More LQG updates #467

baggepinnen · 2021-04-05T07:24:08Z

This PR adds tests for LQG and makes sure it conforms to Glad Ljung

codecov · 2021-04-05T07:56:03Z

Codecov Report

Merging #467 (65db880) into master (0919c03) will decrease coverage by 0.03%.
The diff coverage is 86.71%.

@@            Coverage Diff             @@
##           master     #467      +/-   ##
==========================================
- Coverage   85.28%   85.25%   -0.04%     
==========================================
  Files          31       32       +1     
  Lines        3092     3180      +88     
==========================================
+ Hits         2637     2711      +74     
- Misses        455      469      +14

Impacted Files	Coverage Δ
src/ControlSystems.jl	`100.00% <ø> (ø)`
src/model_augmentation.jl	`64.10% <64.10%> (ø)`
src/types/lqg.jl	`90.90% <96.62%> (+7.09%)`	⬆️
src/synthesis.jl	`65.11% <0.00%> (-6.68%)`	⬇️
src/types/DelayLtiSystem.jl	`73.68% <0.00%> (-0.28%)`	⬇️
src/utilities.jl	`83.67% <0.00%> (-0.17%)`	⬇️
src/connections.jl	`94.28% <0.00%> (-0.04%)`	⬇️
src/types/conversion.jl	`96.92% <0.00%> (-0.03%)`	⬇️
... and 5 more

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mfalt · 2021-04-06T12:24:02Z

src/model_augmentation.jl

+"""
+    add_disturbance(sys::AbstractStateSpace{Continuous}, Ad::AbstractMatrix, Cd::AbstractMatrix)
+
+See CCS pp. 144


I think the description should be a bit better here, I could not figure out what the function was doing without reading the code. Maybe the expression for the new system matrix is enough.

I understand that you probably use this to introduce disturbances, but it seems that it could be called something more general, like 'augment_system'.

Agree, all augmentation functions require better docstrings

Btw, your first comment probably got eaten up by autocorrect ;)

Wow, that was tough to read, fixed now.

mfalt · 2021-04-06T12:28:36Z

src/model_augmentation.jl

+    ss(Ae,Be,Ce,De)
+end
+
+function add_measurement_disturbance(sys::AbstractStateSpace{Continuous}, Ad::AbstractMatrix, Cd::AbstractMatrix)


We should have a docstring if we export. Same for the rest

src/types/lqg.jl

mfalt · 2021-04-06T12:32:57Z

src/types/lqg.jl


    # Extract interesting values
-    if G.integrator # Augment with disturbance model


Why is this removed?

This is no longer stored in the struct, instead the extended statespace object syse is stored. adding an integrator is just a special case of adding disturbance models, corresponding to a low-frequency input disturbance

albheim · 2021-04-06T13:04:50Z

src/model_augmentation.jl

+# Arguments:
+- `sys`: System to augment
+- `Ad`: The dynamics of the disturbance
+- `Cd`: How the disturbance states affect the states of `sys`. This matrix as the shape (sys.nx, size(Ad, 1))


This matrix has the shape...

olof3 · 2021-04-07T06:57:23Z

We have been lacking a simple way of augmenting systems with disturbance/noise models, so it is good that something is finally happening!

How is the intensity of the noise/disturbances handled? would perhaps be convenient to specify these just for the disturbances rather than some noise intensity for the whole A matrix.
I guess for, e.g., a resonant disturbance, 1/(s^2 + 2zetaw0 + w0^2) one would also like to keep track of the B matrix of its state-space realization?
I think it should be possible to add arbitrary dynamics in the form of a linear system as disturbance models. Then I think that we should export some of the methods for creating systems from DemoSystems, at least lag and resonant. (Looking over their names and arguments, making sure that they are acceptable). E.g., I.e., we no need for add_low_frequency_disturbance, etc.
If possible I think it would be desirable to separate how a disturbances affect the system dynamics from various disturbance models that one would like to investigate. Perhaps using some kind of partitioned state space.
The LQG struct seems a bit monolithic/inflexible. Some sort of problem data struct, containing the problem specification would seem useful though, e.g., in order to evaluate other linear controllers. We should fix the feedback function to accept UniformScaling, then all the sensitivity functions would just be one-liners, and perhaps wouldn't be needed to be included as getproperty. Or do we feel a need for defining these generally?

Perhaps you have some examples/use cases? Would be easier to discuss around something a bit more concrete. If I have the time, I will try to put something together as well. And I guess there should be plenty of examples in the literature, any suggestions?

baggepinnen · 2021-04-08T05:05:29Z

How is the intensity of the noise/disturbances handled? would perhaps be convenient to specify these just for the disturbances rather than some noise intensity for the whole A matrix.

It's not handled yet, maybe allowing the user to pass another parameter that is taking the place of the 1 in the C-matrix?

I guess for, e.g., a resonant disturbance, 1/(s^2 + 2_zeta_w0 + w0^2) one would also like to keep track of the B matrix of its state-space realization?

Yes, if it's a known disturbance. The augmentation so far only handles unknown disturbances for which the B-matrix is only extended with zeros.

I think it should be possible to add arbitrary dynamics in the form of a linear system as disturbance models. Then I think that we should export some of the methods for creating systems from DemoSystems, at least lag and resonant. (Looking over their names and arguments, making sure that they are acceptable). E.g., I.e., we no need for add_low_frequency_disturbance, etc.

The add_low_frequency_disturbance really aims to achieve integral action in the LQG controller by modeling a constant input disturbance. It is a good idea to have a way to create typical disturbance models and add those, e.g., add_input_disturbance(sys, step_model()) or something like that.

If possible I think it would be desirable to separate how a disturbances affect the system dynamics from various disturbance models that one would like to investigate. Perhaps using some kind of partitioned state space.

I've been thinking a bit about this and I don't think we need to implement a new system type. It could probably be solved by making the matrices have named components, e.g., through ComponentArrays.jl. I've used this strategy elsewhere and it works quite nicely. The HeteroStateSpace already accepts this kind of matrices.

The LQG struct seems a bit monolithic/inflexible. Some sort of problem data struct, containing the problem specification would seem useful though, e.g., in order to evaluate other linear controllers. We should fix the feedback function to accept UniformScaling, then all the sensitivity functions would just be one-liners, and perhaps wouldn't be needed to be included as getproperty. Or do we feel a need for defining these generally?

I agree, I don't like the design all that much. Maybe it would be better to just break it completely and redesign it so that the structure only contains computed results that are generally useful, and all other results (that are now properties) are just implemented as regular functions instead. The purpose of defining functions is that it might be hard to remember the exact formulations for input/output sensitivity for MIMO systems if you don't have a reference book or pen and paper nearby. Having them as functions prevent you from making simple errors. Getting exactly the same realisation out as matlab also required some gymnastics, at least for output_sensitivity

Perhaps you have some examples/use cases? Would be easier to discuss around something a bit more concrete. If I have the time, I will try to put something together as well. And I guess there should be plenty of examples in the literature, any suggestions?

Double-mass model (4 states) augmented with constant input disturbance (1 state) and resonant measurement disturbance (2 states) to reduce sensitivity at select frequencies. Motor-side states are measured, while references are provided for load-side states (C and M matrices are different) while noise acts on the two velocity states as well as the input-disturbance state. I'll put together some code soon.

baggepinnen added 11 commits April 5, 2021 09:05

merge

b11ee26

pick some

799251b

throw away some comments

0c58595

clarify what controller is

188e33b

simplify handling of Fr Fy

30a05a3

refactor and add some tests

6789ea0

add some model augmentation

9eb1a6f

cp

7f7d269

resolve

797b85b

bugfix in model augmentation

6f77a5d

rm infile tests

65db880

mfalt requested changes Apr 6, 2021

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albheim reviewed Apr 6, 2021

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baggepinnen mentioned this pull request May 17, 2021

add controller function #512

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More LQG updates #467

More LQG updates #467

baggepinnen commented Apr 5, 2021

codecov bot commented Apr 5, 2021 •

edited

mfalt Apr 6, 2021 •

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baggepinnen Apr 6, 2021

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baggepinnen Apr 6, 2021

albheim Apr 6, 2021

olof3 commented Apr 7, 2021 •

edited

baggepinnen commented Apr 8, 2021


		# Extract interesting values
		if G.integrator # Augment with disturbance model

More LQG updates #467

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More LQG updates #467

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olof3 commented Apr 7, 2021 • edited

baggepinnen commented Apr 8, 2021

codecov bot commented Apr 5, 2021 •

edited

mfalt Apr 6, 2021 •

edited

olof3 commented Apr 7, 2021 •

edited