程序代写案例-ENEL809 2021

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Portfolio of work Part 1 ENEL809 2021
Due on Friday of week 5: Friday 16th April 2021 at 9AM (morning!) Submit online. All
documents must be in ONE FILE. Document submitted on Teams and in Microsoft
Word format only – PDF not allowed here.
You must download MATLAB including control systems toolbox and signal processing
toolbox. Download from
https://au.mathworks.com/downloads/web_downloads/select_release Login with AUT login Make sure you select the Signal Processing Toolbox and the Control Systems Toolbox. Also Simulink would be handy but not needed here. Note: if you later require a toolbox that you forgot to add then get it from here https://www.mathworks.com/downloads/
activation key:
10684-24903-08488-17151-26430
A circuit is shown below

(a) Find the state-variable representation for the circuit if the states are defined as two currents and one
voltage: (note in algebraic form). Show ALL working.
1
2
c
i
X i
v
      

Take y(t) to be the voltage across R2 as the system output and u(t) the input. A state variable
description is of the form

X AX Bu, y Cx   . (15 marks)

(b) Draw the signal flow graph from input to output. (algebraic in terms of component values)
(5 marks)

(c) If 1 2 1R 100 R 10 L 0 1H L2 C 100 F, , . ,        , use MATLAB to find and plot where
necessary (i) the transfer-function of the system y/u , (ii) the poles and zeros, (iii) the step-response of
the states (use lsim() in MATLAB) for a voltage  u t 10 over a runtime of 0.1 seconds, (use a
sampling frequency of 20 kHz), (iv) the Bode-plot of the system,(v) the capacitor current. Show
MATLAB code.
(10
marks)


Total 30 marks

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