1.2 Obtain the step response of an LTI from its transfer function

Problem: Find the unit step response for the continuous time system defined by the transfer function

\[ H(s) = \frac {25}{s^{2}+4s+25} \]

Mathematica Clear["Global`*"]; tf=TransferFunctionModel[25/(s^2+4s+25),s]; y = OutputResponse[tf, UnitStep[t], t]; Plot[Evaluate@y, {t, 0, 4}, PlotRange -> {{0, 4}, {0, 1.4}}, Frame -> True, FrameLabel -> {{"y(t)", None}, {t, "step response"}}, GridLines -> Automatic, GridLinesStyle -> Dashed, ImageSize -> {300, 300}, PlotStyle -> Red, AspectRatio -> 1]

 

Matlab clear all; s = tf('s'); sys = 25/(s^2+4*s+25); [y,t] = step(sys,4); plot(t,y,'r'); xlim([0 4]); ylim([0 1.4]); title('step response'); xlabel('t'); ylabel('y(t)'); grid set(gcf,'Position',[10,10,310,310]);

 

Maple restart: with(DynamicSystems): sys := TransferFunction(25/(s^2+4*s+25)): ResponsePlot(sys, Step(),duration=4);