MATLAB

A) (30pts.) Time responses: (unit step, unit ramp, unit impulse responses) Each part (5 pts.). 1) Using MATLAB, obtain the unit-step response, unit-ramp response, and unit-impulse response of the following system: R(s)C(s)=s2+2s+1010 where R(s) and C(s) are Laplace transforms of the input r(t) and output c(t), respectively 2) Using MATLAB, obtain the unit-step response, unit-ramp response, and unit-impulse response of the following system: [[110.50][x1x2]+[0.50]uy=[10][x1x2] where u is the input and y is the output. 3) Using MATLAB obtain computationally the rise time (tr), peak time (tp), percent overshoot (PO), and settling time (ts) in the unit-step response of a closed-loop system given by R(s)C(s)=s2+2s+3636 4) Using MATLAB, obtain the unit-step response curve for the unity-feedback control system whose open-loop transfer function is G(s)=s(s+2)(s+4)10 Using MATLAB, obtain also the rise time, peak time, maximum overshoot, and settling time in the unit-step response curve. 5) Consider the closed-loop system defined by R(s)C(s)s2+2s+12s+1 where 0.2,0.4,0.6,0.8,1.0 Using MATLAB, plot a twodimensional diagram of unit-impulse response curves. Also plot a three-dimensional plot of the response curves