Update prescale function
#465
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src/matrix_comps.jl
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| C = sys.C*S | ||
| normalized_sys = iscontinuous(sys) ? ss(A, B, C, sys.D) : ss(A, B, C, sys.D, sys.Ts) | ||
| return normalized_sys, S | ||
| function prescale(sys::StateSpace) where ST <: AbstractStateSpace |
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| function prescale(sys::StateSpace) where ST <: AbstractStateSpace | |
| function prescale(sys::ST) where ST <: AbstractStateSpace |
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| S, P, B = balance(metasys) | ||
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| # reconstruct A, B and C by taking slices of the balanced metasystem | ||
| bal_metasys = P\B*P # undo permutation |
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Would it be possible to use perm=false to avoid having to undo the permutation?
| such that their column and row norms are closer. | ||
| This results in a system with overall better numerical conditioning. | ||
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| Returns a new scaled state-space object. |
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Do you have any reference to where this method is discussed?
| # create an augmented system to balance the whole system at once | ||
| metasys = [sys.A sys.B; sys.C zeros(p, m)] |
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You are using two terms here, both augmented and meta system. I seem to remember that it is instead typically called a packed representation? I think that is the term used in the Essentials of Robust Control by Zhou & Doyle,
I think it should be okay to just call the packed system representation M as you do in the tests.
| nsys = prescale(sys) | ||
| @test pole(nsys) ≈ pole(sys) | ||
| n, m = size(sys.B) | ||
| p = size(sys.C, 1) | ||
| M = [nsys.A nsys.B; nsys.C zeros(p, m)] | ||
| M2 = [sys.A sys.B; sys.C zeros(p, m)] | ||
| @test cond(M) <= cond(M2) |
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I think it would be reasonable with quite a few more tests. For example to see that the system dynamics isn't changed by the prescaling. E.g. by comparing the frequency response of a MIMO systems before and after.
Prescale function now actually balances the system matrices A, B and C instead of performing a similarity transformation into diagonal form.