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Matlab_Assignment_4_Outline_latest

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11/8/06 Matlab/Simulink Topics Matlab transfer functions / Bode plots 1 tf() 1.1 Use tf() to generate transfer function H from numerator, denominator polynomials 1.2 H = tf(N,D) 2 Poles and Zeros Plot 2.1 pzmap(H), pzplot(H), rlocus(H) % three different ways to generate pole/zero plot of transfer function H 2.2 Using grid command and data cursor to find n ϖ ζ and , (damping and natural frequency). Observing resonant peaks and connecting that back to the value of the damping coefficient. 2.3 Using step(num,den) to plot the step response. 3 Butterworth filter generation (cutoff frequencies in rad/sec) 3.1 Lowpass 3.1.1 [N, D] = butter( order, cutoff, 's') % use s to specify continuous-time filter 3.2 Highpass 3.2.1 [N, D] = butter(order, cutoff, 'high', 's') 3.3 Bandpass 3.3.1 [N, D] = butter(order, [wl wh], 's') % specify corners of passband 4 Plotting response 4.1 Bode plots 4.1.1 bode(H) 4.1.2 bodemag(H) 5 Finding poles / zeros 5.1 poles(H) 5.2 zeros(H) 6 Plotting response 6.1 Impulse response 6.1.1 impulse(H) 6.2 Step response 6.2.1 step(H) % illustrate ringing in 5 th order Butterworth filter 7 Laplace Transforms 7.1 Using MATLAB symbolic toolbox command laplace to find Laplace transforms. 7.2 Using MATLAB symbolic toolbox command ilaplace to find inverse Laplace transforms. 7.3 Using residue command as an aid in partial fraction expansion to take inverse Laplace Transform. 8 Root Locus 8.1 rlocus(N,D) 8.1.1 Grid 8.1.2 Use Data Cursor to find n ϖ ζ and . 8.2 rltool(H) 8.2.1 Adjusting the compensator gain and observing when the system is stable,

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oscillatory, and unstable. 8.2.2 Finding the maximum gain for which the system is stable by hand using the Routh Array and confirming using the rltool GUI. 8.2.3 Using ‘Analysis’ drop-down menu to generate step response and bode plots. 8.2.4 Using tools menu to generate Simulink diagram (To find the step response, change the default sine input to a step input) 8.2.5 Building a Simulink diagram from scratch and looking at the output for different values of K. 9 Feedback 9.1 feedback(H1, H2) 9.1.1 Q = feedback (H1, H2) computes an LTI model for a standard closed-loop feedback system.
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