matlab and simulink 12 labs and every lab 4 questions

Tutorials No 5

All working and MATLAB programs to be kept/typed up in Microsoft

Word, which would be submitted at the end of Term 2

A first order system has the transfer function ( )

i. Showing all of your working, use the frequency response theorem to produce

Bode plots of gain (in decibels) and phase (in degrees) versus . You

may use 20 different values of from .

ii. Use MATLAB to generate the magnitude and phase Bode plots of the first

order system, G(s), for .

iii. From your Bode plots obtained in (ii), at what frequency will the magnitude of

the output and input of the system be equal? What is the phase relationship

between the output and input of the system at this frequency? How will an

increase in the frequency of the input to the system affect the gain? Support

your answer with evidence from your plot in (ii).

iv. If the first order system, ( ), is excited by ( ) , using the

Bode plots generated in (ii), determine the amplitude and phase of the steady

state output response of the system and write the mathematical expression

for the steady state output response.

v. Compare your answers in (iv) with the amplitude and phase of the steady

state output response obtained using the frequency response theorem.