Question

Show Matlab plot comparasion properly please

2) Let a system with an LTI model be 100 G(s) = 2s2 + 24s + 200 a) Determine the zeros, poles, the steady state step response (aka DC gain), the damping ratio, and the natural frequency b) Find the step response of the system manually and plot the y(t) signal on Matlab c) Use Simulink to simulate the same step response and compare both by taking the L2 norm of the error between two outputs obtained through the analytic (manual) and numeric (Simulink) methods. Recall you can use to/from workspace Simulink library block to exchange data between Matlab and Simulink

Answer 1

Using SIMULINK :

untitled - Simulink File Edit View Display Diagram Simulation Analysis Code Tools Help 2 untitled untitled 100 2s2+24s+200 Step Transfer Fen Scope Scope Data To Workspace >> Ready 249% auto(ode45)

Figure 1 le Edit View Insert Tools Desktop Window Help 1 de Block Parameters: To Workspace x To Workspace Write input to specified timeseries, array, or structure in a workspace. For menu-based simulation, data is written in the MATLAB base workspace. Data is not available until the simulation is stopped or paused. 10 To log a bus signal, use "Timeseries" save format. Parameters Variable name: Scope Data Limit data points to last: inf 24 d sfe Decimation: 1 Save format: Structure With Time Log fixed-point data as a fi object Sample time (-1 for inherited): -1 OK Cancel Help Apply

Figure 1 X Command Window File Edit View Insert Tools Desktop Window Help DEE step response 0.6 New to MATLAB? See resources for Getting Started. >> plot (Scopedata.time, ScopeData.signals.values, 'b', 'LineWidth',2); grid on >> xlabel('t (sec)') ylabel('y(t)') title ('step response') grid on fx >> | 0.5 0.4 90.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 t(sec)

using MATLAB code :

ser Editor - C:\Users\user\lab 3\model852.m +97 model841.m x model842.m Xmodel843.m X 1 - clc 2 - close all model844.m X md نيا 4 % a) s=tf('s'); G 100/(2*5^2+24*s+200); = zero (G) poles = pole (G) [Natural_frequency, damping_ratio) 5- 6 - 7- 8- 9- -0 -1 -2 zeros damp (G) — t = 0:0.001:2; xin = heaviside (t); 1sim (G,xin,t); DC_gain = y(end) 3 - y = -4 -5 -7- -8- -9- -0- -1 % b) plot(t,y,'r', 'lineWidth', 2) xlabel('t (sec) ') ylabel('y(t)') title('step response') grid on

Х Figure 1 File Edit View Insert Tools Desktop Window Help step response 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2 1 t(sec)

Command Window New to MATLAB? See resources for Getting Started. zeros = 0xl empty double column vector poles -6.0000 + 8.0000i -6.0000 - 8.0000i Natural_frequency = 10.0000 10.0000 damping_ratio 0.6000 0.6000 DC_gain 0.5000 & »|