ЦiOSSKJrJr SSKJrJr SSKJr SSKJ r SSK J r SSK J r Jr SSKJr SSKJr SS KJr SS KJr SS KJr /S Qr\ "S SS/0\4S9r\ "S5r\(a \R:r\(a\rSr Sr!S!Sjr"S"Sjr#S#Sjr$S"Sjr%S#Sjr&S$Sjr'S%Sjr(S&Sjr)S'Sjr*S(Sjr+S)Sjr,S*Sjr-g )+)Ipi)explog)apart)Dummy) import_module)argAbs)_fast_inverse_laplace)SISOLinearTimeInvariant)LineOver1DRangeSeries)Poly)latex) pole_zero_numerical_datapole_zero_plotstep_response_numerical_datastep_response_plotimpulse_response_numerical_dataimpulse_response_plotramp_response_numerical_dataramp_response_plotbode_magnitude_numerical_databode_phase_numerical_databode_magnitude_plotbode_phase_plot bode_plot matplotlibfromlistpyplot) import_kwargscatchnumpyc[U[5(d [S5eUR5n[ UR 5nUS:a [ S5eUR[5(a [S5eg)zUFunction to check whether the dynamical system passed for plots is compatible or not.z.Only SISO LTI systems are currently supported.zExtra degree of freedom found. Make sure that there are no free symbols in the dynamical system other than the variable of Laplace transform.z#Time delay terms are not supported.N) isinstancer NotImplementedErrorto_exprlen free_symbols ValueErrorhasr)systemsyslen_free_symbolss b/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/physics/control/control_plots.py _check_systemr1!sw f5 6 6!"RSS .. C3++,!78 8 wws||""GHHc[U5 UR5n[URUR5R 5n[UR UR5R 5n[RU[RS9n[RU[RS9n[RU5n[RU5nX44$)a Returns the numerical data of poles and zeros of the system. It is internally used by ``pole_zero_plot`` to get the data for plotting poles and zeros. Users can use this data to further analyse the dynamics of the system or plot using a different backend/plotting-module. Parameters ========== system : SISOLinearTimeInvariant The system for which the pole-zero data is to be computed. Returns ======= tuple : (zeros, poles) zeros = Zeros of the system. NumPy array of complex numbers. poles = Poles of the system. NumPy array of complex numbers. Raises ====== NotImplementedError When a SISO LTI system is not passed. When time delay terms are present in the system. ValueError When more than one free symbol is present in the system. The only variable in the transfer function should be the variable of the Laplace transform. Examples ======== >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import pole_zero_numerical_data >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s) >>> pole_zero_numerical_data(tf1) # doctest: +SKIP ([-0.+1.j 0.-1.j], [-2. +0.j -0.5+0.8660254j -0.5-0.8660254j -1. +0.j ]) See Also ======== pole_zero_plot )dtype) r1doitrnumvar all_coeffsdennparray complex128roots)r-num_polyden_polyzerospoless r0rr2sd& [[]FFJJ +668HFJJ +668Hxx x6Hxx x6H HHX E HHX E <r2c [U5up[RU 5n [RU 5n [RU 5n [RU 5n[R XSSX!S9 [R XSUUS9 [R S5 [RS5 [RS[U5S 3S S 9 U(a[R5 U(a([RS S S9 [RS S S9 U(a[R5 g[$)a Returns the Pole-Zero plot (also known as PZ Plot or PZ Map) of a system. A Pole-Zero plot is a graphical representation of a system's poles and zeros. It is plotted on a complex plane, with circular markers representing the system's zeros and 'x' shaped markers representing the system's poles. Parameters ========== system : SISOLinearTimeInvariant type systems The system for which the pole-zero plot is to be computed. pole_color : str, tuple, optional The color of the pole points on the plot. Default color is blue. The color can be provided as a matplotlib color string, or a 3-tuple of floats each in the 0-1 range. pole_markersize : Number, optional The size of the markers used to mark the poles in the plot. Default pole markersize is 10. zero_color : str, tuple, optional The color of the zero points on the plot. Default color is orange. The color can be provided as a matplotlib color string, or a 3-tuple of floats each in the 0-1 range. zero_markersize : Number, optional The size of the markers used to mark the zeros in the plot. Default zero markersize is 7. grid : boolean, optional If ``True``, the plot will have a grid. Defaults to True. show_axes : boolean, optional If ``True``, the coordinate axes will be shown. Defaults to False. show : boolean, optional If ``True``, the plot will be displayed otherwise the equivalent matplotlib ``plot`` object will be returned. Defaults to True. Examples ======== .. plot:: :context: close-figs :format: doctest :include-source: True >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import pole_zero_plot >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s) >>> pole_zero_plot(tf1) # doctest: +SKIP See Also ======== pole_zero_numerical_data References ========== .. [1] https://en.wikipedia.org/wiki/Pole%E2%80%93zero_plot xnone)mfc markersizecoloro)rFrGz Real AxiszImaginary AxiszPoles and Zeros of $$padrblackrGN)rr:realimagpltplotxlabelylabeltitlergridaxhlineaxvlineshow)r- pole_colorpole_markersize zero_colorzero_markersizerV show_axesrYkwargsr@rA zero_real zero_imag pole_real pole_imags r0rrss~,F3LEIIIIHHY3F" 6HHY3? JJ{JJ II$U6]O152I>    AW % AW %    Jr2c 4US:a [S5e[U5 [S5nUR5UR- n[ X`RSS9n[ X`RU5RU5n[XuX#440UD6R5$)a Returns the numerical values of the points in the step response plot of a SISO continuous-time system. By default, adaptive sampling is used. If the user wants to instead get an uniformly sampled response, then ``adaptive`` kwarg should be passed ``False`` and ``n`` must be passed as additional kwargs. Refer to the parameters of class :class:`sympy.plotting.series.LineOver1DRangeSeries` for more details. Parameters ========== system : SISOLinearTimeInvariant The system for which the unit step response data is to be computed. prec : int, optional The decimal point precision for the point coordinate values. Defaults to 8. lower_limit : Number, optional The lower limit of the plot range. Defaults to 0. upper_limit : Number, optional The upper limit of the plot range. Defaults to 10. kwargs : Additional keyword arguments are passed to the underlying :class:`sympy.plotting.series.LineOver1DRangeSeries` class. Returns ======= tuple : (x, y) x = Time-axis values of the points in the step response. NumPy array. y = Amplitude-axis values of the points in the step response. NumPy array. Raises ====== NotImplementedError When a SISO LTI system is not passed. When time delay terms are present in the system. ValueError When more than one free symbol is present in the system. The only variable in the transfer function should be the variable of the Laplace transform. When ``lower_limit`` parameter is less than 0. Examples ======== >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import step_response_numerical_data >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s) >>> step_response_numerical_data(tf1) # doctest: +SKIP ([0.0, 0.025413462339411542, 0.0484508722725343, ... , 9.670250533855183, 9.844291913708725, 10.0], [0.0, 0.023844582399907256, 0.042894276802320226, ..., 6.828770759094287e-12, 6.456457160755703e-12]) See Also ======== step_response_plot r:Lower limit of time must be greater than or equal to zero.rCTfull r+r1rr(r7rr evalfr get_pointsr-prec lower_limit upper_limitr__xexpr_ys r0rrsDQ%& && sB >> VZZ (D zz -D tZZ 4 : :4 @B +%C   *,r2c [U4UX4S.UD6up[RXUS9 [RS5 [R S5 [R S[ U5S3SS9 U(a[R5 U(a([RS S S9 [RS S S9 U(a[R5 g [$) a Returns the unit step response of a continuous-time system. It is the response of the system when the input signal is a step function. Parameters ========== system : SISOLinearTimeInvariant type The LTI SISO system for which the Step Response is to be computed. color : str, tuple, optional The color of the line. Default is Blue. show : boolean, optional If ``True``, the plot will be displayed otherwise the equivalent matplotlib ``plot`` object will be returned. Defaults to True. lower_limit : Number, optional The lower limit of the plot range. Defaults to 0. upper_limit : Number, optional The upper limit of the plot range. Defaults to 10. prec : int, optional The decimal point precision for the point coordinate values. Defaults to 8. show_axes : boolean, optional If ``True``, the coordinate axes will be shown. Defaults to False. grid : boolean, optional If ``True``, the plot will have a grid. Defaults to True. Examples ======== .. plot:: :context: close-figs :format: doctest :include-source: True >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import step_response_plot >>> tf1 = TransferFunction(8*s**2 + 18*s + 32, s**3 + 6*s**2 + 14*s + 24, s) >>> step_response_plot(tf1) # doctest: +SKIP See Also ======== impulse_response_plot, ramp_response_plot References ========== .. [1] https://www.mathworks.com/help/control/ref/lti.step.html rlrmrnrNTime (s) AmplitudezUnit Step Response of $rIrJrKrrMN) rrQrRrSrTrUrrVrWrXrY r-rGrlrmrnr^rVrYr_rCys r0rrsl ( DT D>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import impulse_response_numerical_data >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s) >>> impulse_response_numerical_data(tf1) # doctest: +SKIP ([0.0, 0.06616480200395854,... , 9.854500743565858, 10.0], [0.9999999799999999, 0.7042848373025861,...,7.170748906965121e-13, -5.1901263495547205e-12]) See Also ======== impulse_response_plot rrerCTrf) r+r1rr(rr7r rirrjrks r0rresDQ%& && sB >> D zz -D tZZ 4 : :4 @B +%C   *,r2c [U4UX4S.UD6up[RXUS9 [RS5 [R S5 [R S[ U5S3SS9 U(a[R5 U(a([RS S S9 [RS S S9 U(a[R5 g [$) a Returns the unit impulse response (Input is the Dirac-Delta Function) of a continuous-time system. Parameters ========== system : SISOLinearTimeInvariant type The LTI SISO system for which the Impulse Response is to be computed. color : str, tuple, optional The color of the line. Default is Blue. show : boolean, optional If ``True``, the plot will be displayed otherwise the equivalent matplotlib ``plot`` object will be returned. Defaults to True. lower_limit : Number, optional The lower limit of the plot range. Defaults to 0. upper_limit : Number, optional The upper limit of the plot range. Defaults to 10. prec : int, optional The decimal point precision for the point coordinate values. Defaults to 8. show_axes : boolean, optional If ``True``, the coordinate axes will be shown. Defaults to False. grid : boolean, optional If ``True``, the plot will have a grid. Defaults to True. Examples ======== .. plot:: :context: close-figs :format: doctest :include-source: True >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import impulse_response_plot >>> tf1 = TransferFunction(8*s**2 + 18*s + 32, s**3 + 6*s**2 + 14*s + 24, s) >>> impulse_response_plot(tf1) # doctest: +SKIP See Also ======== step_response_plot, ramp_response_plot References ========== .. [1] https://www.mathworks.com/help/control/ref/dynamicsystem.impulse.html rsrNrtruzImpulse Response of $rIrJrKrrMN) rrQrRrSrTrUrrVrWrXrYrvs r0rrsl +6 D D>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import ramp_response_numerical_data >>> tf1 = TransferFunction(s, s**2 + 5*s + 8, s) >>> ramp_response_numerical_data(tf1) # doctest: +SKIP (([0.0, 0.12166980856813935,..., 9.861246379582118, 10.0], [1.4504508011325967e-09, 0.006046440489058766,..., 0.12499999999568202, 0.12499999999661349])) See Also ======== ramp_response_plot rz,Slope must be greater than or equal to zero.rerCTrfrh) r-sloperlrmrnr_rorprqs r0rrsL qy Q%& && sB .." "fjj1_ 5D zz -D tZZ 4 : :4 @B +%C   *,r2c  [U4XXES.U D6up[RXUS9 [RS5 [R S5 [R S[ U5SUS3SS 9 U(a[R5 U(a([RS S S9 [RS S S9 U(a[R5 g [$) a Returns the ramp response of a continuous-time system. Ramp function is defined as the straight line passing through origin ($f(x) = mx$). The slope of the ramp function can be varied by the user and the default value is 1. Parameters ========== system : SISOLinearTimeInvariant type The LTI SISO system for which the Ramp Response is to be computed. slope : Number, optional The slope of the input ramp function. Defaults to 1. color : str, tuple, optional The color of the line. Default is Blue. show : boolean, optional If ``True``, the plot will be displayed otherwise the equivalent matplotlib ``plot`` object will be returned. Defaults to True. lower_limit : Number, optional The lower limit of the plot range. Defaults to 0. upper_limit : Number, optional The upper limit of the plot range. Defaults to 10. prec : int, optional The decimal point precision for the point coordinate values. Defaults to 8. show_axes : boolean, optional If ``True``, the coordinate axes will be shown. Defaults to False. grid : boolean, optional If ``True``, the plot will have a grid. Defaults to True. Examples ======== .. plot:: :context: close-figs :format: doctest :include-source: True >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import ramp_response_plot >>> tf1 = TransferFunction(s, (s+4)*(s+8), s) >>> ramp_response_plot(tf1, upper_limit=2) # doctest: +SKIP See Also ======== step_response_plot, impulse_response_plot References ========== .. [1] https://en.wikipedia.org/wiki/Ramp_function )r|rlrmrnrNrtruzRamp Response of $z $ [Slope = ]rJrKrrMN) rrQrRrSrTrUrrVrWrXrY) r-r|rGrlrmrnr^rVrYr_rCrws r0rrQsx ( De D>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import bode_magnitude_numerical_data >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s) >>> bode_magnitude_numerical_data(tf1) # doctest: +SKIP ([1e-05, 1.5148378120533502e-05,..., 68437.36188804005, 100000.0], [-6.020599914256786, -6.0205999155219505,..., -193.4117304087953, -200.00000000260573]) See Also ======== bode_magnitude_plot, bode_phase_numerical_data rad/secHz5Only "rad/sec" and "Hz" are accepted frequency units.wTrOrr{rJ xscaler) r1r(r+rrrsubsr7rr rrj) r- initial_exp final_exp freq_unitr_rp freq_units_wreplw_exprmagrCrws r0rrsv& >> D"J"PQQ s BDtAvbyt YY D) *F SVb ! !C  R_b)m, F5: F>D FFPjl A 4Kr2c [XX'S9up[R"X4SU0UD6 [RS5 [R SU-5 [R S5 [R S[U5S3SS 9 U(a[RS 5 U(a([RS S S 9 [RS S S 9 U(a[R5 g[$)zi Returns the Bode magnitude plot of a continuous-time system. See ``bode_plot`` for all the parameters. )rrrrGrFrequency (%s) [Log Scale]zMagnitude (dB)zBode Plot (Magnitude) of $rIrJrKTrrMrNN) rrQrRrrSrTrUrrVrWrXrY) r-rrrGr^rVrYrr_rCrws r0rrs ) 2DAHHQ))&)JJuJJ+i78JJ II*5=/;ID   AW % AW %    Jr2c [U5 UR5nSnSn X8;a [S5eXI;a [S5e[SSS9n US:Xa[U -S -[ -n O [U -n UR URU 05n US :Xa[U 5S -[ - n O [U 5n [U U S U-S U-44S S0UD6R5upSnU(aUS:Xa[ nOUS :XaS nU(aVS U-n[S[U55H8nUUUUS- - nUU:a UUU- UU'M$UU*:dM-UUU-UU'M: X4$)a Returns the numerical data of the Bode phase plot of the system. It is internally used by ``bode_phase_plot`` to get the data for plotting Bode phase plot. Users can use this data to further analyse the dynamics of the system or plot using a different backend/plotting-module. Parameters ========== system : SISOLinearTimeInvariant The system for which the Bode phase plot data is to be computed. initial_exp : Number, optional The initial exponent of 10 of the semilog plot. Defaults to -5. final_exp : Number, optional The final exponent of 10 of the semilog plot. Defaults to 5. freq_unit : string, optional User can choose between ``'rad/sec'`` (radians/second) and '``'Hz'`` (Hertz) as frequency units. phase_unit : string, optional User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units. phase_unwrap : bool, optional Set to ``True`` by default. Returns ======= tuple : (x, y) x = x-axis values of the Bode phase plot. y = y-axis values of the Bode phase plot. Raises ====== NotImplementedError When a SISO LTI system is not passed. When time delay terms are present in the system. ValueError When more than one free symbol is present in the system. The only variable in the transfer function should be the variable of the Laplace transform. When incorrect frequency or phase units are given as input. Examples ======== >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import bode_phase_numerical_data >>> tf1 = TransferFunction(s**2 + 1, s**4 + 4*s**3 + 6*s**2 + 5*s + 2, s) >>> bode_phase_numerical_data(tf1) # doctest: +SKIP ([1e-05, 1.4472354033813751e-05, 2.035581932165858e-05,..., 47577.3248186011, 67884.09326036123, 100000.0], [-2.5000000000291665e-05, -3.6180885085e-05, -5.08895483066e-05,...,-3.1415085799262523, -3.14155265358979]) See Also ======== bode_magnitude_plot, bode_phase_numerical_data r)raddegrz.Only "rad" and "deg" are accepted phase units.rTrrr{rrrrNrr%) r1r(r+rrrrr7r rrjranger))r-rrr phase_unit phase_unwrapr_rpr phase_unitsrrrphaserCrwhalfunitidiffs r0rr s~& >> D"J K"PQQ$IJJ s BDtAvbyt YY D) *FUF C"F   R_b)m, F5: F>D FFPjl A D  D 5 D vq#a&!AQ4!AE(?Dd{!t !!t ! " 4Kr2c [XX'XS9up[R"X4SU0U D6 [RS5 [R SU-5 [R SU-5 [R S[U5S3SS 9 U(a[RS 5 U(a([RS S S 9 [RS S S 9 U(a[R5 g[$)ze Returns the Bode phase plot of a continuous-time system. See ``bode_plot`` for all the parameters. )rrrrrrGrrz Phase (%s)zBode Plot (Phase) of $rIrJrKTrrMrNN) rrQrRrrSrTrUrrVrWrXrY) r-rrrGr^rVrYrrrr_rCrws r0rrvs %VZ dDAHHQ))&)JJuJJ+i78JJ|j()II&uV}oQ7RI@   AW % AW %    Jr2c Z[RS5 [U4XSX4US.U D6n U RS[ U5S3SS9 U R S5 [RS 5 [ U4XSX4XgUS .U D6RS5 U(a[R5 g[$) a, Returns the Bode phase and magnitude plots of a continuous-time system. Parameters ========== system : SISOLinearTimeInvariant type The LTI SISO system for which the Bode Plot is to be computed. initial_exp : Number, optional The initial exponent of 10 of the semilog plot. Defaults to -5. final_exp : Number, optional The final exponent of 10 of the semilog plot. Defaults to 5. show : boolean, optional If ``True``, the plot will be displayed otherwise the equivalent matplotlib ``plot`` object will be returned. Defaults to True. prec : int, optional The decimal point precision for the point coordinate values. Defaults to 8. grid : boolean, optional If ``True``, the plot will have a grid. Defaults to True. show_axes : boolean, optional If ``True``, the coordinate axes will be shown. Defaults to False. freq_unit : string, optional User can choose between ``'rad/sec'`` (radians/second) and ``'Hz'`` (Hertz) as frequency units. phase_unit : string, optional User can choose between ``'rad'`` (radians) and ``'deg'`` (degree) as phase units. Examples ======== .. plot:: :context: close-figs :format: doctest :include-source: True >>> from sympy.abc import s >>> from sympy.physics.control.lti import TransferFunction >>> from sympy.physics.control.control_plots import bode_plot >>> tf1 = TransferFunction(1*s**2 + 0.1*s + 7.5, 1*s**4 + 0.12*s**3 + 9*s**2, s) >>> bode_plot(tf1, initial_exp=0.2, final_exp=0.7) # doctest: +SKIP See Also ======== bode_magnitude_plot, bode_phase_plot F)rrrYrVr^rzBode Plot of $rIrJrKN)rrrYrVr^rrr)rQsubplotrrUrrSrrY) r-rrrVr^rYrrrr_rs r0rrsdKK f '+  '% 'CIIuV}oQ/RI8JJtKKFE imyE~DEFKFKLPFQ    Jr2N)bluerorangeTTT)rr)brrrFTT)r%rrr)r%rrrrFTT)r)rrrFTTr)rrrrT) rrrFTTrrT)rrTFTrrT).sympy.core.numbersrr&sympy.functions.elementary.exponentialrrsympy.polys.partfracrsympy.core.symbolrsympy.externalr sympy.functionsr r sympy.integrals.laplacer sympy.physics.control.ltir sympy.plotting.seriesrsympy.polys.polytoolsrsympy.printing.latexr__all__ RuntimeErrorrr#r rQr:r1rrrrrrrrrrrrrr2r0rs"$=&#($9=7&& ;Z($<o  g   C BI">B?AAE Xv>?K\?@59FRABK\BC59FR89!RjHI59L^M`;<@I:fR78jn812_c@r2