control loop is passed in the direction of increasing frequencies.

Model of the controlled plant has three roots of characteristic equation: s1=-2 s2=-1+0,5j s3=-1-0,5j Which statements about the controlled plant are true? The roots of...
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