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GeezerVison is showing github.com — python-control/control/freqplot.py at master · Marxlp/python-control Expand file tree/ Copy pathfreqplot.pyMore file actions 547 lines (482 loc) · 20.5 KB / Copy pathfreqplot.pyFile metadata and controls547 lines (482 loc) · 20.5 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 # freqplot.py - frequency domain plots for control systems # # Author: Richard M. Murray # Date: 24 May 09 # # This file contains some standard control system plots: Bode plots, # Nyquist plots and pole-zero diagrams. The code for Nichols charts # is in nichols.py. # # Copyright (c) 2010 by California Institute 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 name of the California Institute 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. # # $Id$ import matplotlib.pyplot as plt import scipy as sp import numpy as np from .ctrlutil import unwrap from .bdalg import feedback __all__ = ['bode_plot', 'nyquist_plot', 'gangof4_plot', 'bode', 'nyquist', 'gangof4'] # # Main plotting functions # # This section of the code contains the functions for generating # frequency domain plots # # Bode plot def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None, Plot=True, omega_limits=None, omega_num=None, *args, **kwargs): """Bode plot for a system Plots a Bode plot for the system over a (optional) frequency range. Parameters ---------- syslist : linsys List of linear input/output systems (single system is OK) omega : freq_range Range of frequencies in rad/sec dB : boolean If True, plot result in dB Hz : boolean If True, plot frequency in Hz (omega must be provided in rad/sec) deg : boolean If True, plot phase in degrees (else radians) Plot : boolean If True, plot magnitude and phase omega_limits: tuple, list, ... of two values Limits of the to generate frequency vector. If Hz=True the limits are in Hz otherwise in rad/s. omega_num: int number of samples *args, **kwargs: Additional options to matplotlib (color, linestyle, etc) Returns ------- mag : array (list if len(syslist) > 1) magnitude phase : array (list if len(syslist) > 1) phase in radians omega : array (list if len(syslist) > 1) frequency in rad/sec Notes ----- 1. Alternatively, you may use the lower-level method (mag, phase, freq) = sys.freqresp(freq) to generate the frequency response for a system, but it returns a MIMO response. 2. If a discrete time model is given, the frequency response is plotted along the upper branch of the unit circle, using the mapping z = exp(j \omega dt) where omega ranges from 0 to pi/dt and dt is the discrete time base. If not timebase is specified (dt = True), dt is set to 1. Examples -------- >>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.") >>> mag, phase, omega = bode(sys) """ # Set default values for options from . import config if (dB is None): dB = config.bode_dB if (deg is None): deg = config.bode_deg if (Hz is None): Hz = config.bode_Hz # If argument was a singleton, turn it into a list if (not getattr(syslist, '__iter__', False)): syslist = (syslist,) if omega is None: if omega_limits is None: # Select a default range if none is provided omega = default_frequency_range(syslist, Hz=Hz, number_of_samples=omega_num) else: omega_limits = np.array(omega_limits) if Hz: omega_limits *= 2.*np.pi if omega_num: omega = sp.logspace(np.log10(omega_limits[0]), np.log10(omega_limits[1]), num=omega_num, endpoint=True) else: omega = sp.logspace(np.log10(omega_limits[0]), np.log10(omega_limits[1]), endpoint=True) mags, phases, omegas, nyquistfrqs = [], [], [], [] for sys in syslist: if (sys.inputs > 1 or sys.outputs > 1): # TODO: Add MIMO bode plots. raise NotImplementedError("Bode is currently only implemented for SISO systems.") else: omega_sys = np.array(omega) if sys.isdtime(True): nyquistfrq = 2. * np.pi * 1. / sys.dt / 2. omega_sys = omega_sys[omega_sys < nyquistfrq] # TODO: What distance to the Nyquist frequency is appropriate? else: nyquistfrq = None # Get the magnitude and phase of the system mag_tmp, phase_tmp, omega_sys = sys.freqresp(omega_sys) mag = np.atleast_1d(np.squeeze(mag_tmp)) phase = np.atleast_1d(np.squeeze(phase_tmp)) phase = unwrap(phase) nyquistfrq_plot = None if Hz: omega_plot = omega_sys / (2. * np.pi) if nyquistfrq: nyquistfrq_plot = nyquistfrq / (2. * np.pi) else: omega_plot = omega_sys if nyquistfrq: nyquistfrq_plot = nyquistfrq mags.append(mag) phases.append(phase) omegas.append(omega_sys) nyquistfrqs.append(nyquistfrq) # Get the dimensions of the current axis, which we will divide up #! TODO: Not current implemented; just use subplot for now if (Plot): # Magnitude plot ax_mag = plt.subplot(211); if dB: pltline = ax_mag.semilogx(omega_plot, 20 * np.log10(mag), *args, **kwargs) else: pltline = ax_mag.loglog(omega_plot, mag, *args, **kwargs) if nyquistfrq_plot: ax_mag.axvline(nyquistfrq_plot, color=pltline[0].get_color()) # Add a grid to the plot + labeling ax_mag.grid(True, which='both') ax_mag.set_ylabel("Magnitude (dB)" if dB else "Magnitude") # Phase plot ax_phase = plt.subplot(212, sharex=ax_mag); if deg: phase_plot = phase * 180. / np.pi else: phase_plot = phase ax_phase.semilogx(omega_plot, phase_plot, *args, **kwargs) if nyquistfrq_plot: ax_phase.axvline(nyquistfrq_plot, color=pltline[0].get_color()) # Add a grid to the plot + labeling ax_phase.set_ylabel("Phase (deg)" if deg else "Phase (rad)") def genZeroCenteredSeries(val_min, val_max, period): v1 = np.ceil(val_min / period - 0.2) v2 = np.floor(val_max / period + 0.2) return np.arange(v1, v2 + 1) * period if deg: ylim = ax_phase.get_ylim() ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], 45.)) ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], 15.), minor=True) else: ylim = ax_phase.get_ylim() ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], np.pi / 4.)) ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], np.pi / 12.), minor=True) ax_phase.grid(True, which='both') # ax_mag.grid(which='minor', alpha=0.3) # ax_mag.grid(which='major', alpha=0.9) # ax_phase.grid(which='minor', alpha=0.3) # ax_phase.grid(which='major', alpha=0.9) # Label the frequency axis ax_phase.set_xlabel("Frequency (Hz)" if Hz else "Frequency (rad/sec)") if len(syslist) == 1: return mags[0], phases[0], omegas[0] else: return mags, phases, omegas # Nyquist plot def nyquist_plot(syslist, omega=None, Plot=True, color='b', labelFreq=0, *args, **kwargs): """Nyquist plot for a system Plots a Nyquist plot for the system over a (optional) frequency range. Parameters ---------- syslist : list of LTI List of linear input/output systems (single system is OK) omega : freq_range Range of frequencies (list or bounds) in rad/sec Plot : boolean If True, plot magnitude labelFreq : int Label every nth frequency on the plot *args, **kwargs: Additional options to matplotlib (color, linestyle, etc) Returns ------- real : array real part of the frequency response array imag : array imaginary part of the frequency response array freq : array frequencies Examples -------- >>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.") >>> real, imag, freq = nyquist_plot(sys) """ # If argument was a singleton, turn it into a list if (not getattr(syslist, '__iter__', False)): syslist = (syslist,) # Select a default range if none is provided if omega is None: omega = default_frequency_range(syslist) # Interpolate between wmin and wmax if a tuple or list are provided elif (isinstance(omega, list) | isinstance(omega, tuple)): # Only accept tuple or list of length 2 if (len(omega) != 2): raise ValueError("Supported frequency arguments are (wmin,wmax) tuple or list, or frequency vector. ") omega = np.logspace(np.log10(omega[0]), np.log10(omega[1]), num=50, endpoint=True, base=10.0) for sys in syslist: if (sys.inputs > 1 or sys.outputs > 1): # TODO: Add MIMO nyquist plots. raise NotImplementedError("Nyquist is currently only implemented for SISO systems.") else: # Get the magnitude and phase of the system mag_tmp, phase_tmp, omega = sys.freqresp(omega) mag = np.squeeze(mag_tmp) phase = np.squeeze(phase_tmp) # Compute the primary curve x = sp.multiply(mag, sp.cos(phase)); y = sp.multiply(mag, sp.sin(phase)); if (Plot): # Plot the primary curve and mirror image plt.plot(x, y, '-', color=color, *args, **kwargs); plt.plot(x, -y, '--', color=color, *args, **kwargs); # Mark the -1 point plt.plot([-1], [0], 'r+') # Label the frequencies of the points if (labelFreq): ind = slice(None, None, labelFreq) for xpt, ypt, omegapt in zip(x[ind], y[ind], omega[ind]): # Convert to Hz f = omegapt / (2 * sp.pi) # Factor out multiples of 1000 and limit the # result to the range [-8, 8]. pow1000 = max(min(get_pow1000(f), 8), -8) # Get the SI prefix. prefix = gen_prefix(pow1000) # Apply the text. (Use a space before the text to # prevent overlap with the data.) # # np.round() is used because 0.99... appears # instead of 1.0, and this would otherwise be # truncated to 0. plt.text(xpt, ypt, ' ' + str(int(np.round(f / 1000 ** pow1000, 0))) + ' ' + prefix + 'Hz') return x, y, omega # Gang of Four #! TODO: think about how (and whether) to handle lists of systems def gangof4_plot(P, C, omega=None): """Plot the "Gang of 4" transfer functions for a system Generates a 2x2 plot showing the "Gang of 4" sensitivity functions [T, PS; CS, S] Parameters ---------- P, C : LTI Linear input/output systems (process and control) omega : array Range of frequencies (list or bounds) in rad/sec Returns ------- None """ if (P.inputs > 1 or P.outputs > 1 or C.inputs > 1 or C.outputs > 1): # TODO: Add MIMO go4 plots. raise NotImplementedError("Gang of four is currently only implemented for SISO systems.") else: # Select a default range if none is provided #! TODO: This needs to be made more intelligent if omega is None: omega = default_frequency_range((P, C)) # Compute the senstivity functions L = P * C; S = feedback(1, L); T = L * S; # Plot the four sensitivity functions #! TODO: Need to add in the mag = 1 lines mag_tmp, phase_tmp, omega = T.freqresp(omega); mag = np.squeeze(mag_tmp) phase = np.squeeze(phase_tmp) plt.subplot(221); plt.loglog(omega, mag); mag_tmp, phase_tmp, omega = (P * S).freqresp(omega); mag = np.squeeze(mag_tmp) phase = np.squeeze(phase_tmp) plt.subplot(222); plt.loglog(omega, mag); mag_tmp, phase_tmp, omega = (C * S).freqresp(omega); mag = np.squeeze(mag_tmp) phase = np.squeeze(phase_tmp) plt.subplot(223); plt.loglog(omega, mag); mag_tmp, phase_tmp, omega = S.freqresp(omega); mag = np.squeeze(mag_tmp) phase = np.squeeze(phase_tmp) plt.subplot(224); plt.loglog(omega, mag); # # Utility functions # # This section of the code contains some utility functions for # generating frequency domain plots # # Compute reasonable defaults for axes def default_frequency_range(syslist, Hz=None, number_of_samples=None, feature_periphery_decade=None): """Compute a reasonable default frequency range for frequency domain plots. Finds a reasonable default frequency range by examining the features (poles and zeros) of the systems in syslist. Parameters ---------- syslist : list of LTI List of linear input/output systems (single system is OK) Hz: boolean If True, the limits (first and last value) of the frequencies are set to full decades in Hz so it fits plotting with logarithmic scale in Hz otherwise in rad/s. Omega is always returned in rad/sec. number_of_samples: int Number of samples to generate feature_periphery_decade: float Defines how many decades shall be included in the frequency range on both sides of features (poles, zeros). Example: If there is a feature, e.g. a pole, at 1Hz and feature_periphery_decade=1. then the range of frequencies shall span 0.1 .. 10 Hz. The default value is read from config.bode_feature_periphery_decade. Returns ------- omega : array Range of frequencies in rad/sec Examples -------- >>> from matlab import ss >>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.") >>> omega = default_frequency_range(sys) """ # This code looks at the poles and zeros of all of the systems that # we are plotting and sets the frequency range to be one decade above # and below the min and max feature frequencies, rounded to the nearest # integer. It excludes poles and zeros at the origin. If no features # are found, it turns logspace(-1, 1) # Set default values for options from . import config if (number_of_samples is None): number_of_samples = config.bode_number_of_samples if (feature_periphery_decade is None): feature_periphery_decade = config.bode_feature_periphery_decade # Find the list of all poles and zeros in the systems features = np.array(()) freq_interesting = [] # detect if single sys passed by checking if it is sequence-like if (not getattr(syslist, '__iter__', False)): syslist = (syslist,) for sys in syslist: try: # Add new features to the list if sys.isctime(): features_ = np.concatenate((np.abs(sys.pole()), np.abs(sys.zero()))) # Get rid of poles and zeros at the origin features_ = features_[features_ != 0.0]; features = np.concatenate((features, features_)) elif sys.isdtime(strict=True): fn = np.pi * 1. / sys.dt # TODO: What distance to the Nyquist frequency is appropriate? freq_interesting.append(fn * 0.9) features_ = np.concatenate((sys.pole(), sys.zero())) # Get rid of poles and zeros # * at the origin and real <= 0 & imag==0: log! # * at 1.: would result in omega=0. (logaritmic plot!) features_ = features_[(features_.imag != 0.0) | (features_.real > 0.)] features_ = features_[np.bitwise_not((features_.imag == 0.0) & (np.abs(features_.real - 1.0) < 1.e-10))] # TODO: improve features__ = np.abs(np.log(features_) / (1.j * sys.dt)) features = np.concatenate((features, features__)) else: # TODO raise NotImplementedError('type of system in not implemented now') except: pass # Make sure there is at least one point in the range if (features.shape[0] == 0): features = np.array([1.]); if Hz: features /= 2.*np.pi features = np.log10(features) lsp_min = np.floor(np.min(features) - feature_periphery_decade) lsp_max = np.ceil(np.max(features) + feature_periphery_decade) lsp_min += np.log10(2.*np.pi) lsp_max += np.log10(2.*np.pi) else: features = np.log10(features) lsp_min = np.floor(np.min(features) - feature_periphery_decade) lsp_max = np.ceil(np.max(features) + feature_periphery_decade) if freq_interesting: lsp_min = min(lsp_min, np.log10(min(freq_interesting))) lsp_max = max(lsp_max, np.log10(max(freq_interesting))) #! TODO: Add a check in discrete case to make sure we don't get aliasing (Attention: there is a list of system but only one omega vector) # Set the range to be an order of magnitude beyond any features if number_of_samples: omega = sp.logspace(lsp_min, lsp_max, num=number_of_samples, endpoint=True) else: omega = sp.logspace(lsp_min, lsp_max, endpoint=True) return omega # # KLD 5/23/11: Two functions to create nice looking labels # def get_pow1000(num): '''Determine the exponent for which the significand of a number is within the range [1, 1000). ''' # Based on algorithm from http://www.mail-archive.com/[email protected]/msg14433.html, accessed 2010/11/7 # by Jason Heeris 2009/11/18 from decimal import Decimal from math import floor dnum = Decimal(str(num)) if dnum == 0: return 0 elif dnum < 0: dnum = -dnum return int(floor(dnum.log10() / 3)) def gen_prefix(pow1000): '''Return the SI prefix for a power of 1000. ''' # Prefixes according to Table 5 of [BIPM 2006] (excluding hecto, # deca, deci, and centi). if pow1000 < -8 or pow1000 > 8: raise ValueError("Value is out of the range covered by the SI prefixes.") return ['Y', # yotta (10^24) 'Z', # zetta (10^21) 'E', # exa (10^18) 'P', # peta (10^15) 'T', # tera (10^12) 'G', # giga (10^9) 'M', # mega (10^6) 'k', # kilo (10^3) '', # (10^0) 'm', # milli (10^-3) r'$\mu$', # micro (10^-6) 'n', # nano (10^-9) 'p', # pico (10^-12) 'f', # femto (10^-15) 'a', # atto (10^-18) 'z', # zepto (10^-21) 'y'][8 - pow1000] # yocto (10^-24) # Function aliases bode = bode_plot nyquist = nyquist_plot gangof4 = gangof4_plot |
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