Question

Q1, pease help asap, please write clearly. Thanks in advance.

1. Given the transfer function of the control system. (60%) G(s) S) 5s+13 R(s) +6s+13 Y (1) Sketch the state diagram in the form of signal flow graph. (2) Find the state equations. (3) Find the output equation. (4) Find the fundamental matrix 2(t). (5) Find the state-transition matrix D(t) (6) Find the state vector x(t) if the input r(t) 2 and y(0)= (0) = 0 .

Answer 1

5S 13 GC RCS) 5S+13 (sXs) R(S) X(s) Xs) RCS) Let (E)6 13 X(t) Let (A)hg = (9)x. = (17x = 5S+13 Let xs) state diagm -3

equation state AX Bu A System matn A- whene sate Vania bles 1& u input outpet egelation C Du u cutpet where, ч — state tanstion masix: 6ST-A de) 3 S(s+6+13 -13

S+6 S+6 (s +-j2)(s+3+j2) s6st13 s+-j2] -3+2+6A (-3t2 432 3+2 A S= -3-J2 C-8-243-J2 -3-j2 6= 3-j2 -J4 2-i3) S+6 S+t2 S+3-i2) s26s13 A S+3-32) -6+13 A = J4 246st13 s+3-J2 s+3 t12 A S+32 S+3 12 GS3 A -3+2342 -3+j2 Sz3+2 -3 2 A= 32+3 -j2) -3 -j2 -3-J2 J

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