#16 Assignment ECSE-2410 Signals & Systems - Fall 2005 Due Tue 11/15/05
1(20) Consider the feedback system shown. (a) For D(s)
D(s)
X(s) +
K
0 , find
Y ( s) . X ( s) Y (s) . D( s )
-
(s 2) s(s 1)
+ + Y(s)
(b) For X (s)
0 find
(c) Write the characteristic equation for the closed loop system. (d) Find the value of K so that the closed-loop system is critically damped.
2(10) Text 11.2 3(10) Text 11.4 4(10) Text 11.21 5(32) Text 11.24 Sketch only for K 0 . Show asymptotes all and the direction of increasing K . Calculate all asymptote locations (centroids) and all asymptote angles. Don't worry about calculating break-away and re-entry points or j -axis crossings. A 6(18) Text 11.49. Note that when a transfer function is written in the form H ( s) , the parameter 1 s is called the time constant. The 3dB bandwidth of the system (that is, the point at which the 1 magnitude is decreased by a factor of 2 from its value at DC) is .