Adding noise to feedback in a transfer function
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I would like to add Gaussian noise to a transfer function model, not at the input, but to the feedback term in the model. To simplify my system, lets say it is the prototypical closed loop http://en.wikipedia.org/wiki/Closed-loop_transfer_function with
Y/X = G/(1+G*H), where H represents negative feedback control block based on a measurement of the output.
I'd like to then use lsim to quantify the noise in the response to a sine wave input. How do I add 5% noise to the feedback signal, such that the noise is greater when there is greater mismatch between actual and desired signal? I.e. if Y is the output signal, I'd want to feedback Y' = Y*(1 + .1*randn(1)) at each point in time during a simulation. Is the only choice to implement the model numerical in discrete time?
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