The cascade system

Write the following Step 1? Please do all of parts (a), (b), and (c)L —————————————————————————— ‘ IYKS) Figure 1: Cascaded system with negative feedback. Consider a cascade of two systems 5 = 3152 depicted in Figure 1. The cascade system has the input 33(75) and the output y(t). Negative feedback with gain K E R is used to stabilize the system. Let Mt) and H(s) denote the impulse response function and the transfer function of the whole system, respectively.The impulse response functions of 31 and 32 systems are given below: but) = £—1[H1<s)1 = 60: — 2)1120:) = rivets» = 6mm + 2) Step 1) a) Find the expressions for the impulse response function Mt) and thetransfer function H (s) of the whole feedback system.b) Find values of gain K for which the system becomes stable.c) Choose arbitrary gains K1 and K2 that make the system unstable andstable, respectively. Then use MATLAB to show pole-zero plots of thetransfer function H(s) when K = K1 and when K = K2.Hint: You can use build-in function “pzplot” for pole-zero plot. Forexample, if system has transfer function H (s) = %, the followingcode to generate the plot: sys = tf([2 l],[l l 2]);% Argument [2, 11 defines the coefficients of numerator …polynomial; % Argument [1, l, 2] defines the coefficients of …denominator polynomial;h = pzplot(sy3);