Automatic Control

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Automatic Control

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Review Feedback Terminology In Block diagrams, we use not the time domain variables, but their Laplace Transforms. Always denote Transforms by (s)! – PowerPoint PPT presentation

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Title: Automatic Control

1
Automatic Control
Review
2
Feedback Terminology
In Block diagrams, we use not the time domain
variables, but their Laplace Transforms. Always
denote Transforms by (s)!
3
State-Variable Form

Deriving differential equations in state-variable
form consists of writing them as a vector
equation as follows

where is the
output and u
is the input
4
Transfer Function
5
The transfer function of the system shown is

MEG 421 Chapter 3
5
6
The transfer function of the system shown is
The stability of the closed loop is determined by

(A) G1 alone
(B) closed loop Num. and Denom.
(C) closed loop Denom. alone
(D) Gain K alone
(E) The product KG1(s)

7
The transfer function of the system shown is
The stability of the closed loop is determined by

(A) G1 alone
(B) closed loop Num. and Denom.
(C) closed loop Denom. alone
(D) Gain K alone
(E) The product KG1(s)

8
The Steady-state error ess of the closed loop to
a unit step R(s) 1/s is

(A) ess 1/K
(B) ess 1
(C) ess 0
(D) ess ?

9
The Steady-state error ess of the closed loop to
a unit step R(s) 1/s is

(A) ess 1/K
(B) ess 1
(C) ess 0
(D) ess ?

10
For tracking control (following a ramp reference)
the minimum number of integrators in the control
loop is

(A) n 0
(B) n 1
(C) n 2
(D) the number of integrators is not relevant.

11
For tracking control (following a ramp reference)
the minimum number of integrators in the control
loop is

(A) n 0
(B) n 1
(C) n 2
(D) the number of integrators is not relevant.

12
The Root Locus Branches of the system shown
originate for K 0 at

(A) s0, -1, -1
(B) s0, -1/2, -1
(C) s0, -2, -1
(D) s0, -1
(E) s0, 0.5, 1

13
The Root Locus Branches of the system shown
originate for K 0 at

(A) s0, -1, -1
(B) s0, -1/2, -1
(C) s0, -2, -1
(D) s0, -1
(E) s0, 0.5, 1

14
The Root Locus branches of the system shown
terminate for K ? infinity at

(A) closed-loop poles
(B) zero
(C) infinity
(D) Two branches terminate at infinity, one at
zero
(E) One branch terminates at infinity, two at zero

15
The Root Locus branches of the system shown
terminate for K ? infinity at

(A) closed-loop poles
(B) zero
(C) infinity
(D) Two branches terminate at infinity, one at
zero
(E) One branch terminates at infinity, two at zero

16
The Root Locus exists on the real axis between

(A) infgtxgt0 and 0gtxgt-2 and -3gtxgt-4
(B) -1gtxgt-2 and -3gtxgt-4
(C) 0gtxgt-2 and -3gtxgt-4
(D) 0gtxgt-1 and -3gtxgt-4 and -4gtxgt-inf
(E) 0gtxgt-1 and -3gtxgt-4

17
The Root Locus exists on the real axis between

(A) infgtxgt0 and 0gtxgt-2 and -3gtxgt-4
(B) -1gtxgt-2 and -3gtxgt-4
(C) 0gtxgt-2 and -3gtxgt-4
(D) 0gtxgt-1 and -3gtxgt-4 and -4gtxgt-inf
(E) 0gtxgt-1 and -3gtxgt-4

18
The RLocus of an unstable system with transfer
function is shown at left. We can stabilize
the closed loop by
X
X
X

(A) adding poles on the negative real axis
(B) adding a lead element on the negative real
axis, with the zero between 0 and -4
(C) adding a lead element on the negative real
axis, with the zero to the left of -4
(D) adding a lag element on the negative real
axis, with the pole close to the origin.
(E) the closed loop cannot be stabilized

19
The RLocus of an unstable system with transfer
function is shown at left. We can stabilize
the closed loop by
X
X
X

(A) adding poles on the negative real axis
(B) adding a lead element on the negative real
axis, with the zero between 0 and -4
(C) adding a lead element on the negative real
axis, with the zero to the left of -4
(D) adding a lag element on the negative real
axis, with the pole close to the origin.
(E) the closed loop cannot be stabilized

20
The open-loop TF of the Root Locus plot shown at
left is