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Answer all parts in MATLAB code. Laplace transform and transfer function A system's step response is y ( t ) = [ 1 - e
Answer all parts in MATLAB code.
Laplace transform and transfer function
A system's step response is
Part : Step response and transfer function
a Use the symbolic math toolbox to express the step response and assign to variable
b Plot the step response. The plot command cannot be used since is a symbolic variable, but fplot can plot a function or expression.
c Use the symbolic laplace function to find the Laplace transform of and assign the result to variable
d Use the symbolic simplifyFraction function to merge the partial fractions into a single saved in variable Ys
e Find the system transfer function Assign the result to variable
Part : Finding the system's response to a cosine input, using the transfer function
a Find the system's response to the input The Laplace transform of should be saved in variable
The Laplace transformed output is Y
because
b Find the output in time domain using the ilaplace function, saved as
c Plot the output using fplot
d What is the maximum value of Save the value to the variable yMax.
Note: the max function cannot be used on directly, without converting the symbolic to remove the variable t But
double
does the conversion, subs substitutes the numbers in vector for the symbolic and evaluates to a vector of symbolic expressions. Then max finds the symbolic max value, and double evaluates the expression to a number. can be to seconds with a time step of seconds.
e What is the period of The period can be found either by calculation or by inspecting the plot. Call the value yPeriod.
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