StateSpace

class sharpy.linear.src.libss.StateSpace(A, B, C, D, dt=None)

Wrap state-space models allocation into a single class and support both full and sparse matrices. The class emulates

scipy.signal.ltisys.StateSpaceContinuous scipy.signal.ltisys.StateSpaceDiscrete

but supports sparse matrices and other functionalities.

Methods: - get_mats: return matrices as tuple - check_types: check matrices types are supported - freqresp: calculate frequency response over range. - addGain: project inputs/outputs - scale: allows scaling a system

addGain(K, where)

Projects input u or output y the state-space system through the gain matrix K. The input ‘where’ determines whether inputs or outputs are projected as:

• where=’in’: inputs are projected such that:

  u_new -> u=K*u_new -> SS -> y => u_new -> SSnew -> y

• where=’out’: outputs are projected such that:

  u -> SS -> y -> y_new=K*y => u -> SSnew -> ynew

Parameters

• K (np.array or Gain) – gain matrix or Gain object

• where (str) – in or out

Warning

This is not a wrapper of the addGain method in this module, as the state-space matrices are directly overwritten.

disc2cont()

Transform a discrete time system to a continuous time system using a bilinear (Tustin) transformation.

Wrapper of disc2cont()

eigvals()

Returns

Eigenvalues of the system

Return type

np.ndarray

freqresp(wv)

Calculate frequency response over frequencies wv

Note: this wraps frequency response function.

classmethod from_scipy(scipy_ss)

Transforms a scipy.signal.lti or dlti into a StateSpace class

Parameters

scipy_ss (scipy.signal.ltisys.StateSpaceContinous or scipy.signal.ltisys.StateSpaceDiscrete) – Scipy State Space object.

Returns

SHARPy state space object

Return type

StateSpace

property inputs

Number of inputs \(m\) to the system.

classmethod load_from_h5(h5_file_name)

Loads a state-space object from an h5 file, including variable information

Parameters

h5_file_name (str) – Path to file

Returns

loaded state-space from file

Return type

StateSpace

max_eig()

Returns most unstable eigenvalue

property outputs

Number of outputs \(p\) of the system.

project(wt, v)

Given 2 transformation matrices, (WT, V) of shapes (Nk, self.states) and (self.states, Nk) respectively, this routine projects the state space model states according to:

\[Anew = WT A V \ Bnew = WT B \ Cnew = C V \ Dnew = D \\]

The projected model has the same number of inputs/outputs as the original one, but Nk states.

Parameters

• wt (Gain or np.ndarray) – Left projection matrix

• v (Gain or np.ndarray) – Righty projection matrix

remove_inputs(*input_remove_list)

Removes inputs through their variable names.

Needs that the StateSpace attribute input_variables is defined.

Parameters

input_remove_list (list(str)) – List of inputs to remove

remove_outputs(*output_remove_list)

Removes outputs through their variable names.

Needs that the StateSpace attribute output_variables is defined.

Parameters

output_remove_list (list(str)) – List of outputs to remove

retain_inout_channels(retain_channels, where)

Retain selected input or output channels only.

Parameters

• retain_channels (list) – List of channels to retain

• where (str) – in or out for input/output channels

save(path)

Save state-space object to h5 file

scale(input_scal=1.0, output_scal=1.0, state_scal=1.0)

Given a state-space system, scales the equations such that the original state, input and output, (x, u and y), are substituted by

xad=x/state_scal uad=u/input_scal yad=y/output_scal

The entries input_scal/output_scal/state_scal can be:

• floats: in this case all input/output are scaled by the same value

• lists/arrays of length Nin/Nout: in this case each dof will be scaled

by a different factor

If the original system has form:

xnew=A*x+B*u y=C*x+D*u

the transformation is such that:

xnew=A*x+(B*uref/xref)*uad yad=1/yref( C*xref*x+D*uref*uad )

property states

Number of states \(n\) of the system.

transfer_function_evaluation(s)

Returns the transfer function of the system evaluated at \(s\in\mathbb{C}\).

Parameters

s (complex) – Point in the complex plane at which to evaluate the transfer function.

Returns

Transfer function evaluated at \(s\).

Return type

np.ndarray

truncate(N)

Retains only the first N states.