diff --git a/control/grid.py b/control/grid.py new file mode 100644 index 000000000..33fc9e975 --- /dev/null +++ b/control/grid.py @@ -0,0 +1,182 @@ +import numpy as np +from numpy import cos, sin, sqrt, linspace, pi, exp +import matplotlib.pyplot as plt +from mpl_toolkits.axisartist import SubplotHost +from mpl_toolkits.axisartist.grid_helper_curvelinear import GridHelperCurveLinear +import mpl_toolkits.axisartist.angle_helper as angle_helper +from matplotlib.projections import PolarAxes +from matplotlib.transforms import Affine2D + +class FormatterDMS(object): + '''Transforms angle ticks to damping ratios''' + def __call__(self,direction,factor,values): + angles_deg = values/factor + damping_ratios = np.cos((180-angles_deg)*np.pi/180) + ret = ["%.2f"%val for val in damping_ratios] + return ret + +class ModifiedExtremeFinderCycle(angle_helper.ExtremeFinderCycle): + '''Changed to allow only left hand-side polar grid''' + def __call__(self, transform_xy, x1, y1, x2, y2): + x_, y_ = np.linspace(x1, x2, self.nx), np.linspace(y1, y2, self.ny) + x, y = np.meshgrid(x_, y_) + lon, lat = transform_xy(np.ravel(x), np.ravel(y)) + + with np.errstate(invalid='ignore'): + if self.lon_cycle is not None: + lon0 = np.nanmin(lon) + lon -= 360. * ((lon - lon0) > 360.) # Changed from 180 to 360 to be able to span only 90-270 (left hand side) + if self.lat_cycle is not None: + lat0 = np.nanmin(lat) + lat -= 360. * ((lat - lat0) > 360.) # Changed from 180 to 360 to be able to span only 90-270 (left hand side) + + lon_min, lon_max = np.nanmin(lon), np.nanmax(lon) + lat_min, lat_max = np.nanmin(lat), np.nanmax(lat) + + lon_min, lon_max, lat_min, lat_max = \ + self._adjust_extremes(lon_min, lon_max, lat_min, lat_max) + + return lon_min, lon_max, lat_min, lat_max + +def sgrid(): + # From matplotlib demos: + # https://matplotlib.org/gallery/axisartist/demo_curvelinear_grid.html + # https://matplotlib.org/gallery/axisartist/demo_floating_axis.html + + # PolarAxes.PolarTransform takes radian. However, we want our coordinate + # system in degree + tr = Affine2D().scale(np.pi/180., 1.) + PolarAxes.PolarTransform() + # polar projection, which involves cycle, and also has limits in + # its coordinates, needs a special method to find the extremes + # (min, max of the coordinate within the view). + + # 20, 20 : number of sampling points along x, y direction + sampling_points = 20 + extreme_finder = ModifiedExtremeFinderCycle(sampling_points, sampling_points, + lon_cycle=360, + lat_cycle=None, + lon_minmax=(90,270), + lat_minmax=(0, np.inf),) + + grid_locator1 = angle_helper.LocatorDMS(15) + tick_formatter1 = FormatterDMS() + grid_helper = GridHelperCurveLinear(tr, + extreme_finder=extreme_finder, + grid_locator1=grid_locator1, + tick_formatter1=tick_formatter1 + ) + + fig = plt.figure() + ax = SubplotHost(fig, 1, 1, 1, grid_helper=grid_helper) + + # make ticklabels of right invisible, and top axis visible. + visible = True + ax.axis[:].major_ticklabels.set_visible(visible) + ax.axis[:].major_ticks.set_visible(False) + ax.axis[:].invert_ticklabel_direction() + + ax.axis["wnxneg"] = axis = ax.new_floating_axis(0, 180) + axis.set_ticklabel_direction("-") + axis.label.set_visible(False) + ax.axis["wnxpos"] = axis = ax.new_floating_axis(0, 0) + axis.label.set_visible(False) + ax.axis["wnypos"] = axis = ax.new_floating_axis(0, 90) + axis.label.set_visible(False) + axis.set_axis_direction("left") + ax.axis["wnyneg"] = axis = ax.new_floating_axis(0, 270) + axis.label.set_visible(False) + axis.set_axis_direction("left") + axis.invert_ticklabel_direction() + axis.set_ticklabel_direction("-") + + # let left axis shows ticklabels for 1st coordinate (angle) + ax.axis["left"].get_helper().nth_coord_ticks = 0 + ax.axis["right"].get_helper().nth_coord_ticks = 0 + ax.axis["left"].get_helper().nth_coord_ticks = 0 + ax.axis["bottom"].get_helper().nth_coord_ticks = 0 + + fig.add_subplot(ax) + + ### RECTANGULAR X Y AXES WITH SCALE + #par2 = ax.twiny() + #par2.axis["top"].toggle(all=False) + #par2.axis["right"].toggle(all=False) + #new_fixed_axis = par2.get_grid_helper().new_fixed_axis + #par2.axis["left"] = new_fixed_axis(loc="left", + # axes=par2, + # offset=(0, 0)) + #par2.axis["bottom"] = new_fixed_axis(loc="bottom", + # axes=par2, + # offset=(0, 0)) + ### FINISH RECTANGULAR + + ax.grid(True, zorder=0,linestyle='dotted') + + _final_setup(ax) + return ax, fig + +def _final_setup(ax): + ax.set_xlabel('Real') + ax.set_ylabel('Imaginary') + ax.axhline(y=0, color='black', lw=1) + ax.axvline(x=0, color='black', lw=1) + plt.axis('equal') + +def nogrid(): + f = plt.figure() + ax = plt.axes() + + _final_setup(ax) + return ax, f + +def zgrid(zetas=None, wns=None): + '''Draws discrete damping and frequency grid''' + + fig = plt.figure() + ax = fig.gca() + + # Constant damping lines + if zetas is None: + zetas = linspace(0, 0.9, 10) + for zeta in zetas: + # Calculate in polar coordinates + factor = zeta/sqrt(1-zeta**2) + x = linspace(0, sqrt(1-zeta**2),200) + ang = pi*x + mag = exp(-pi*factor*x) + # Draw upper part in retangular coordinates + xret = mag*cos(ang) + yret = mag*sin(ang) + ax.plot(xret,yret, 'k:', lw=1) + # Draw lower part in retangular coordinates + xret = mag*cos(-ang) + yret = mag*sin(-ang) + ax.plot(xret,yret,'k:', lw=1) + # Annotation + an_i = int(len(xret)/2.5) + an_x = xret[an_i] + an_y = yret[an_i] + ax.annotate(str(round(zeta,2)), xy=(an_x, an_y), xytext=(an_x, an_y), size=7) + + # Constant natural frequency lines + if wns is None: + wns = linspace(0, 1, 10) + for a in wns: + # Calculate in polar coordinates + x = linspace(-pi/2,pi/2,200) + ang = pi*a*sin(x) + mag = exp(-pi*a*cos(x)) + # Draw in retangular coordinates + xret = mag*cos(ang) + yret = mag*sin(ang) + ax.plot(xret,yret,'k:', lw=1) + # Annotation + an_i = -1 + an_x = xret[an_i] + an_y = yret[an_i] + num = '{:1.1f}'.format(a) + ax.annotate("$\\frac{"+num+"\pi}{T}$", xy=(an_x, an_y), xytext=(an_x, an_y), size=9) + + _final_setup(ax) + return ax, fig + diff --git a/control/pzmap.py b/control/pzmap.py index ee91ec9b9..252d10011 100644 --- a/control/pzmap.py +++ b/control/pzmap.py @@ -40,15 +40,17 @@ # # $Id:pzmap.py 819 2009-05-29 21:28:07Z murray $ -from numpy import real, imag -from .lti import LTI +from numpy import real, imag, linspace, exp, cos, sin, sqrt +from math import pi +from .lti import LTI, isdtime, isctime +from .grid import sgrid, zgrid, nogrid __all__ = ['pzmap'] # TODO: Implement more elegant cross-style axes. See: # http://matplotlib.sourceforge.net/examples/axes_grid/demo_axisline_style.html # http://matplotlib.sourceforge.net/examples/axes_grid/demo_curvelinear_grid.html -def pzmap(sys, Plot=True, title='Pole Zero Map'): +def pzmap(sys, Plot=True, grid=False, title='Pole Zero Map'): """ Plot a pole/zero map for a linear system. @@ -59,6 +61,8 @@ def pzmap(sys, Plot=True, title='Pole Zero Map'): Plot: bool If ``True`` a graph is generated with Matplotlib, otherwise the poles and zeros are only computed and returned. + grid: boolean (default = False) + If True plot omega-damping grid. Returns ------- @@ -75,18 +79,22 @@ def pzmap(sys, Plot=True, title='Pole Zero Map'): if (Plot): import matplotlib.pyplot as plt + + if grid: + if isdtime(sys, strict=True): + ax, fig = zgrid() + else: + ax, fig = sgrid() + else: + ax, fig = nogrid() + # Plot the locations of the poles and zeros if len(poles) > 0: - plt.scatter(real(poles), imag(poles), s=50, marker='x') + ax.scatter(real(poles), imag(poles), s=50, marker='x', facecolors='k') if len(zeros) > 0: - plt.scatter(real(zeros), imag(zeros), s=50, marker='o', - facecolors='none') - # Add axes - #Somewhat silly workaround - plt.axhline(y=0, color='black') - plt.axvline(x=0, color='black') - plt.xlabel('Re') - plt.ylabel('Im') + ax.scatter(real(zeros), imag(zeros), s=50, marker='o', + facecolors='none', edgecolors='k') + plt.title(title) diff --git a/control/rlocus.py b/control/rlocus.py index e22a31c25..487ca3863 100644 --- a/control/rlocus.py +++ b/control/rlocus.py @@ -47,12 +47,15 @@ # Packages used by this module import numpy as np -from scipy import array, poly1d, row_stack, zeros_like, real, imag +from scipy import array, poly1d, row_stack, zeros_like, real, imag, exp, sin, cos, linspace, sqrt +from math import pi import scipy.signal # signal processing toolbox import pylab # plotting routines from .xferfcn import _convertToTransferFunction from .exception import ControlMIMONotImplemented from functools import partial +from .lti import isdtime +from .grid import sgrid, zgrid, nogrid __all__ = ['root_locus', 'rlocus'] @@ -82,7 +85,7 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None, plotstr='-', Plot=True, If True, report mouse clicks when close to the root-locus branches, calculate gain, damping and print grid: boolean (default = False) - If True plot s-plane grid. + If True plot omega-damping grid. Returns ------- @@ -110,12 +113,18 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None, plotstr='-', Plot=True, while new_figure_name in figure_title: new_figure_name = "Root Locus " + str(rloc_num) rloc_num += 1 - f = pylab.figure(new_figure_name) + if grid: + if isdtime(sys, strict=True): + ax, f = zgrid() + else: + ax, f = sgrid() + else: + ax, f = nogrid() + pylab.title(new_figure_name) if PrintGain: f.canvas.mpl_connect( 'button_release_event', partial(_RLFeedbackClicks, sys=sys)) - ax = pylab.axes() # plot open loop poles poles = array(denp.r) @@ -128,17 +137,13 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None, plotstr='-', Plot=True, # Now plot the loci for col in mymat.T: - ax.plot(real(col), imag(col), plotstr) + ax.plot(real(col), imag(col), plotstr, lw=3) # Set up plot axes and labels if xlim: ax.set_xlim(xlim) if ylim: ax.set_ylim(ylim) - ax.set_xlabel('Real') - ax.set_ylabel('Imaginary') - if grid: - _sgrid_func() return mymat, kvect @@ -350,88 +355,4 @@ def _RLFeedbackClicks(event, sys): print("Clicked at %10.4g%+10.4gj gain %10.4g damp %10.4g" % (s.real, s.imag, K.real, -1 * s.real / abs(s))) - -def _sgrid_func(fig=None, zeta=None, wn=None): - if fig is None: - fig = pylab.gcf() - ax = fig.gca() - xlocator = ax.get_xaxis().get_major_locator() - - ylim = ax.get_ylim() - ytext_pos_lim = ylim[1] - (ylim[1] - ylim[0]) * 0.03 - xlim = ax.get_xlim() - xtext_pos_lim = xlim[0] + (xlim[1] - xlim[0]) * 0.0 - - if zeta is None: - zeta = _default_zetas(xlim, ylim) - - angules = [] - for z in zeta: - if (z >= 1e-4) and (z <= 1): - angules.append(np.pi/2 + np.arcsin(z)) - else: - zeta.remove(z) - y_over_x = np.tan(angules) - - # zeta-constant lines - - index = 0 - - for yp in y_over_x: - ax.plot([0, xlocator()[0]], [0, yp*xlocator()[0]], color='gray', - linestyle='dashed', linewidth=0.5) - ax.plot([0, xlocator()[0]], [0, -yp * xlocator()[0]], color='gray', - linestyle='dashed', linewidth=0.5) - an = "%.2f" % zeta[index] - if yp < 0: - xtext_pos = 1/yp * ylim[1] - ytext_pos = yp * xtext_pos_lim - if np.abs(xtext_pos) > np.abs(xtext_pos_lim): - xtext_pos = xtext_pos_lim - else: - ytext_pos = ytext_pos_lim - ax.annotate(an, textcoords='data', xy=[xtext_pos, ytext_pos], fontsize=8) - index += 1 - ax.plot([0, 0], [ylim[0], ylim[1]], color='gray', linestyle='dashed', linewidth=0.5) - - angules = np.linspace(-90, 90, 20)*np.pi/180 - if wn is None: - wn = _default_wn(xlocator(), ylim) - - for om in wn: - if om < 0: - yp = np.sin(angules)*np.abs(om) - xp = -np.cos(angules)*np.abs(om) - ax.plot(xp, yp, color='gray', - linestyle='dashed', linewidth=0.5) - an = "%.2f" % -om - ax.annotate(an, textcoords='data', xy=[om, 0], fontsize=8) - - -def _default_zetas(xlim, ylim): - """Return default list of dumps coefficients""" - sep1 = -xlim[0]/4 - ang1 = [np.arctan((sep1*i)/ylim[1]) for i in np.arange(1, 4, 1)] - sep2 = ylim[1] / 3 - ang2 = [np.arctan(-xlim[0]/(ylim[1]-sep2*i)) for i in np.arange(1, 3, 1)] - - angules = np.concatenate((ang1, ang2)) - angules = np.insert(angules, len(angules), np.pi/2) - zeta = np.sin(angules) - return zeta.tolist() - - -def _default_wn(xloc, ylim): - """Return default wn for root locus plot""" - - wn = xloc - sep = xloc[1]-xloc[0] - while np.abs(wn[0]) < ylim[1]: - wn = np.insert(wn, 0, wn[0]-sep) - - while len(wn) > 7: - wn = wn[0:-1:2] - - return wn - rlocus = root_locus pFad - Phonifier reborn

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