Question

matlab please

(4) Consider the system described by the following difference equation y(n)1.77y(n-1)-0.81y(n 2)a(n)- 0.5(n -1) (a) Assuming a unit-step input, and using a long enough section of the input constant output y(n) is observed for large n, hence plot the output and determine the value of this constant called G so that a Note: G, y(n) for n0o. (b) Determine and plot the transient response given by: n(n) = y(n)- Go (c) Find the energy of the transient response signal (d) After how many samples does the output reach steady-state? Write a Matlab pro- gram to determine the beginning of the steady-state (end of the transient) period.

matlab please

Answer 1

a)

1- clear all 2- clc Fiqure 1 t (1)-0 tt-5 d-0.01 n-tf/d 3 File Edit View Insert Tools Desktop Window Help su (0) 1: 0.25 y(1) 0 y (2) 0 y(3) 0 9 10 11- 0.2 12 13 Efor i-1:n 14 u (1) 1; 15 - end 0.15 16 for i-3: (n) 17 18 19 dy (1)((-1.77) *y (1-1) ) - (0.81*y (1-2) ) +u (1) -0 . 5*u (1-1) 0.1 (i+1) y(i) +dy (i) *d 20 end 0.05 plot (y, 'g) axis ([0 500 0 0.25]) : xlabel('time (sec) '); ylabel'output') 150 50 100 200 250 300 350 400 450 500 (A) ozurdaas time(sec) splot (x, 'r') adino

ans =

RiseTime: 81.0732
SettlingTime: 147.3944
SettlingMin: 0.1749
SettlingMax: 0.1938
Overshoot: 0
Undershoot: 0
Peak: 0.1938
PeakTime: 501

G0 = 1. as n->infinity all the coeeficients of y(n) ->0 and only input x(n) ->1.

b)d) The response is settled after 250sec

clear al1 1- Figure 1 2 clc t (1)-0: Tools Desktop File Edit View Insert Window Help tf-5 EE 5 d-0.01: n-tf /d: u (0)-1 6 7 0 9 y(1) 0: -0.1 10- y (2) 0: y(3) 0 11- -0.2 12 Efor i-1:n 13- -0.3 u (i)-1 14 15- end -0.4 16 for i-3 : (n) 17- -0.5 18 -0.6 9 dy (i) (-1.77) *y (i-1) ) - (0.81*y (i-2) ) +u (i) -0 .5*u (i-1) (i+1)-y (i) +dy (i) *d; y1 (1)-y(1)-1 20 -0.7 21 -0.8 end -0.9 plot (y1, 'g') -1 0 100 120 60 180 axis( I 20 40 80 140 160 200 time(sec) (pas) aurT.) TageTY 9- 30- tput') stepinfo (y) output