Question

uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described by the following differential equation dt2 dt i) Find the state transition equations and state matrices A, B, C and D (controllable canonical form) ii) Find the state transition matrix e(At) ii Find the 0-input response for initial state values of (0 and 1) iv) Find the forced response for u(t) 1 for the same initial conditions as in ii).

Answer 1

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-1 S+5 (S+ 2) S+3 245)3 A 3 -3+2 S+3 S+2 3t Ge-e

Sespoie Il uput stae epua ton x(S): But hare ue dom bnoO x, t mentienedim

dyce de ) Stata equalien A stałe mabices atv u-41,-44.2 9. = State equal ios -4-411%. 01 71

At 4 S+4 S+4 -4 S S+ 4 A- S-2) d ,-上 ad-be -Ca n a S+4 SI-A

St 4 1-2 S+2 S42-2 Staj 2. 2t 2 ST-A -4tě | ;;)) f d Zero inpd.roespanre -ta ,nehaJ 삯ah values Co &A) S-+4

S122 4+ 2 e t2te t e Std -zt S (S42 xlt)te 210 t e 2t