Controltools

This file contains some functions that are quite helpful when designing feedback laws. This collection is not complete and does not aim to be so. For a more sophisticated collection have a look at the symbtools (https://github.com/TUD-RST/symbtools) or control package which are not used in this package to keep a small footprint.

pymoskito.controltools.calc_prefilter(a_mat, b_mat, c_mat, k_mat=None)[source]

Calculate the prefilter matrix

$\boldsymbol{V} = - \left[\boldsymbol{C} \left(\boldsymbol{A} - \boldsymbol{B}\boldsymbol{K}\right)^{-1}\boldsymbol{B}\right]^{-1}$

Parameters:

a_mat (numpy.ndarray) – system matrix
b_mat (numpy.ndarray) – input matrix
c_mat (numpy.ndarray) – output matrix
k_mat (numpy.ndarray) – control matrix

Returns:

Prefilter matrix

Return type:

numpy.ndarray

pymoskito.controltools.char_coefficients(poles)[source]

Calculate the coefficients of a characteristic polynomial.

Parameters:: poles (list or numpy.ndarray) – pol configuration
Returns:: coefficients
Return type:: numpy.ndarray

pymoskito.controltools.controllability_matrix(a_mat, b_mat)[source]

Calculate controllability matrix and check controllability of the system.

$\boldsymbol{Q_{c}} = \begin{pmatrix} \boldsymbol{B} & \boldsymbol{A}\boldsymbol{B} & \boldsymbol{A}^{2} \boldsymbol{B} & \cdots & \boldsymbol{A}^{n-1}\boldsymbol{B}\\ \end{pmatrix}$

Parameters:

a_mat (numpy.ndarray) – system matrix
b_mat (numpy.ndarray) – manipulating matrix

Returns:

controllability matrix $\boldsymbol{Q_{c}}$

Return type:

numpy.ndarray

pymoskito.controltools.lie_derivatives(h, f, x, order=1)[source]

Calculates the Lie-Derivative from a scalar field $h(x)$ along a vector field $f(x)$ .

Parameters:

h (sympy.matrix) – scalar field
f (sympy.matrix) – vector field
x (sympy.matrix) – symbolic representation of the states
order (int) – order

Returns:

lie derivatives in ascending order

Return type:

list of sympy.matrix

pymoskito.controltools.observability_matrix(a_mat, c_mat)[source]

Calculate observability matrix and check observability of the system.

$\boldsymbol{Q_{o}} = \begin{pmatrix} \boldsymbol{C}\\ \boldsymbol{C}\boldsymbol{A}\\ \boldsymbol{C}\boldsymbol{A}^{2}\\ \vdots \\ \boldsymbol{C}\boldsymbol{A}^{n-1}\\ \end{pmatrix}$