WIP: Robust toolbox dev #192
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This branch is now up to date with local changes, and now includes a robust bilinear transformation for discrete time synthesis as well as tests for some of the code.
…detailing the intended structure of the tests and all of the points which are to be tested.
…ma, required to check the stabilizability conditions for applying the dual ARE-method
…bility and detectability checks
…ge in the assumptions check of necessary in the dual Riccati approach
…erses are done correctly, a necessary compnent for checking the assumptions which have to be satisfied before proceeding with the H-infinity synthesis
…in the psudoinverse compuatation method
…throws a method error when using non-matrix types as arguments
…nverse exists when the matrix M is rank deficient
…ts that establish the spectral radius condition to be handled correctly
…n-feasible when violating the positive definiteness check
…from continuous to discrete- and back to continuous-time works, as well as discrete- to continuous- to discrete-time. Works simply means that the frequency response matches across a set of 1001 discrete points in the frequency domain.Test that the SS-type data is discretized correctly, and that moving from continuous to discrete- and back to continuous-time works, as well as discrete- to continuous- to discrete-time. Works simply means that the frequency response matches across a set of 1001 discrete points in the frequency domain.
… resulting controller
…he resulting controller in the MIT open courseware example
…that the code runs
… in the quadtank example
…pose matrices with size zero
…nst the resulting closed loop transfer functions
…nction to visualize the synthesized controllers
example/hinf_example_MIMO.jl
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| WSe = tf([0.1,1],[1000,1]) | ||
| #WS = [WSe 0 0 ; 0 WSe 0 ; 0 0 WSe] | ||
| WS = [WSe 0 0 0 ; 0 WSe 0 0 ; 0 0 WSe 0 ; 0 0 0 WSe] | ||
| WS = [WS 0*WS; WS*0 WS] |
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Perhaps best to try to avoid redefining local variables.
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Thanks, the general MIMO example should be removed, as it is currently dysfunctional - I have yet to add a loop shift in the controller synthesis - I'll remove this script in its entirety for now.
| below, and is best read alongside the complementary report in [2] | ||
| (mgreiff2019report). For the LMI-experiments see the third bibentry [3]. | ||
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| @article{glover1988state, |
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How should we reference papers @mfalt , @baggepinnen ? Is this reasonable, or perhaps something a bit more concise?
src/hinfinity_design.jl
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| A, B1, B2, C1, C2, D11, D12, D21, D22 = ssdata(P) | ||
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| # Check assumption A1 | ||
| if !_is_stabilizable(A, B2) |
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Should we consider making is_stabilizable a publicly available?
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Quite possibly, and I think that the bilinear discretization could be useful outside of the hinf_design module too, and should probably be implemented in the c2d() function. Similarly, we also have its inverse in bilineard2c(), which could be implemented in some function d2c().
I can start to migrate the functions to discrete.jl and matrix_comp.jl if you like.
src/hinfinity_design.jl
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| min(size(M))==rank(M). Used for checking assumptions A5 and A6 in [1], see the | ||
| section on the generalized | ||
| """ | ||
| function _compute_pseudoinverse(M::AbstractMatrix) |
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Does pinv work here?
Is this function (or enclosing function) somewhat performance critical? If so, there are some issues like type stability and inv insead of / that we should consider.
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Thanks, pinv works and has now been implemented instead of the _compute_pseudoinverse() function!
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Some random comments
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src/hinfinity_design.jl
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| future revisions, we could suggest possible changes to P should the system not | ||
| be feasible for synthesis. However, this has not been too successful so far..! | ||
| """ | ||
| function hInf_assumptions(P::ExtendedStateSpace; verbose=true) |
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Preferable with consistent function naming https://docs.julialang.org/en/v1/manual/style-guide/index.html
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Thanks for linking the style guide. All function names have been changed, and hopefully, they are now compliant with the style guide.
src/hinfinity_design.jl
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| end | ||
| return false | ||
| end | ||
| if !_is_detectable(A, C2) |
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We have
is_detectable(A, C) = is_stabilizable(A', C')
Good to avoid redundant code. Should there be a function is_detectable defined according to this, or should we just use is_stabilizable(A', C') here?
| HX = [A zeros(size(A)); -C1'*C1 -A'] - ([B; -C1'*D1dot]/R)*[D1dot'*C1 B']; | ||
| HY = [A' zeros(size(A)); -B1*B1' -A] - ([C';-B1*Ddot1']/Rbar)*[Ddot1*B1' C]; | ||
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| # Solve matrix equations |
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Perhaps try to avoid redundant code by using the existing care method.
src/hinfinity_design.jl
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| min(size(M))==rank(M). Used for checking assumptions A5 and A6 in [1], see the | ||
| section on the generalized | ||
| """ | ||
| function _compute_pseudoinverse(M::AbstractMatrix) |
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If the existing pinv in Julia is not acceptable it would be a great with a comment why this is the case.
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Very good point - it is definitely acceptable, and I have now removed the compute_pseudoinverse function.
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Is MIMO still broken? |
Let's discuss the changes here.