MaplePrimes - answers and comments on Question, How to find the transfer function from a given state-space form?

DynamicSystems

Joe Riel — Mon, 28 Jan 2013 04:24:57 Z

You can do

A := ImportMatrix("A.txt"):
B := ImportMatrix("B.txt"):
C := ImportMatrix("C.txt"):

with(DynamicSystems):

ss := StateSpace(A,B,C):

BodePlot(ss, range = 0.1..100);

The system has 2 inputs and 14 outputs, so you get 28 superimposed plots. You can plot just one by doing, say

BodePlot(ss, range = 0..1000, subsystem=[1,2]);

finding the infinity norm of the transfer function

STHence — Mon, 28 Jan 2013 08:03:13 Z

I have a way of finding the infinity norm of the transfer function as follows:

1. identityMAtrix

>II:= IdentityMatrix(7);

2. find the infinity norm of H(jω)

>f:=s->MatrixNorm(C.(s*II-A)^-1 .B )

3. plot the function f, the maximum of f(s) is the infinity norm of the transfer function

>loglogplot(f,10^-5..10^-5)

How to find infinity-norm of the transfer function

STHence — Mon, 28 Jan 2013 07:10:13 Z

Hi Joe,

thank you very much for your code. It works perfect.

I have one more question: how to find the infinity-norm of the transfer function?

There is an error that I have when using "MatrixNorm", and "TransferFunction" functions in Maple:

"Error, (in LinearAlgebra:-MatrixNorm) invalid input: LinearAlgebra:-MatrixNorm expects its 1st argument, M, to be of type Matrix but received (module () description "Transfer Function"; export tf, inputcount, outputcount, statecount, sampletime, discrete, systemname, inputvariable, outputvariable, statevariable, systemtype, ModulePrint; option _cmtransferfunction; end module)-(module () description "Transfer Function"; export tf, inputcount, outputcount, statecount, sampletime, discrete, systemname, inputvariable, outputvariable, statevariable, systemtype, ModulePrint; option _cmtransferfunction; end module)"