Bài tập chương 2
1) For each of the following transfer functions, write, by inspection, the general form of
the step response:
400
s  12s  400
900
b) G ( s )  2
s  90s  900
225
c) G( s)  2
s  30s  225
625
d ) G(s)  2
s  625
a ) G( s) 
2
ANSWERS :
a ) c(t )  A  Be 6t cos(19.08t   )
b) c(t )  A  Be 78.54 t  Ce 11.46t
a ) c(t )  A  Be 15t  Cte 15t
a ) c(t )  A  B cos(25t   )
2) Find ; n; Ts; Tp; Tr, and %OS for a system whose transfer function is:
G( s) 
361
s  16s  361
2
ANSWERS :
  0.421; n  19; Ts  0.5s; T p  0.182s; Tr  0.079s; %OS  23.3%
3) The following figure shows a mechanical vibratory system.When 2 lb of force (step
input) is applied to the system, the mass oscillates, as shown in the figure. Determine
m, b, and k of the system from this response curve.The displacement x is measured
from the equilibrium position.
ANSWERS :
k  20lb f / ft; m  167lb; b  12.2lb f / ft / sec
4) Determine the unit-step response c(t) of the following higher-order system:
(Obtain the partial-fraction expansion with MATLAB’s residue command)
C ( s)
3s 3  25s 2  72s  80
 4
R( s ) s  8s 3  40s 2  96s  80
ANSWERS :
c(t )  0.5626e 2 t cos 4t  0.3438e 2 t sin 4t  0.4375e 2 t  0.375te 2 t  1
5) Consider a higher-order system defined by:
C ( s)
6.3223s 2  18s  12.811
 4
R( s ) s  6s 3  11.3223s 2  18s  12.811
Using MATLAB, plot the unit-step response curve of this system. Using MATLAB, obtain
the rise time, peak time, maximum overshoot, and settling time.
ANSWERS :
tt  0.58; t p  1.66;
M p  0.6182; t s  10.02