(Answered): using MATLAB . Find the corresponding transfer functions Find the poles and zeros and plot the pole- ...

. Find the corresponding transfer functions Find the poles and zeros and plot the pole-zero map Determine if the system is stable, asymptotically stable or unstable by both analyzing the poles and zeros and by plotting the impulse response of the system. d?y dy +4 + 3y(t) dt2 dt 1. = dx + 3x(t) dt d?y dt3 2. + 3 day dy + dt2 dt - 5y(t) = d²x dx -7 dt2 dt + 12x(t) d'y dt +3 døy day dt3 dt2 5 dydx dt dt2 = dx 10 + 21x(t) dt 3. Suppose we want to find the poles and zeros directly from the following transfer function: H(s) = S2 - 23s + 132 S3 – 6s2 - 9s + 14 CF To do so, the following commands can be used: >> H = tf([1 -23 132], [1 -6 -9 14]); >> [p,z) = pzmap(H) Note: pzmap command is the pole-zero plot of dynamic system Suppose a system can be modeled by means of the following differential equation (second order system): + 01 dt do dt? dy dx dy + ayy(t) = bo ?t + b?x(t) (1) Transforming the above equation to the Laplace domain, we get: Time domain yo dy/dt d?y/dt? x dx/dt Laplace domain YS) SYS s'Y) XS SX(S) ans?Y(s) + a,sY(s) + a,Y(s) = bosX(s) + b X(s) Y(s). (a.s? +213 +a)) = X(). (bos + b) Therefore, the transfer function of the system is: H(S) Y(s) bos+b X(S) ans? +0,8 + ay (2)