1 Consider a 3rd order proper rational system alone,with initial conditions on its input and output Input is a step signal with arbitrary value. Calculate and plot the following:

1. Y_{zero - state}(t). Y_{zero - input} (t) and Y(t)

2. Y_natural(t),  Yforced(t) and y(t)

3. Plot all the above using MATLAB writing a code.

2. Consider non-conflicting design requirements of T_rise, T_setting and %age Overshoot for a 2^nd order system, and do the following:

a. Find out the boundaries of ς, ω_n σ and j_ωetc. from these requirements,

b. Illustrate these boundaries and the regions where all these requirements are met, c Define the two system poles and find out the transfer function,

d. Plot a step response in MATLAB. and confirm if all the requirements are met.

3. Consider example systems (at least 5^th order) for all the four cases (normal, left column zero, row of zeros and repeated roots) and do the Routh-kurwitz analysis to judge the stability of these systems.

a Consider a complex gt.C/spring-mass-damper system (at least 4^th order) with a variable component. Through the Routh-Hurwitz procedure, find out the minimum and maximum values of this variable component for system stability.

Attachment:- Question.rar