Whats the difference between calculating the tracking error with mag(L) vs. the sensitivity function?
Submitted by: asa Submitted on: November 29, 2004 Identifier: H7 , H8 For exact calculations of the frequency at which the error is less than a certain bound, you should use H_{er}, the sensitivity function. This gives you a measure of the error directly related to the input. The magnitude of L can be used as a quick approximation — generally, 1/(1+mag(L)) will be close to mag(1/(1+L)). However, for precise work (i.e. not approximations), you should use H_{er}. [Back to Top] • What do you mean by “If the integral is surjective (as a linear operator), then we can find an input to achieve any desired state”? Submitted by: asa Submitted on: December 6, 2004 Identifier: L5.1 Surjective is what is commonly known as “onto”. That is, if we have an operator f: X -> Y, then the image of f is all of Y. In this context, we have a linear operator (the operator, with integral, etc., that takes a system state plus input at time 0 to the system state at time T). This is an operator from the space of
