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add reference gain design pattern to create_statefbk_iosystem #1071

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murrayrm merged 5 commits into python-control:main from murrayrm:create_statefbk-29Nov2024

Dec 7, 2024

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add reference gain design pattern to create_statefbk_iosystem #1071

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8780bdc

add feedfwd keyword arguments (no functionality yet)

murrayrm Nov 29, 2024

391d29c

update StateSpace size checks/error messages to be more informative

murrayrm Nov 29, 2024

9ed4817

initial implementation, docstrings for refgain pattern

murrayrm Nov 30, 2024

96b7b73

documentation updates

murrayrm Dec 2, 2024

bb52b70

addressed @slivingston review comments

murrayrm Dec 7, 2024

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169 changes: 122 additions & 47 deletions 169 control/statefbk.py

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Original file line number	Diff line number	Diff line change
Expand Up		@@ -39,24 +39,25 @@
		#
		# $Id$

		# External packages and modules
		import warnings

		import numpy as np
		import scipy as sp
		import warnings

		from . import statesp
		from .mateqn import care, dare, _check_shape
		from .statesp import StateSpace, _ssmatrix, _convert_to_statespace, ss
		from .config import _process_legacy_keyword
		from .exception import ControlArgument, ControlDimension, \
		ControlNotImplemented, ControlSlycot
		from .iosys import _process_indices, _process_labels, isctime, isdtime
		from .lti import LTI
		from .iosys import isdtime, isctime, _process_indices, _process_labels
		from .mateqn import _check_shape, care, dare
		from .nlsys import NonlinearIOSystem, interconnect
		from .exception import ControlSlycot, ControlArgument, ControlDimension, \
		ControlNotImplemented
		from .config import _process_legacy_keyword
		from .statesp import StateSpace, _convert_to_statespace, _ssmatrix, ss

		# Make sure we have access to the right slycot routines
		try:
		from slycot import sb03md57

		# wrap without the deprecation warning
		def sb03md(n, C, A, U, dico, job='X',fact='N',trana='N',ldwork=None):
		ret = sb03md57(A, U, C, dico, job, fact, trana, ldwork)
Expand Down Expand Up		@@ -581,8 +582,9 @@ def dlqr(args, *kwargs):

		# Function to create an I/O sytems representing a state feedback controller
		def create_statefbk_iosystem(
		sys, gain, integral_action=None, estimator=None, controller_type=None,
		xd_labels=None, ud_labels=None, gainsched_indices=None,
		sys, gain, feedfwd_gain=None, integral_action=None, estimator=None,
		controller_type=None, xd_labels=None, ud_labels=None, ref_labels=None,
		feedfwd_pattern='trajgen', gainsched_indices=None,
		gainsched_method='linear', control_indices=None, state_indices=None,
		name=None, inputs=None, outputs=None, states=None, **kwargs):
		r"""Create an I/O system using a (full) state feedback controller.
Expand All		@@ -592,7 +594,7 @@ def create_statefbk_iosystem(

		.. math:: u = u_d - K_p (x - x_d) - K_i \int(C x - C x_d)

		It can be called in the form::
		by calling

		ctrl, clsys = ct.create_statefbk_iosystem(sys, K)

Expand All		@@ -608,6 +610,18 @@ def create_statefbk_iosystem(

		where :math:`\mu` represents the scheduling variable.

		Alternatively, a controller of the form

		.. math:: u = k_f r - K_p x - K_i \int(C x - r)

		can be created by calling

		ctrl, clsys = ct.create_statefbk_iosystem(
		sys, K, kf, feedfwd_pattern='refgain')

		In either form, an estimator can also be used to compute the estimated
		state from the input and output measurements.

		Parameters
		----------
		sys : NonlinearIOSystem
Expand All		@@ -631,14 +645,15 @@ def create_statefbk_iosystem(
		If an I/O system is given, the error e = x - xd is passed to the
		system and the output is used as the feedback compensation term.

		xd_labels, ud_labels : str or list of str, optional
		Set the name of the signals to use for the desired state and
		inputs. If a single string is specified, it should be a format
		string using the variable `i` as an index. Otherwise, a list of
		strings matching the size of `x_d` and `u_d`, respectively, should
		be used. Default is "xd[{i}]" for xd_labels and "ud[{i}]" for
		ud_labels. These settings can also be overridden using the
		`inputs` keyword.
		feedfwd_gain : array_like, optional
		Specify the feedforward gain, `k_f`. Used only for the reference
		gain design pattern. If not given and if `sys` is a `StateSpace`
		(linear) system, will be computed as -1/(C (A-BK)^{-1}) B.

		feedfwd_pattern : str, optional
		If set to 'refgain', the reference gain design pattern is used to
		create the controller instead of the trajectory generation
		('trajgen') pattern.

		integral_action : ndarray, optional
		If this keyword is specified, the controller can include integral
Expand Down Expand Up		@@ -680,17 +695,19 @@ def create_statefbk_iosystem(
		Returns
		-------
		ctrl : NonlinearIOSystem
		Input/output system representing the controller. This system
		takes as inputs the desired state `x_d`, the desired input
		`u_d`, and either the system state `x` or the estimated state
		`xhat`. It outputs the controller action `u` according to the
		formula `u = u_d - K(x - x_d)`. If the keyword
		`integral_action` is specified, then an additional set of
		integrators is included in the control system (with the gain
		matrix `K` having the integral gains appended after the state
		gains). If a gain scheduled controller is specified, the gain
		(proportional and integral) are evaluated using the scheduling
		variables specified by `gainsched_indices`.
		Input/output system representing the controller. For the 'trajgen'
		design pattern (default), this system takes as inputs the desired
		state `x_d`, the desired input `u_d`, and either the system state
		`x` or the estimated state `xhat`. It outputs the controller
		action `u` according to the formula `u = u_d - K(x - x_d)`. For
		the 'refgain' design pattern, the system takes as inputs the
		reference input `r` and the system or estimated state. If the
		keyword `integral_action` is specified, then an additional set of
		integrators is included in the control system (with the gain matrix
		`K` having the integral gains appended after the state gains). If
		a gain scheduled controller is specified, the gain (proportional
		and integral) are evaluated using the scheduling variables
		specified by `gainsched_indices`.

		clsys : NonlinearIOSystem
		Input/output system representing the closed loop system. This
Expand All		@@ -716,6 +733,15 @@ def create_statefbk_iosystem(
		specified as either integer offsets or as estimator/system output
		signal names. If not specified, defaults to the system states.

		xd_labels, ud_labels, ref_labels : str or list of str, optional
		Set the name of the signals to use for the desired state and inputs
		or the reference inputs (for the 'refgain' design pattern). If a
		single string is specified, it should be a format string using the
		variable `i` as an index. Otherwise, a list of strings matching
		the size of `x_d` and `u_d`, respectively, should be used. Default
		is "xd[{i}]" for xd_labels and "ud[{i}]" for ud_labels. These
		settings can also be overridden using the `inputs` keyword.

		inputs, outputs, states : str, or list of str, optional
		List of strings that name the individual signals of the transformed
		system. If not given, the inputs, outputs, and states are the same
Expand Down Expand Up		@@ -753,6 +779,11 @@ def create_statefbk_iosystem(
		if kwargs:
		raise TypeError("unrecognized keywords: ", str(kwargs))

		# Check for consistency of positional parameters
		if feedfwd_gain is not None and feedfwd_pattern != 'refgain':
		raise ControlArgument(
		"feedfwd_gain specified but feedfwd_pattern != 'refgain'")

		# Figure out what inputs to the system to use
		control_indices = _process_indices(
		control_indices, 'control', sys.input_labels, sys.ninputs)
Expand Down Expand Up		@@ -812,14 +843,18 @@ def create_statefbk_iosystem(
		# Check for gain scheduled controller
		if len(gain) != 2:
		raise ControlArgument("gain must be a 2-tuple for gain scheduling")
		elif feedfwd_pattern != 'trajgen':
		raise NotImplementedError(
		"Gain scheduling is not implemented for pattern "
		f"'{feedfwd_pattern}'")
		gains, points = gain[0:2]

		# Stack gains and points if past as a list
		gains = np.stack(gains)
		points = np.stack(points)
		gainsched = True

		elif isinstance(gain, NonlinearIOSystem):
		elif isinstance(gain, NonlinearIOSystem) and feedfwd_pattern != 'refgain':
		if controller_type not in ['iosystem', None]:
		raise ControlArgument(
		f"incompatible controller type '{controller_type}'")
Expand All		@@ -841,20 +876,29 @@ def create_statefbk_iosystem(
		raise ControlArgument(f"unknown controller_type '{controller_type}'")

		# Figure out the labels to use
		xd_labels = _process_labels(
		xd_labels, 'xd', ['xd[{i}]'.format(i=i) for i in range(sys_nstates)])
		ud_labels = _process_labels(
		ud_labels, 'ud', ['ud[{i}]'.format(i=i) for i in range(sys_ninputs)])

		# Create the signal and system names
		if inputs is None:
		inputs = xd_labels + ud_labels + estimator.output_labels
		if feedfwd_pattern == 'trajgen':
		xd_labels = _process_labels(xd_labels, 'xd', [
		'xd[{i}]'.format(i=i) for i in range(sys_nstates)])
		ud_labels = _process_labels(ud_labels, 'ud', [
		'ud[{i}]'.format(i=i) for i in range(sys_ninputs)])

		# Create the signal and system names
		if inputs is None:
		inputs = xd_labels + ud_labels + estimator.output_labels
		elif feedfwd_pattern == 'refgain':
		ref_labels = _process_labels(ref_labels, 'r', [
		f'r[{i}]' for i in range(sys_ninputs)])
		if inputs is None:
		inputs = ref_labels + estimator.output_labels
		else:
		raise NotImplementedError(f"unknown pattern '{feedfwd_pattern}'")

		if outputs is None:
		outputs = [sys.input_labels[i] for i in control_indices]
		if states is None:
		states = nintegrators

		# Process gainscheduling variables, if present
		# Process gain scheduling variables, if present
		if gainsched:
		# Create a copy of the scheduling variable indices (default = xd)
		gainsched_indices = _process_indices(
Expand Down Expand Up		@@ -897,7 +941,7 @@ def _compute_gain(mu):
		return K

		# Define the controller system
		if controller_type == 'nonlinear':
		if controller_type == 'nonlinear' and feedfwd_pattern == 'trajgen':
		# Create an I/O system for the state feedback gains
		def _control_update(t, states, inputs, params):
		# Split input into desired state, nominal input, and current state
Expand Down Expand Up		@@ -931,7 +975,7 @@ def _control_output(t, states, inputs, params):
		_control_update, _control_output, name=name, inputs=inputs,
		outputs=outputs, states=states, params=params)

		elif controller_type == 'iosystem':
		elif controller_type == 'iosystem' and feedfwd_pattern == 'trajgen':
		# Use the passed system to compute feedback compensation
		def _control_update(t, states, inputs, params):
		# Split input into desired state, nominal input, and current state
Expand All		@@ -955,7 +999,7 @@ def _control_output(t, states, inputs, params):
		_control_update, _control_output, name=name, inputs=inputs,
		outputs=outputs, states=fbkctrl.state_labels, dt=fbkctrl.dt)

		elif controller_type == 'linear' or controller_type is None:
		elif controller_type in 'linear' and feedfwd_pattern == 'trajgen':
		# Create the matrices implementing the controller
		if isctime(sys):
		# Continuous time: integrator
Expand All		@@ -973,6 +1017,37 @@ def _control_output(t, states, inputs, params):
		A_lqr, B_lqr, C_lqr, D_lqr, dt=sys.dt, name=name,
		inputs=inputs, outputs=outputs, states=states)

		elif feedfwd_pattern == 'refgain':
		if controller_type not in ['linear', 'iosystem']:
		raise ControlArgument(
		"refgain design pattern only supports linear controllers")

		if feedfwd_gain is None:
		raise ControlArgument(
		"'feedfwd_gain' required for reference gain pattern")

		# Check to make sure the reference gain is valid
		Kf = np.atleast_2d(feedfwd_gain)
		if Kf.ndim != 2 or Kf.shape[0] != sys.ninputs or \
		Kf.shape[1] != sys.ninputs:
		raise ControlArgument("feedfwd_gain is not the right shape")

		# Create the matrices implementing the controller
		# [r, x]->[u]: u = k_f r - K_p x - K_i \int(C x - r)
		if isctime(sys):
		# Continuous time: integrator
		A_lqr = np.zeros((C.shape[0], C.shape[0]))
		else:
		# Discrete time: summer
		A_lqr = np.eye(C.shape[0])
		B_lqr = np.hstack([-np.eye(C.shape[0], sys_ninputs), C])
		C_lqr = -K[:, sys_nstates:] # integral gain (opt)
		D_lqr = np.hstack([Kf, -K])

		ctrl = ss(
		A_lqr, B_lqr, C_lqr, D_lqr, dt=sys.dt, name=name,
		inputs=inputs, outputs=outputs, states=states)

		else:
		raise ControlArgument(f"unknown controller_type '{controller_type}'")

Expand Down Expand Up		@@ -1020,7 +1095,7 @@ def ctrb(A, B, t=None):
		bmat = _ssmatrix(B)
		n = np.shape(amat)[0]
		m = np.shape(bmat)[1]


		if t is None or t > n:
		t = n

Expand All		@@ -1042,7 +1117,7 @@ def obsv(A, C, t=None):
		Dynamics and output matrix of the system
		t : None or integer
		maximum time horizon of the controllability matrix, max = A.shape[0]


		Returns
		-------
		O : 2D array (or matrix)
Expand All		@@ -1062,14 +1137,14 @@ def obsv(A, C, t=None):
		cmat = _ssmatrix(C)
		n = np.shape(amat)[0]
		p = np.shape(cmat)[0]


		if t is None or t > n:
		t = n

		# Construct the observability matrix
		obsv = np.zeros((t * p, n))
		obsv[:p, :] = cmat


		for k in range(1, t):
		obsv[k * p:(k + 1) * p, :] = np.dot(obsv[(k - 1) * p:k * p, :], amat)

Expand Down

27 changes: 16 additions & 11 deletions 27 control/statesp.py

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Original file line number	Diff line number	Diff line change
Expand Up		@@ -252,6 +252,12 @@ def __init__(self, args, *kwargs):
		D = np.zeros((C.shape[0], B.shape[1]))
		D = _ssmatrix(D)

		# If only direct term is present, adjust sizes of C and D if needed
		if D.size > 0 and B.size == 0:
		B = np.zeros((0, D.shape[1]))
		if D.size > 0 and C.size == 0:
		C = np.zeros((D.shape[0], 0))

		# Matrices defining the linear system
		self.A = A
		self.B = B
Expand All		@@ -268,7 +274,7 @@ def __init__(self, args, *kwargs):

		# Process iosys keywords
		defaults = args[0] if len(args) == 1 else \
		{'inputs': D.shape[1], 'outputs': D.shape[0],
		{'inputs': B.shape[1], 'outputs': C.shape[0],
		'states': A.shape[0]}
		name, inputs, outputs, states, dt = _process_iosys_keywords(
		kwargs, defaults, static=(A.size == 0))
Expand All		@@ -295,16 +301,15 @@ def __init__(self, args, *kwargs):
		# Check to make sure everything is consistent
		#
		# Check that the matrix sizes are consistent
		if A.shape[0] != A.shape[1] or self.nstates != A.shape[0]:
		raise ValueError("A must be square.")
		if self.nstates != B.shape[0]:
		raise ValueError("A and B must have the same number of rows.")
		if self.nstates != C.shape[1]:
		raise ValueError("A and C must have the same number of columns.")
		if self.ninputs != B.shape[1] or self.ninputs != D.shape[1]:
		raise ValueError("B and D must have the same number of columns.")
		if self.noutputs != C.shape[0] or self.noutputs != D.shape[0]:
		raise ValueError("C and D must have the same number of rows.")
		def _check_shape(matrix, expected, name):
		if matrix.shape != expected:
		raise ValueError(
		f"{name} is the wrong shape; "
		f"expected {expected} instead of {matrix.shape}")
		_check_shape(A, (self.nstates, self.nstates), "A")
		_check_shape(B, (self.nstates, self.ninputs), "B")
		_check_shape(C, (self.noutputs, self.nstates), "C")
		_check_shape(D, (self.noutputs, self.ninputs), "D")

		#
		# Final processing
Expand Down

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