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e180716 toe82e2afComparecoveralls commentedJan 28, 2021 • edited
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…be unneccesary and to avoid a merge conbflict withpython-control#521
control/iosys.py Outdated
| @@ -450,6 +450,10 @@ def issiso(self): | |||
| """Check to see if a system is single input, single output""" | |||
| return self.ninputs == 1 and self.noutputs == 1 | |||
| def isstatic(self): | |||
sawyerbfullerJan 28, 2021 • edited
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statespace and xferfcn have methodsis_static_gain() I added. should we choose a standard conventiuon? I would lean towardisstatic() because it is shorter and matchesissiso(),
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I agree we should be uniform. I'm not sure thatis_static_gain() would make sense for a nonlinear system, so that is another reason to opt forisstatic().
Also: these are mainly internally used functions, so I think it is OK to stick withisstatic/issiso rather thanis_static/is_siso.
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Converted to_isstatic in latest push since this really is an internal function, not intended to be seen by the user.
@sawyerbfuller: when we updateis_static_gain, we can either change to_isstatic if all usage is internal or change toisstatic (and updatedescfcn.py for consistency).
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renamed in#524
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I'll try to review fromdescribing_function_plot on later this weekend.
control/descfcn.py Outdated
| # Class for nonlinearities with a built-in describing function | ||
| class DescribingFunctionNonlinearity(): | ||
| """Base class for nonlinear functions with a describing function |
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| """Baseclassfornonlinearfunctionswithadescribingfunction | |
| """Baseclassfornonlinearsystemswithadescribingfunction |
control/descfcn.py Outdated
| """Base class for nonlinear functions with a describing function | ||
| This class is intended to be used as a base class for nonlinear functions | ||
| that have a analytically defined describing function (accessed via the |
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| thathaveaanalyticallydefineddescribingfunction (accessedviathe | |
| thathaveananalyticallydefineddescribingfunction (accessedviathe |
control/descfcn.py Outdated
| # | ||
| """The :mod:~control.descfcn` module contains function for performing | ||
| closed loop analysis of systems with static nonlinearities using |
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I find thestatic terminology a little confusing, especially given that some of the describing functions declared here, e.g. hysteresis, returnFalse in their_isstatic methods. Maybe "non-linearities with frequency-independent describing functions", though that is rather long-winded.
| implement a `call` method that evaluates the nonlinearity at a given point | ||
| and an `_isstatic` method that is `True` if the nonlinearity has no | ||
| internal state. | ||
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How about: "Subclasses should override thedescribing_function,__call__, and_isstatic methods."
It looks like__call__ 's inputs and outputsmust be scalar, since__call__ is allowed to change instance memory, so the sequence of calls matters.
Candescribing_function be called with anumpy.ndarray of amplitude values? This seems like a reasonable thing to want to do.
If I understand correctly, if__call__ updates any instance state, then_isstatic must returnFalse -- it would be good to mention that too.
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I've updated the documentation a bit to address the comments above.
In terms of callingDescribingFunctionNonlinearity.description_function with an array: the intent is that this is a low level function that just evaluates the describing function at a scalar value. Thedescribing_function function has the code to evaluate on an array.
| """ | ||
| # If there is an analytical solution, trying using that first | ||
| if try_method and hasattr(F, 'describing_function'): |
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thehasattr check will succeed for any base class ofDescribingFunctionNonlinearity - shouldn't you also catch theNotImplementedError ?
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Good catch. Fixed.
control/descfcn.py Outdated
| # | ||
| # Evaluate over a full range of angles | ||
| theta = np.linspace(0, 2*np.pi, num_points) |
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this is not something I'm not at all sure about: should this omit the final point, so it's more like a discrete Fourier transform?
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Good catch. We are approximating the integral by a discrete sum with the assumption that the function is constant on each small interval. But this means that we don't want to include the value at 2pi (since we already captured the segment just before 2pi in the previous evaluation).
control/descfcn.py Outdated
| # Save the scaling factor for to make the formulas simpler | ||
| scale = dtheta / np.pi / a | ||
| # Evaluate the function (twice) along a sinusoid (for internal state) |
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I don't see how this is evaluating the function twice over the sinusoid (assume that means two periods of sinusoid).
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Left over from an earlier iteration (before I implemented_isstatic). Fixed.
control/descfcn.py Outdated
| # | ||
| # N(A) = M_1(A) e^{j \phi_1(A)} / A | ||
| # | ||
| # To compute this, we compute F(\theta) for \theta between 0 and 2 \pi, |
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| # To compute this, we compute F(\theta) for \theta between 0 and 2 \pi, | |
| # To compute this, we compute F(A\sin\theta) for \theta between 0 and 2 \pi, |
control/descfcn.py Outdated
| # | ||
| # and then integrate the product against \sin\theta and \cos\theta to obtain | ||
| # | ||
| # \int_0^{2\pi} F(a\sin\theta) \sin\theta d\theta = M_1 \pi \cos\phi |
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| # \int_0^{2\pi} F(a\sin\theta) \sin\theta d\theta = M_1 \pi \cos\phi | |
| # \int_0^{2\pi} F(A\sin\theta) \sin\theta d\theta = M_1 \pi \cos\phi |
control/descfcn.py Outdated
| # and then integrate the product against \sin\theta and \cos\theta to obtain | ||
| # | ||
| # \int_0^{2\pi} F(a\sin\theta) \sin\theta d\theta = M_1 \pi \cos\phi | ||
| # \int_0^{2\pi} F(a\sin\theta) \cos\theta d\theta = M_1 \pi \sin\phi |
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| # \int_0^{2\pi} F(a\sin\theta) \cos\theta d\theta = M_1 \pi \sin\phi | |
| # \int_0^{2\pi} F(A\sin\theta) \cos\theta d\theta = M_1 \pi \sin\phi |
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Searching for the intersections will be O(m * n).
We could look libraries we can pull in to find the intersection of H(jw) and N(A). I googled "numpy polyline intersection" and found pointers tohttps://pypi.org/project/Shapely/, but that may be over the top.
We could also look at usingscipy.optimize.root, though I don't see an obvious way to bound the domain of search. And we'd have to handle the multiple roots ourselves.
When N(A) is strictly real (saturation, deadzone, relay), we could probably specialize the solver.
control/descfcn.py Outdated
| self.ub = ub | ||
| def __call__(self, x): | ||
| return np.maximum(self.lb, np.minimum(x, self.ub)) |
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| returnnp.maximum(self.lb,np.minimum(x,self.ub)) | |
| returnnp.clip(x,self.lb,self.ub) |
control/freqplot.py Outdated
| @@ -508,7 +508,7 @@ def gen_zero_centered_series(val_min, val_max, period): | |||
| def nyquist_plot(syslist, omega=None, plot=True, label_freq=0, | |||
| arrowhead_length=0.1, arrowhead_width=0.1, | |||
| color=None, *args, **kwargs): | |||
| mirror='--',color=None, *args, **kwargs): | |||
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This new argument should be documented. Are we going to allowNone for no mirror? Below you checked forFalse.
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Updated documentation. Should either be a linestyle or False if you don't want to plot the mirror image at all. Setting it to (explicitly) to None will generate an error (from matplotlib).
| if self.lb <= A and A <= self.ub: | ||
| return 1. | ||
| else: | ||
| alpha, beta = math.asin(self.ub/A), math.asin(-self.lb/A) |
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FWIW, the expression in Slotine & Li, and alsohttps://ocw.mit.edu/courses/aeronautics-and-astronautics/16-30-estimation-and-control-of-aerospace-systems-spring-2004/readings/gelb_ch2_ocr.pdf andhttps://ocw.mit.edu/resources/res-6-010-electronic-feedback-systems-spring-2013/textbook/MITRES_6-010S13_chap06.pdf are different to what you have here, but they may be equivalent. All these references restrict themselves to saturation with odd symmetry, though.
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It's equivalent (I checked, but also the unit tests check this).
| # Backlash nonlinearity (#48 in Gelb and Vander Velde, 1968) | ||
| class backlash_nonlinearity(DescribingFunctionNonlinearity): | ||
| """Backlash nonlinearity for use in describing function analysis |
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Friction-controlled backlash? (https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-30-estimation-and-control-of-aerospace-systems-spring-2004/readings/gelb_ch2_ocr.pdf p. 68?)
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I saw that, but couldn't figure out what the "friction-controlled" had to do with it exactly. It seemed to me that you just had backlash as in a gear and so the output just followed the input (modulo the backlash action).
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Maybe it's not important, but I remember a colleague always talking about the two backlash types (friction-controlled and inertia-controlled), and I thought it was standard nomenclature. The inertia-controlled case is discussed in the reference above immediately after friction-controlled.
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Sorry, I was looking at something different (probably just the table in Appendix B, which didn't have the explanation). I'll update.
control/descfcn.py Outdated
| # Convert input to an array | ||
| x_array = np.array(x) | ||
| y = [] |
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there's an inconsistency here: you've allowed a vector input for this__call__, but not the others.
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Good catch.
control/tests/descfcn_test.py Outdated
| # Static function via a class | ||
| class saturation_class(): |
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| classsaturation_class(): | |
| classsaturation_class: |
control/tests/descfcn_test.py Outdated
| np.testing.assert_array_equal(satsys([0.]), [0.]) | ||
| # Test SIMO nonlinearity | ||
| def _simofcn(t, x, u, params={}): |
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| def_simofcn(t,x,u,params={}): | |
| def_simofcn(t,x,u,params): |
control/tests/descfcn_test.py Outdated
| return np.array([np.sin(u[0]) * np.cos(u[1])]) | ||
| miso_sys = ct.NonlinearIOSystem(None, outfcn=_misofcn, input=2, output=1) | ||
| np.testing.assert_array_equal(miso_sys([0, 0]), [0]) | ||
| np.testing.assert_array_equal(miso_sys([0, 0]), [0]) |
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| np.testing.assert_array_equal(miso_sys([0, 0]), [0]) |
| # Test saturation describing function in multiple ways | ||
| def test_saturation_describing_function(satsys): |
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I think you mean to test with the functionsaturation here, but this testssaturation_class twice.
doc/descfcn.rst Outdated
| linear system and a static nonlinearity, it is possible to obtain a | ||
| generalization of Nyquist's stability criterion based on the idea of | ||
| describing functions. The basic concept involves approximating the | ||
| response of a static nonlinearity to an input :math:`u = A e^{\omega |
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e^{j\omega t} ?
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This PR adds a basic describing function capability, mainly captured in the new
describing_function_plotcommand. Almost all of the new code is in thedescfcn.pyfile, with a few changes elsewhere to support some of the patterns. There is a Jupyter notebook demonstrating the use of the code.Additional changes:
mirrorkeyword tonyquist_plotthat sets the line style used for plotting the complementary portion of the Nyquist plot. This defaults to--, which matches the FBS convention._isstaticmethod to theNonlinearIOSystemclass that allows passing a nonlinear I/O object as the argument for computing describing functions.__call__method to theNonlinearIOSystemclass that direct calling of a static nonlinear input/output function (returning the value of the function at the given input).