Add support for continuous delay systems #1148

MythasNauveili · 2025-05-11T07:08:06Z

This PR introduces initial support for linear time-invariant (LTI) systems with time delays in python-control, inspired by the capabilities of ControlSystems.jl package, and the InternalDelay.py script from Skogestad-Python.

Key features

Creation of delay sytems Systems with delays can now be intuitively constructed by multiplying a TransferFunction object with a delay(tau) object or an exp(-tau*s) expression:
```
tf_delay = tf([1], [1,1]) * delay(2)
# or
s = tf("s")
tf_delay = tf([1], [1,1]) * exp(-2*s)
```
Underlying Representation: The approach utilizes Linear Fractional Transformations (LFT) with a PartitionedStateSpace representation (implemented in partitionedssp.py). The DelayLTI class (in delaylti.py) serves as the core object for these systems.
Operations: Standard operations such as addition, multiplication, and feedback are supported for DelayLTI objects.
Time and Frequency Responses: Time responses for delayed systems are computed by solving the underlying Delay Differential Equations (DDEs). Frequency responses are also supported.
Retrocompatibility: Maintain retrocompatibility with existing functionalities.

Implementation Details:

DDE Solver: Time responses for delayed systems are computed by solving DDEs. After exploring alternatives, a custom DDE solver based on the Method of Steps, wrapping SciPy's solve_ivp, was implemented in dde.py.
- Accuracy Note: While this solver performs well for many cases, for stiff problems, it may require smaller step sizes for convergence compared to specialized DDE solvers (like those in ControlSystems.jl). In tested scenarios, the error typically remains at least three orders of magnitude below the system response with reasonable step sizes. (An error estimation algorithm could be a valuable future addition).
Validation: A Julia script (control/julia/compute_tests.jl) using ControlSystems.jl has been added to generate reference results, which are exported to a JSON file. These results are used in the test suite (control/tests/delay_lti_test.py and control/tests/dde_test.py) to benchmark the accuracy of the DelayLTI implementation and DDE solver.

Current Scope and Limitations:

This implementation currently focuses on continuous-time delay systems. Discrete-time delay systems are not yet covered.
The DDE solver may benefit from further enhancements for stiff problems or adaptive step sizing.

Discussion Points:
This PR represents the initial groundwork for this feature. I'm submitting this draft to share these first steps and would appreciate feedback on:

The overall approach and class design (DelayLTI, PartitionedStateSpace).
The DDE solver implementation and its current performance.
Any potential integration issues or API considerations.

I'm aware there is still work to be done for this feature to be ready for a full release, but I believe this provides a solid foundation.

…m to solve delay ODE in timeresp. Add litlle tests about timereps

…n the DDE integration

implemented only basic dde solving based on Skogestad python

…improve doc and julia notebook. Clean the code

…alize with json file. Fix scalar multiplication

…ests. TODO: clean dde file, test functions in it, and reloacate dde response tests. More tests also like mimo force response are needed

murrayrm

Initial round of comments. I haven't yet checked functionality, but found a few style issues that should be updated.

murrayrm · 2025-05-12T04:25:25Z

control/dde.py

+    U = _check_convert_array(
+        U, legal_shapes, "Parameter `U`: ", squeeze=False, transpose=transpose
+    )
+    print("U shape: ", U.shape)


This looks like a debugging statement that was left in the code?

removed in last commit

murrayrm · 2025-05-12T04:25:56Z

control/dde.py

+            discontinuity_times.remove(t_stop)
+        local_t_eval = [t for t in T if current_t < t <= t_stop]
+
+        print("Integrate bewtween ", current_t, " and ", t_stop)


Debugging statement?

removed in last commit

murrayrm · 2025-05-12T04:27:26Z

control/__init__.py

@@ -89,6 +89,7 @@

 # Allow access to phase_plane functions as ct.phaseplot.fcn or ct.pp.fcn
 from . import phaseplot as phaseplot
+


Was there a reason to add an extraneous blank line here?

no, blank line is removed in the last commit

murrayrm · 2025-05-12T04:30:16Z

control/dde.py

+    )
+
+
+def pchip_interp_u(T, U):


This looks like it is probably an internal function. If so, add underscore to start of function name.

underscore added

murrayrm · 2025-05-12T04:31:28Z

control/dde.py

+        return np.array([negative_wrapper(PchipInterpolator(T, ui)) for ui in U])
+
+
+class DdeHistory:


This might be better named DDEHistory (since DDE is a standard abbreviation, like LTI)?

Also, if this is an internal class, begin the class name with an underscore.

Changed the name and added the underscore

murrayrm · 2025-05-12T04:41:22Z

control/delaylti.py

+
+    Notes
+    -----
+    The way to create a DelayLTI object is by multiplying a transfert


Typo: transfert → transfer

murrayrm · 2025-05-12T04:42:16Z

control/delaylti.py

+    It's possible to MIMO delayed systems from arrays of SISO delayed systems,
+    see function mimo_delay


It's possible to MIMO → It is possible to create

Also missing a period at the end.

murrayrm · 2025-05-12T04:44:03Z

control/delaylti.py

+
+    # Poles and zeros functions for DelayLTI are not supported by julia ControlSystems.jl
+    # might not be accurate for delayLTI, to be discussed
+    # Here the poles and zeros computed are the ones of the system without taking into accoutn the delay


Typo + may be longer than 78 char (PEP8).

murrayrm · 2025-05-12T04:49:55Z

control/delaylti.py

+            # Check dimensions of K
+            if K.shape != (self.nu, self.ny):
+                raise ValueError(
+                    f"Feedback gain K has incompatible shape. Expected ({self.nu}, {self.ny}), got {K.shape}."


Update to avoid line with more than 78 characters and put closing parenthesis at end of string, for consistency with current code base.

murrayrm · 2025-05-12T04:51:20Z

control/delaylti.py

+    def issiso(self):
+        """Check if the system is single-input, single-output."""
+        # Based on EXTERNAL dimensions
+        return self.nu == 1 and self.ny == 1


This should be handled by the parent class (InputOutputSystem).

This is now moved to InputOutputSystem

murrayrm · 2025-05-12T04:55:42Z

This would be a great contribution, @MythasNauveili. Thanks for working on it!

There are some issues with unit tests. In addition to the failed ruff and doctest checks, it looks like some of the standard tests might be hanging. Not sure if that is due to the new code or if something is messed up in the GitHub actions. I'll try to come back and take a look at that later.

In the meantime, some style things to adjust in your next pass.

…or delayLTI to iosys.py

MythasNauveili · 2025-05-12T19:36:36Z

Thanks for the first feedback @murrayrm. I tried to fix the most in the two last commits. For the tests hanging, it might be because of debug plots that I did not disable in dde_test.py (this should be done now).

coveralls · 2025-05-12T23:10:00Z

coverage: 94.16% (-0.6%) from 94.746%
when pulling 1150646 on MythasNauveili:dev-delay
into 632391c on python-control:main.

murrayrm · 2025-05-13T02:13:35Z

@MythasNauveili There are still two unit tests failing. Click on the links above to see the issues. The ruff checks should be straightforward. For the doctest, it looks like something is printing out spurious information; not sure where that is happening.

…_test

MythasNauveili · 2025-05-13T06:18:47Z

@murrayrm it might be ok now, I just removed a forgotten debug print in timeresp.py that was the source of the dxdt = [...]

MythasNauveili and others added 15 commits March 26, 2025 08:56

implement delayLTI and PartionedStateSpace classes and first algorith…

de5a61f

…m to solve delay ODE in timeresp. Add litlle tests about timereps

Merge branch 'python-control:main' into dev-delay

848d763

ongoing tests with julia notebooks, feedback bug solved

2c74ca1

mimo building of delay systems

b6c0cde

implementation of working frequency response for delayed siso system

8dcab54

__call__ implementation to use lti frequency response function

9b7b062

delay systems handle freq plots (julia comparison ok). Time to work o…

e8a197b

…n the DDE integration

add dde.py file to improve readibility in timeresp.py

29081b5

implemented only basic dde solving based on Skogestad python

add tests and docstrings, tests are all passing. ToDo: refine tests, …

8f43ab9

…improve doc and julia notebook. Clean the code

improve tests by scripting julia code to mimic python tests, and seri…

30c05b9

…alize with json file. Fix scalar multiplication

methods of steps implemented, 1E-5 accuracy against julia for first t…

53641f4

…ests. TODO: clean dde file, test functions in it, and reloacate dde response tests. More tests also like mimo force response are needed

Merge branch 'python-control:main' into dev-delay

b0f2cd3

cleaning old dde methods

4172ce8

mimo forced response passed. TODO: clean

a460513

docstrings, ruff check and format

f56e5de

murrayrm requested changes May 12, 2025

View reviewed changes

MythasNauveili added 2 commits May 12, 2025 20:36

improve formatting, underscore internal functions, add file description

36ad284

implement delay case in input_output_response, move and test issiso f…

4870463

…or delayLTI to iosys.py

remove forgotten debug print in timeresp, and unused imports in delay…

1150646

…_test

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Add support for continuous delay systems #1148

Add support for continuous delay systems #1148

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murrayrm commented May 13, 2025

MythasNauveili commented May 13, 2025

		@@ -89,6 +89,7 @@

		# Allow access to phase_plane functions as ct.phaseplot.fcn or ct.pp.fcn
		from . import phaseplot as phaseplot

		return np.array([negative_wrapper(PchipInterpolator(T, ui)) for ui in U])


		class DdeHistory:

		It's possible to MIMO delayed systems from arrays of SISO delayed systems,
		see function mimo_delay

Add support for continuous delay systems #1148

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murrayrm commented May 12, 2025

MythasNauveili commented May 12, 2025

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murrayrm commented May 13, 2025

MythasNauveili commented May 13, 2025

coveralls commented May 12, 2025 •

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