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GeezerVison is showing github.com — python-control/control/frdata.py at 0.9.1 · python-control/python-control Expand file tree/ Copy pathfrdata.pyMore file actions 658 lines (537 loc) · 25.4 KB / Copy pathfrdata.pyFile metadata and controls658 lines (537 loc) · 25.4 KB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 # Copyright (c) 2010 by California Institute of Technology # Copyright (c) 2012 by Delft University of Technology # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # 3. Neither the names of the California Institute of Technology nor # the Delft University of Technology nor # the names of its contributors may be used to endorse or promote # products derived from this software without specific prior # written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS # "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT # LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS # FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CALTECH # OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, # SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT # LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF # USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND # ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, # OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT # OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF # SUCH DAMAGE. # # Author: M.M. (Rene) van Paassen (using xferfcn.py as basis) # Date: 02 Oct 12 """ Frequency response data representation and functions. This module contains the FRD class and also functions that operate on FRD data. """ # External function declarations from warnings import warn import numpy as np from numpy import angle, array, empty, ones, \ real, imag, absolute, eye, linalg, where, sort from scipy.interpolate import splprep, splev from .lti import LTI, _process_frequency_response from . import config __all__ = ['FrequencyResponseData', 'FRD', 'frd'] class FrequencyResponseData(LTI): """FrequencyResponseData(d, w[, smooth]) A class for models defined by frequency response data (FRD). The FrequencyResponseData (FRD) class is used to represent systems in frequency response data form. Parameters ---------- d : 1D or 3D complex array_like The frequency response at each frequency point. If 1D, the system is assumed to be SISO. If 3D, the system is MIMO, with the first dimension corresponding to the output index of the FRD, the second dimension corresponding to the input index, and the 3rd dimension corresponding to the frequency points in omega w : iterable of real frequencies List of frequency points for which data are available. smooth : bool, optional If ``True``, create an interpolation function that allows the frequency response to be computed at any frequency within the range of frequencies give in ``w``. If ``False`` (default), frequency response can only be obtained at the frequencies specified in ``w``. Attributes ---------- ninputs, noutputs : int Number of input and output variables. omega : 1D array Frequency points of the response. fresp : 3D array Frequency response, indexed by output index, input index, and frequency point. Notes ----- The main data members are 'omega' and 'fresp', where 'omega' is a 1D array of frequency points and and 'fresp' is a 3D array of frequency responses, with the first dimension corresponding to the output index of the FRD, the second dimension corresponding to the input index, and the 3rd dimension corresponding to the frequency points in omega. For example, >>> frdata[2,5,:] = numpy.array([1., 0.8-0.2j, 0.2-0.8j]) means that the frequency response from the 6th input to the 3rd output at the frequencies defined in omega is set to the array above, i.e. the rows represent the outputs and the columns represent the inputs. A frequency response data object is callable and returns the value of the transfer function evaluated at a point in the complex plane (must be on the imaginary access). See :meth:`~control.FrequencyResponseData.__call__` for a more detailed description. """ # Allow NDarray * StateSpace to give StateSpace._rmul_() priority # https://docs.scipy.org/doc/numpy/reference/arrays.classes.html __array_priority__ = 11 # override ndarray and matrix types # # Class attributes # # These attributes are defined as class attributes so that they are # documented properly. They are "overwritten" in __init__. # #: Number of system inputs. #: #: :meta hide-value: ninputs = 1 #: Number of system outputs. #: #: :meta hide-value: noutputs = 1 _epsw = 1e-8 #: Bound for exact frequency match def __init__(self, *args, **kwargs): """Construct an FRD object. The default constructor is FRD(d, w), where w is an iterable of frequency points, and d is the matching frequency data. If d is a single list, 1d array, or tuple, a SISO system description is assumed. d can also be To call the copy constructor, call FRD(sys), where sys is a FRD object. To construct frequency response data for an existing LTI object, other than an FRD, call FRD(sys, omega) """ # TODO: discrete-time FRD systems? smooth = kwargs.get('smooth', False) if len(args) == 2: if not isinstance(args[0], FRD) and isinstance(args[0], LTI): # not an FRD, but still a system, second argument should be # the frequency range otherlti = args[0] self.omega = sort(np.asarray(args[1], dtype=float)) # calculate frequency response at my points if otherlti.isctime(): s = 1j * self.omega self.fresp = otherlti(s, squeeze=False) else: z = np.exp(1j * self.omega * otherlti.dt) self.fresp = otherlti(z, squeeze=False) else: # The user provided a response and a freq vector self.fresp = array(args[0], dtype=complex) if len(self.fresp.shape) == 1: self.fresp = self.fresp.reshape(1, 1, len(args[0])) self.omega = array(args[1], dtype=float) if len(self.fresp.shape) != 3 or \ self.fresp.shape[-1] != self.omega.shape[-1] or \ len(self.omega.shape) != 1: raise TypeError( "The frequency data constructor needs a 1-d or 3-d" " response data array and a matching frequency vector" " size") elif len(args) == 1: # Use the copy constructor. if not isinstance(args[0], FRD): raise TypeError( "The one-argument constructor can only take in" " an FRD object. Received %s." % type(args[0])) self.omega = args[0].omega self.fresp = args[0].fresp else: raise ValueError( "Needs 1 or 2 arguments; received %i." % len(args)) # create interpolation functions if smooth: self.ifunc = empty((self.fresp.shape[0], self.fresp.shape[1]), dtype=tuple) for i in range(self.fresp.shape[0]): for j in range(self.fresp.shape[1]): self.ifunc[i, j], u = splprep( u=self.omega, x=[real(self.fresp[i, j, :]), imag(self.fresp[i, j, :])], w=1.0/(absolute(self.fresp[i, j, :]) + 0.001), s=0.0) else: self.ifunc = None LTI.__init__(self, self.fresp.shape[1], self.fresp.shape[0]) def __str__(self): """String representation of the transfer function.""" mimo = self.ninputs > 1 or self.noutputs > 1 outstr = ['Frequency response data'] for i in range(self.ninputs): for j in range(self.noutputs): if mimo: outstr.append("Input %i to output %i:" % (i + 1, j + 1)) outstr.append('Freq [rad/s] Response') outstr.append('------------ ---------------------') outstr.extend( ['%12.3f %10.4g%+10.4gj' % (w, re, im) for w, re, im in zip(self.omega, real(self.fresp[j, i, :]), imag(self.fresp[j, i, :]))]) return '\n'.join(outstr) def __repr__(self): """Loadable string representation, limited for number of data points. """ return "FrequencyResponseData({d}, {w}{smooth})".format( d=repr(self.fresp), w=repr(self.omega), smooth=(self.ifunc and ", smooth=True") or "") def __neg__(self): """Negate a transfer function.""" return FRD(-self.fresp, self.omega) def __add__(self, other): """Add two LTI objects (parallel connection).""" if isinstance(other, FRD): # verify that the frequencies match if len(other.omega) != len(self.omega) or \ (other.omega != self.omega).any(): warn("Frequency points do not match; expect " "truncation and interpolation.") # Convert the second argument to a frequency response function. # or re-base the frd to the current omega (if needed) other = _convert_to_FRD(other, omega=self.omega) # Check that the input-output sizes are consistent. if self.ninputs != other.ninputs: raise ValueError("The first summand has %i input(s), but the \ second has %i." % (self.ninputs, other.ninputs)) if self.noutputs != other.noutputs: raise ValueError("The first summand has %i output(s), but the \ second has %i." % (self.noutputs, other.noutputs)) return FRD(self.fresp + other.fresp, other.omega) def __radd__(self, other): """Right add two LTI objects (parallel connection).""" return self + other def __sub__(self, other): """Subtract two LTI objects.""" return self + (-other) def __rsub__(self, other): """Right subtract two LTI objects.""" return other + (-self) def __mul__(self, other): """Multiply two LTI objects (serial connection).""" # Convert the second argument to a transfer function. if isinstance(other, (int, float, complex, np.number)): return FRD(self.fresp * other, self.omega, smooth=(self.ifunc is not None)) else: other = _convert_to_FRD(other, omega=self.omega) # Check that the input-output sizes are consistent. if self.ninputs != other.noutputs: raise ValueError( "H = G1*G2: input-output size mismatch: " "G1 has %i input(s), G2 has %i output(s)." % (self.ninputs, other.noutputs)) inputs = other.ninputs outputs = self.noutputs fresp = empty((outputs, inputs, len(self.omega)), dtype=self.fresp.dtype) for i in range(len(self.omega)): fresp[:, :, i] = self.fresp[:, :, i] @ other.fresp[:, :, i] return FRD(fresp, self.omega, smooth=(self.ifunc is not None) and (other.ifunc is not None)) def __rmul__(self, other): """Right Multiply two LTI objects (serial connection).""" # Convert the second argument to an frd function. if isinstance(other, (int, float, complex, np.number)): return FRD(self.fresp * other, self.omega, smooth=(self.ifunc is not None)) else: other = _convert_to_FRD(other, omega=self.omega) # Check that the input-output sizes are consistent. if self.noutputs != other.ninputs: raise ValueError( "H = G1*G2: input-output size mismatch: " "G1 has %i input(s), G2 has %i output(s)." % (other.ninputs, self.noutputs)) inputs = self.ninputs outputs = other.noutputs fresp = empty((outputs, inputs, len(self.omega)), dtype=self.fresp.dtype) for i in range(len(self.omega)): fresp[:, :, i] = other.fresp[:, :, i] @ self.fresp[:, :, i] return FRD(fresp, self.omega, smooth=(self.ifunc is not None) and (other.ifunc is not None)) # TODO: Division of MIMO transfer function objects is not written yet. def __truediv__(self, other): """Divide two LTI objects.""" if isinstance(other, (int, float, complex, np.number)): return FRD(self.fresp * (1/other), self.omega, smooth=(self.ifunc is not None)) else: other = _convert_to_FRD(other, omega=self.omega) if (self.ninputs > 1 or self.noutputs > 1 or other.ninputs > 1 or other.noutputs > 1): raise NotImplementedError( "FRD.__truediv__ is currently only implemented for SISO " "systems.") return FRD(self.fresp/other.fresp, self.omega, smooth=(self.ifunc is not None) and (other.ifunc is not None)) # TODO: Remove when transition to python3 complete def __div__(self, other): return self.__truediv__(other) # TODO: Division of MIMO transfer function objects is not written yet. def __rtruediv__(self, other): """Right divide two LTI objects.""" if isinstance(other, (int, float, complex, np.number)): return FRD(other / self.fresp, self.omega, smooth=(self.ifunc is not None)) else: other = _convert_to_FRD(other, omega=self.omega) if (self.ninputs > 1 or self.noutputs > 1 or other.ninputs > 1 or other.noutputs > 1): raise NotImplementedError( "FRD.__rtruediv__ is currently only implemented for " "SISO systems.") return other / self # TODO: Remove when transition to python3 complete def __rdiv__(self, other): return self.__rtruediv__(other) def __pow__(self, other): if not type(other) == int: raise ValueError("Exponent must be an integer") if other == 0: return FRD(ones(self.fresp.shape), self.omega, smooth=(self.ifunc is not None)) # unity if other > 0: return self * (self**(other-1)) if other < 0: return (FRD(ones(self.fresp.shape), self.omega) / self) * \ (self**(other+1)) # Define the `eval` function to evaluate an FRD at a given (real) # frequency. Note that we choose to use `eval` instead of `evalfr` to # avoid confusion with :func:`evalfr`, which takes a complex number as its # argument. Similarly, we don't use `__call__` to avoid confusion between # G(s) for a transfer function and G(omega) for an FRD object. # update Sawyer B. Fuller 2020.08.14: __call__ added to provide a uniform # interface to systems in general and the lti.frequency_response method def eval(self, omega, squeeze=None): """Evaluate a transfer function at angular frequency omega. Note that a "normal" FRD only returns values for which there is an entry in the omega vector. An interpolating FRD can return intermediate values. Parameters ---------- omega : float or 1D array_like Frequencies in radians per second squeeze : bool, optional If squeeze=True, remove single-dimensional entries from the shape of the output even if the system is not SISO. If squeeze=False, keep all indices (output, input and, if omega is array_like, frequency) even if the system is SISO. The default value can be set using config.defaults['control.squeeze_frequency_response']. Returns ------- fresp : complex ndarray The frequency response of the system. If the system is SISO and squeeze is not True, the shape of the array matches the shape of omega. If the system is not SISO or squeeze is False, the first two dimensions of the array are indices for the output and input and the remaining dimensions match omega. If ``squeeze`` is True then single-dimensional axes are removed. """ omega_array = np.array(omega, ndmin=1) # array-like version of omega # Make sure that we are operating on a simple list if len(omega_array.shape) > 1: raise ValueError("input list must be 1D") # Make sure that frequencies are all real-valued if any(omega_array.imag > 0): raise ValueError("FRD.eval can only accept real-valued omega") if self.ifunc is None: elements = np.isin(self.omega, omega) # binary array if sum(elements) < len(omega_array): raise ValueError( "not all frequencies omega are in frequency list of FRD " "system. Try an interpolating FRD for additional points.") else: out = self.fresp[:, :, elements] else: out = empty((self.noutputs, self.ninputs, len(omega_array)), dtype=complex) for i in range(self.noutputs): for j in range(self.ninputs): for k, w in enumerate(omega_array): frraw = splev(w, self.ifunc[i, j], der=0) out[i, j, k] = frraw[0] + 1.0j * frraw[1] return _process_frequency_response(self, omega, out, squeeze=squeeze) def __call__(self, s, squeeze=None): """Evaluate system's transfer function at complex frequencies. Returns the complex frequency response `sys(s)` of system `sys` with `m = sys.ninputs` number of inputs and `p = sys.noutputs` number of outputs. To evaluate at a frequency omega in radians per second, enter ``s = omega * 1j`` or use ``sys.eval(omega)`` For a frequency response data object, the argument must be an imaginary number (since only the frequency response is defined). Parameters ---------- s : complex scalar or 1D array_like Complex frequencies squeeze : bool, optional (default=True) If squeeze=True, remove single-dimensional entries from the shape of the output even if the system is not SISO. If squeeze=False, keep all indices (output, input and, if omega is array_like, frequency) even if the system is SISO. The default value can be set using config.defaults['control.squeeze_frequency_response']. Returns ------- fresp : complex ndarray The frequency response of the system. If the system is SISO and squeeze is not True, the shape of the array matches the shape of omega. If the system is not SISO or squeeze is False, the first two dimensions of the array are indices for the output and input and the remaining dimensions match omega. If ``squeeze`` is True then single-dimensional axes are removed. Raises ------ ValueError If `s` is not purely imaginary, because :class:`FrequencyDomainData` systems are only defined at imaginary frequency values. """ # Make sure that we are operating on a simple list if len(np.atleast_1d(s).shape) > 1: raise ValueError("input list must be 1D") if any(abs(np.atleast_1d(s).real) > 0): raise ValueError("__call__: FRD systems can only accept " "purely imaginary frequencies") # need to preserve array or scalar status if hasattr(s, '__len__'): return self.eval(np.asarray(s).imag, squeeze=squeeze) else: return self.eval(complex(s).imag, squeeze=squeeze) def freqresp(self, omega): """(deprecated) Evaluate transfer function at complex frequencies. .. deprecated::0.9.0 Method has been given the more pythonic name :meth:`FrequencyResponseData.frequency_response`. Or use :func:`freqresp` in the MATLAB compatibility module. """ warn("FrequencyResponseData.freqresp(omega) will be removed in a " "future release of python-control; use " "FrequencyResponseData.frequency_response(omega), or " "freqresp(sys, omega) in the MATLAB compatibility module " "instead", DeprecationWarning) return self.frequency_response(omega) def feedback(self, other=1, sign=-1): """Feedback interconnection between two FRD objects.""" other = _convert_to_FRD(other, omega=self.omega) if (self.noutputs != other.ninputs or self.ninputs != other.noutputs): raise ValueError( "FRD.feedback, inputs/outputs mismatch") # TODO: handle omega re-mapping # reorder array axes in order to leverage numpy broadcasting myfresp = np.moveaxis(self.fresp, 2, 0) otherfresp = np.moveaxis(other.fresp, 2, 0) I_AB = eye(self.ninputs)[np.newaxis, :, :] + otherfresp @ myfresp resfresp = (myfresp @ linalg.inv(I_AB)) fresp = np.moveaxis(resfresp, 0, 2) return FRD(fresp, other.omega, smooth=(self.ifunc is not None)) # # Allow FRD as an alias for the FrequencyResponseData class # # Note: This class was initially given the name "FRD", but this caused # problems with documentation on MacOS platforms, since files were generated # for control.frd and control.FRD, which are not differentiated on most MacOS # filesystems, which are case insensitive. Renaming the FRD class to be # FrequenceResponseData and then assigning FRD to point to the same object # fixes this problem. # FRD = FrequencyResponseData def _convert_to_FRD(sys, omega, inputs=1, outputs=1): """Convert a system to frequency response data form (if needed). If sys is already an frd, and its frequency range matches or overlaps the range given in omega then it is returned. If sys is another LTI object or a transfer function, then it is converted to a frequency response data at the specified omega. If sys is a scalar, then the number of inputs and outputs can be specified manually, as in: >>> frd = _convert_to_FRD(3., omega) # Assumes inputs = outputs = 1 >>> frd = _convert_to_FRD(1., omegs, inputs=3, outputs=2) In the latter example, sys's matrix transfer function is [[1., 1., 1.] [1., 1., 1.]]. """ if isinstance(sys, FRD): omega.sort() if len(omega) == len(sys.omega) and \ (abs(omega - sys.omega) < FRD._epsw).all(): # frequencies match, and system was already frd; simply use return sys raise NotImplementedError( "Frequency ranges of FRD do not match, conversion not implemented") elif isinstance(sys, LTI): omega = np.sort(omega) if sys.isctime(): fresp = sys(1j * omega) else: fresp = sys(np.exp(1j * omega * sys.dt)) if len(fresp.shape) == 1: fresp = fresp[np.newaxis, np.newaxis, :] return FRD(fresp, omega, smooth=True) elif isinstance(sys, (int, float, complex, np.number)): fresp = ones((outputs, inputs, len(omega)), dtype=float)*sys return FRD(fresp, omega, smooth=True) # try converting constant matrices try: sys = array(sys) outputs, inputs = sys.shape fresp = empty((outputs, inputs, len(omega)), dtype=float) for i in range(outputs): for j in range(inputs): fresp[i, j, :] = sys[i, j] return FRD(fresp, omega, smooth=True) except Exception: pass raise TypeError('''Can't convert given type "%s" to FRD system.''' % sys.__class__) def frd(*args): """frd(d, w) Construct a frequency response data model frd models store the (measured) frequency response of a system. This function can be called in different ways: ``frd(response, freqs)`` Create an frd model with the given response data, in the form of complex response vector, at matching frequency freqs [in rad/s] ``frd(sys, freqs)`` Convert an LTI system into an frd model with data at frequencies freqs. Parameters ---------- response: array_like, or list complex vector with the system response freq: array_lik or lis vector with frequencies sys: LTI (StateSpace or TransferFunction) A linear system Returns ------- sys: FRD New frequency response system See Also -------- FRD, ss, tf """ return FRD(*args) |
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