Block performs a nonlinear transformation of state variables (state coordinates) according to the exact linearization procedure. It is used together with the Linearizing control law block in order to ensure a transformation of the nonlinear state-space equations of a SISO system
Following notations are used: x = (x1,x2,...,xN)T denotes the states vector of the nonlinear system, u and y denote the system input and output, respectively. Vector q = (q1,q2,...,qNr)T is the states vector and v the input of the linear system resulting from the transformation. The transformation formula can be specified either by a symbolic expression or by an identifier of a symbolic variable defined in MATLAB workspace - see detailed description of block parameters below. The formula can be computed by the ExaktSiso program application included in the NelinSys tool.
Positive integer specifying the number of state variables of the nonlinear system i.e. the length of the states vector x.
Positive integer lower than or equal to system order specifying the number of state variables of the linear system resulting from the transformation i.e. the length of the q vector.
Symbolic expression defining the transformation function (transformation matrix) q = q(x); the convention for writing mathematical operations is the same as the one used by MATLAB's Symbolic Math Toolbox. State variables have to be denoted as x1, x2, ..., xN. If the transformation formula is not specified by a symbolic expression but by an identifier of a variable (see below), it is necessary to leave this field blank.
Identifier of a symbolic variable (a class sym object) containing the expression for q = q(x). If the transformation formula is not specified by an identifier of a variable but by a symbolic expression (see previous parameter), it is necessary to set this field to 0 (zero).
See demo Exact linearization of a SISO system