scale_SS¶

Given a state-space system, scales the equations such that the original input and output, \(u\) and \(y\), are substituted by \(u_{AD}=\frac{u}{u_{ref}}\) and \(y_{AD}=\frac{y}{y_{ref}}\).

If the original system has form:

\[\begin{split}\mathbf{x}^{n+1} &= \mathbf{A\,x}^n + \mathbf{B\,u}^n \\ \mathbf{y}^{n} &= \mathbf{C\,x}^{n} + \mathbf{D\,u}^n\end{split}\]

the transformation is such that:

\[\begin{split}\mathbf{x}^{n+1} &= \mathbf{A\,x}^n + \mathbf{B}\,\frac{u_{ref}}{x_{ref}}\mathbf{u_{AD}}^n \\ \mathbf{y_{AD}}^{n+1} &= \frac{1}{y_{ref}}(\mathbf{C}\,x_{ref}\,\mathbf{x}^{n+1} + \mathbf{D}\,u_{ref}\,\mathbf{u_{AD}}^n)\end{split}\]

By default, the state-space model is manipulated by reference (byref=True)

param input_scal:
param SSin:	original state-space formulation
type SSin:	scsig.dlti
	input scaling factor \(u_{ref}\). It can be a float or an array, in which case the each element of the input vector will be scaled by a different factor.
type input_scal:
	float or np.ndarray
param output_scal:
	output scaling factor \(y_{ref}\). It can be a float or an array, in which case the each element of the output vector will be scaled by a different factor.
type output_scal:
	float or np.ndarray
param state_scal:
	state scaling factor \(x_{ref}\). It can be a float or an array, in which case the each element of the state vector will be scaled by a different factor.
type state_scal:
	float or np.ndarray
param byref:	state space manipulation order
type byref:	bool
returns:	scaled state space formulation
rtype:	scsig.dlti