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Discrete omega-damping plot and tweaks#193
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dc8410c Added discrete grid to pzmap function.
4117489 Revert "Added discrete grid to pzmap function."
f8c497e Added discrete grid to pzmap function.
3d0bf03 Tweaked axis lines and zero/pole markers.
89dc937 Refactored sgrid based on matplotlib projections and moved sgrid and …
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182 changes: 182 additions & 0 deletionscontrol/grid.py
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -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 | ||
32 changes: 20 additions & 12 deletionscontrol/pzmap.py
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107 changes: 14 additions & 93 deletionscontrol/rlocus.py
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