Expand Up @@ -3,12 +3,12 @@ from control.exception import ControlMIMONotImplemented from .freqplot import bode_plot from .timeresp import step_response from .namedio importissiso, common_timebase, isctime, isdtime from .namedio import common_timebase, isctime, isdtime from .xferfcn import tf from .iosys import ss from .bdalg import append, connect from .iosys importtf2io, ss2io , summing_junction, interconnect from control.statesp import _convert_to_statespace, StateSpace from .iosys importss, tf2io , summing_junction, interconnect from control.statesp import _convert_to_statespace from . import config import numpy as np import matplotlib.pyplot as plt Expand All @@ -22,8 +22,8 @@ def sisotool(sys, initial_gain=None, xlim_rlocus=None, ylim_rlocus=None, plotstr_rlocus='C0', rlocus_grid=False, omega=None, dB=None, Hz=None, deg=None, omega_limits=None, omega_num=None, margins_bode=True, tvect=None, kvect=None): """ Sisotool style collection of plots inspired by MATLAB's sisotool. """Sisotool style collection of plots inspired by MATLAB's sisotool. The left two plots contain the bode magnitude and phase diagrams. The top right plot is a clickable root locus plot, clicking on the root locus will change the gain of the system. The bottom left plot Expand All @@ -32,52 +32,52 @@ def sisotool(sys, initial_gain=None, xlim_rlocus=None, ylim_rlocus=None, Parameters ---------- sys : LTI object Linear input/output systems. If sys is SISO, use the same system for the root locus and step response. If it is desired to see a different step response than feedback(K*sys,1), such as a disturbance response, sys can be provided as a two-input, two-output system (e.g. by using :func:`bdgalg.connect' or :func:`iosys.interconnect`). For two-input, two-output system, sisotool inserts the negative of the selected gain K between the first output and first input and uses the second input and output for computing the step response. To see the disturbance response, configure your plant to have as its second input the disturbance input. To view the step response with a feedforward controller, give your plant two identical inputs, and sum your feedback controller and your feedforward controller and multiply them into your plant's second input. It is also possible to accomodate a system with a gain in the feedback. Linear input/output systems. If sys is SISO, use the same system for the root locus and step response. If it is desired to see a different step response than feedback(K*sys,1), such as a disturbance response, sys can be provided as a two-input, two-output system (e.g. by using :func:`bdgalg.connect' or :func:`iosys.interconnect`). For two-input, two-output system, sisotool inserts the negative of the selected gain K between the first output and first input and uses the second input and output for computing the step response. To see the disturbance response, configure your plant to have as its second input the disturbance input. To view the step response with a feedforward controller, give your plant two identical inputs, and sum your feedback controller and your feedforward controller and multiply them into your plant's second input. It is also possible to accomodate a system with a gain in the feedback. initial_gain : float, optional Initial gain to use for plotting root locus. Defaults to 1 (config.defaults['sisotool.initial_gain']). xlim_rlocus : tuple or list, optional control of x-axis range, normally with tupleControl of x-axis range, normally with tuple (see :doc:`matplotlib:api/axes_api`). ylim_rlocus : tuple or list, optional control of y-axis range plotstr_rlocus : :func:`matplotlib.pyplot.plot` format string, optional plotting style for the root locus plot(color, linestyle, etc)Plotting style for the root locus plot(color, linestyle, etc). rlocus_grid : boolean (default = False) If True plot s- or z-plane grid. omega : array_like List of frequencies in rad/sec to be used for bode plot List of frequencies in rad/sec to be used for bode plot. dB : boolean If True, plot result in dB for the bode plot If True, plot result in dB for the bode plot. Hz : boolean If True, plot frequency in Hz for the bode plot (omega must be provided in rad/sec) If True, plot frequency in Hz for the bode plot (omega must be provided in rad/sec). deg : boolean If True, plot phase in degrees for the bode plot (else radians) If True, plot phase in degrees for the bode plot (else radians). omega_limits : array_like of two values Limits of the to generate frequency vector. If Hz=True the limits are in Hz otherwise in rad/s. Ignored if omegais provided, and auto-generated if omitted. Limits of the to generate frequency vector. If Hz=True the limits are in Hz otherwise in rad/s. Ignored if omega is provided, and auto-generated if omitted. omega_num : int Number of samples to plot. Defaults to config.defaults['freqplot.number_of_samples']. margins_bode : boolean If True, plot gain and phase margin in the bode plot If True, plot gain and phase margin in the bode plot. tvect : list or ndarray, optional List of timesteps to use for closed loop step response List of timesteps to use for closed loop step response. Examples -------- Expand Down Expand Up @@ -202,28 +202,47 @@ def _SisotoolUpdate(sys, fig, K, bode_plot_params, tvect=None): # contributed by Sawyer Fuller, minster@uw.edu 2021.11.02, based on # an implementation in Matlab by Martin Berg. def rootlocus_pid_designer(plant, gain='P', sign=+1, input_signal='r', Kp0=0, Ki0=0, Kd0=0, tau=0.01, Kp0=0, Ki0=0, Kd0=0,deltaK=0.001, tau=0.01, C_ff=0, derivative_in_feedback_path=False, plot=True): """Manual PID controller design based on root locus using Sisotool Uses `Sisotool ` to investigate the effect of adding or subtracting an Uses `sisotool ` to investigate the effect of adding or subtracting an amount `deltaK` to the proportional, integral, or derivative (PID) gains of a controller. One of the PID gains, `Kp`, `Ki`, or `Kd`, respectively, can be modified at a time. `Sisotool` plots the step response, frequency response, and root locus. When first run, `deltaK` is set to 0; click on a branch of the root locus plot to try a different value. Each click updates plots and prints the corresponding `deltaK`. To tune all three PID gains, repeatedly call `rootlocus_pid_designer`, and select a different `gain` each time (`'P'`, `'I'`, or `'D'`). Make sure to add the resulting `deltaK` to your chosen initial gain on the next iteration. response, and root locus of the closed-loop system controlling the dynamical system specified by `plant`. Can be used with either non- interactive plots (e.g. in a Jupyter Notebook), or interactive plots. To use non-interactively, choose starting-point PID gains `Kp0`, `Ki0`, and `Kd0` (you might want to start with all zeros to begin with), select which gain you would like to vary (e.g. gain=`'P'`, `'I'`, or `'D'`), and choose a value of `deltaK` (default 0.001) to specify by how much you would like to change that gain. Repeatedly run `rootlocus_pid_designer` with different values of `deltaK` until you are satisfied with the performance for that gain. Then, to tune a different gain, e.g. `'I'`, make sure to add your chosen `deltaK` to the previous gain you you were tuning. Example: to examine the effect of varying `Kp` starting from an intial value of 10, use the arguments `gain='P', Kp0=10`. Suppose a `deltaK` value of 5 gives satisfactory performance. Then on the next iteration, to tune the derivative gain, use the arguments `gain='D', Kp0=15`. value of 10, use the arguments `gain='P', Kp0=10` and try varying values of `deltaK`. Suppose a `deltaK` of 5 gives satisfactory performance. Then, to tune the derivative gain, add your selected `deltaK` to `Kp0` in the next call using the arguments `gain='D', Kp0=15`, to see how adding different values of `deltaK` to your derivative gain affects performance. To use with interactive plots, you will need to enable interactive mode if you are in a Jupyter Notebook, e.g. using `%matplotlib`. See `Interactive Plots <https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ion.html>`_ for more information. Click on a branch of the root locus plot to try different values of `deltaK`. Each click updates plots and prints the corresponding `deltaK`. It may be helpful to zoom in using the magnifying glass on the plot to get more locations to click. Just make sure to deactivate magnification mode when you are done by clicking the magnifying glass. Otherwise you will not be able to be able to choose a gain on the root locus plot. When you are done, `%matplotlib inline` returns to inline, non-interactive ploting. By default, all three PID terms are in the forward path C_f in the diagram shown below, that is, Expand Down Expand Up @@ -253,26 +272,23 @@ def rootlocus_pid_designer(plant, gain='P', sign=+1, input_signal='r', If `plant` is a 2-input system, the disturbance `d` is fed directly into its second input rather than being added to `u`. Remark: It may be helpful to zoom in using the magnifying glass on the plot. Just ake sure to deactivate magnification mode when you are done by clicking the magnifying glass. Otherwise you will not be able to be able to choose a gain on the root locus plot. Parameters ---------- plant : :class:`LTI` (:class:`TransferFunction` or :class:`StateSpace` system) The dynamical system to be controlled The dynamical system to be controlled. gain : string (optional) Which gain to vary by `deltaK`. Must be one of `'P'`, `'I'`, or `'D'` (proportional, integral, or derative) (proportional, integral, or derative). sign : int (optional) The sign of deltaK gain perturbation The sign of deltaK gain perturbation. input : string (optional) The input used for the step response; must be `'r'` (reference) or `'d'` (disturbance) (see figure above) `'d'` (disturbance) (see figure above). Kp0, Ki0, Kd0 : float (optional) Initial values for proportional, integral, and derivative gains, respectively respectively. deltaK : float (optional) Perturbation value for gain specified by the `gain` keywoard. tau : float (optional) The time constant associated with the pole in the continuous-time derivative term. This is required to make the derivative transfer Expand All @@ -291,16 +307,20 @@ def rootlocus_pid_designer(plant, gain='P', sign=+1, input_signal='r', closedloop : class:`StateSpace` system The closed-loop system using initial gains. Notes ----- When running using iPython or Jupyter, use `%matplotlib` to configure the session for interactive support. """ plant = _convert_to_statespace(plant) if plant.ninputs == 1: plant =ss2io (plant, inputs='u', outputs='y') plant =ss (plant, inputs='u', outputs='y') elif plant.ninputs == 2: plant =ss2io (plant, inputs=['u', 'd'], outputs='y') plant =ss (plant, inputs=['u', 'd'], outputs='y') else: raise ValueError("plant must have one or two inputs") C_ff =ss2io (_convert_to_statespace(C_ff), inputs='r', outputs='uff') C_ff =ss (_convert_to_statespace(C_ff), inputs='r', outputs='uff') dt = common_timebase(plant, C_ff) # create systems used for interconnections Expand Down Expand Up @@ -335,13 +355,13 @@ def rootlocus_pid_designer(plant, gain='P', sign=+1, input_signal='r', # for the gain that is varied, replace gain block with a special block # that has an 'input' and an 'output' that creates loop transfer function if gain in ('P', 'p'): Kpgain =ss2io( ss([],[],[],[[0, 1], [-sign, Kp0]]) , Kpgain = ss([],[],[],[[0, 1], [-sign, Kp0]], inputs=['input', 'prop_e'], outputs=['output', 'ufb']) elif gain in ('I', 'i'): Kigain =ss2io( ss([],[],[],[[0, 1], [-sign, Ki0]]) , Kigain = ss([],[],[],[[0, 1], [-sign, Ki0]], inputs=['input', 'int_e'], outputs=['output', 'ufb']) elif gain in ('D', 'd'): Kdgain =ss2io( ss([],[],[],[[0, 1], [-sign, Kd0]]) , Kdgain = ss([],[],[],[[0, 1], [-sign, Kd0]], inputs=['input', 'deriv'], outputs=['output', 'ufb']) else: raise ValueError(gain + ' gain not recognized.') Expand All @@ -352,6 +372,6 @@ def rootlocus_pid_designer(plant, gain='P', sign=+1, input_signal='r', inplist=['input', input_signal], outlist=['output', 'y'], check_unused=False) if plot: sisotool(loop,kvect=(0.,) ) sisotool(loop,initial_gain=deltaK ) cl = loop[1, 1] # closed loop transfer function with initial gains returnStateSpace (cl.A, cl.B, cl.C, cl.D, cl.dt) returnss (cl.A, cl.B, cl.C, cl.D, cl.dt)