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. Yzero - state(t). Yzero - input (t) and Y(t)
2. Ynatural(t), Yforced(t) and y(t)
3. Plot all the above using MATLAB writing a code.
2. Consider non-conflicting design requirements of Trise, Tsetting and %age Overshoot for a 2nd order system, and do the following:
a. Find out the boundaries of ς, ωn σ and jωetc. 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 5th 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 4th order) with a variable component. Through the Routh-Hurwitz procedure, find out the minimum and maximum values of this variable component for system stability.
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