create a system object - Maple Help

Home : Support : Online Help : Science and Engineering : Dynamic Systems : System Object : DynamicSystems/NewSystem

DynamicSystems[NewSystem] - create a system object

 Calling Sequence NewSystem(opts) NewSystem(sys, opts) NewSystem(tf, opts) NewSystem(z, p, k, opts) NewSystem(num, den, opts) NewSystem(a, b, c, d, opts) NewSystem(de, invars, outvars, opts)

Parameters

 sys - System; system object tf - algebraic or Matrix(algebraic); transfer function z - list(algebraic) or Matrix(list(algebraic)); zeros p - list(algebraic) or Matrix(list(algebraic)); poles k - algebraic or Matrix(algebraic); gain(s) num - list(algebraic) or Matrix (list(algebraic)); numerator coefficients den - list(algebraic) or Matrix (list(algebraic)); denominator coefficients a - Matrix; state-space matrix A b - Matrix; state-space matrix B c - Matrix; state-space matrix C d - Matrix; state-space matrix D de - equation or list(equation); diff-equations invars - name, anyfunc(name) or list of same; input variables outvars - name, anyfunc(name) or list of same; output variables opts - (optional) equation(s) of the form option = value; specify options for the NewSystem command

Description

 • The NewSystem command creates a System object. Five system types are supported: transfer-function (TF), zero-pole-gain (ZPK), coefficients (Coeff), state-space (SS), and differential/difference equations (DE).
 • The input can be specified as one of the five system types. The output has the same type as the input.
 • If no input is provided, a unity-gain transfer-function system is created.
 • The parameter sys is a system object; it is copied to the output. All options are ignored.
 • The optional parameter tf is the transfer function of a TF system. For a single-input/single-output system, tf is a rational function (ratpoly). For a multi-input/multi-output system, tf is a Matrix of rational functions. The indeterminate of the polynomials depends on whether the system is continuous or discrete; a continuous system typically uses s while a discrete system typically uses z as the indeterminate. The actual names are assigned by DynamicSystems[SystemOptions].
 • The optional parameters z, p, and k are the zeros, poles, and gain, respectively, of a ZPK system. For a single-input/single-output system, z and p are lists and k is an algebraic expression. For a multi-input/multi-output system, z and p are Matrices of lists and k is a Matrix of algebraic expressions.
 • The optional parameters num and den are the coefficients of the numerator and denominator, respectively, of a Coeff system. For a single-input/single-output system, num and den are lists, the first element being the coefficient of the highest order term. For a multi-input/multi-output system, num and den are Matrices of lists.
 • The optional parameters a, b, c, and d are the four state-space matrices, A, B, C, and D, respectively, of an SS system.
 • The optional parameter de is the difference/differential equation(s) of a DE system. A list is used to specify more than one equation.
 • The parameters invars and outvars specify the input and output variables of difference/differential equations. They are not required, but if either is not specified then the corresponding keyword parameter inputvariable or outputvariable must be assigned. If both positional and keyword parameters are specified, the keyword parameter take precedence.

Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{sys1}:=\mathrm{NewSystem}\left(\right)$
 ${\mathrm{sys1}}{:=}\left[\begin{array}{c}{\mathbf{Algebraic Equation}}\\ {\mathrm{continuous}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{u}{}\left({t}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{y}{}\left({t}\right)\right]\end{array}\right$ (1)
 > $\mathrm{PrintSystem}\left(\mathrm{sys1}\right)$
 $\left[\begin{array}{l}{\mathbf{Algebraic Equation}}\\ {\mathrm{continuous}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{u}{}\left({t}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{y}{}\left({t}\right)\right]\\ {\mathrm{ae}}{=}\left[{y}{}\left({t}\right){=}{u}{}\left({t}\right)\right]\end{array}\right$ (2)
 > $\mathrm{sys2}:=\mathrm{NewSystem}\left(\left[1,2\right],\left[1,2,3\right]\right)$
 ${\mathrm{sys2}}{:=}\left[\begin{array}{c}{\mathbf{Coefficients}}\\ {\mathrm{continuous}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{\mathrm{u1}}{}\left({s}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{y1}}{}\left({s}\right)\right]\end{array}\right$ (3)
 > $\mathrm{PrintSystem}\left(\mathrm{sys2}\right)$
 $\left[\begin{array}{l}{\mathbf{Coefficients}}\\ {\mathrm{continuous}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{\mathrm{u1}}{}\left({s}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{y1}}{}\left({s}\right)\right]\\ {{\mathrm{num}}}_{{1}{,}{1}}{=}\left[{1}{,}{2}\right]\\ {{\mathrm{den}}}_{{1}{,}{1}}{=}\left[{1}{,}{2}{,}{3}\right]\end{array}\right$ (4)
 > $\mathrm{tf_mimo_z}:=\mathrm{Matrix}\left(\left[\left[\frac{1}{{z}^{2}},\frac{{z}^{2}}{{z}^{3}+5{z}^{2}+7z+6}\right],\left[\frac{1}{z},\frac{c}{{z}^{2}+az+b}\right]\right]\right)$
 ${\mathrm{tf_mimo_z}}{:=}\left[\begin{array}{cc}\frac{{1}}{{{z}}^{{2}}}& \frac{{{z}}^{{2}}}{{{z}}^{{3}}{+}{5}{}{{z}}^{{2}}{+}{7}{}{z}{+}{6}}\\ \frac{{1}}{{z}}& \frac{{c}}{{a}{}{z}{+}{{z}}^{{2}}{+}{b}}\end{array}\right]$ (5)
 > $\mathrm{sys3}:=\mathrm{NewSystem}\left(\mathrm{tf_mimo_z},\mathrm{discrete},\mathrm{sampletime}=0.001,\mathrm{systemname}="Sample discrete MIMO system"\right)$
 ${\mathrm{sys3}}{:=}\left[\begin{array}{c}{\mathbf{Transfer Function}}\\ {\mathrm{discrete; sampletime = .1e-2}}\\ {\mathrm{systemname}}{=}{\mathrm{Sample discrete MIMO system}}\\ {\mathrm{2 output\left(s\right); 2 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{\mathrm{u1}}{}\left({z}\right){,}{\mathrm{u2}}{}\left({z}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{y1}}{}\left({z}\right){,}{\mathrm{y2}}{}\left({z}\right)\right]\end{array}\right$ (6)
 > $\mathrm{PrintSystem}\left(\mathrm{sys3}\right)$
 $\left[\begin{array}{l}{\mathbf{Transfer Function}}\\ {\mathrm{discrete; sampletime = .1e-2}}\\ {\mathrm{systemname}}{=}{\mathrm{Sample discrete MIMO system}}\\ {\mathrm{2 output\left(s\right); 2 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{\mathrm{u1}}{}\left({z}\right){,}{\mathrm{u2}}{}\left({z}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{y1}}{}\left({z}\right){,}{\mathrm{y2}}{}\left({z}\right)\right]\\ {{\mathrm{tf}}}_{{1}{,}{1}}{=}\frac{{1}}{{{z}}^{{2}}}\\ {{\mathrm{tf}}}_{{2}{,}{1}}{=}\frac{{1}}{{z}}\\ {{\mathrm{tf}}}_{{1}{,}{2}}{=}\frac{{{z}}^{{2}}}{{{z}}^{{3}}{+}{5}{}{{z}}^{{2}}{+}{7}{}{z}{+}{6}}\\ {{\mathrm{tf}}}_{{2}{,}{2}}{=}\frac{{c}}{{{z}}^{{2}}{+}{a}{}{z}{+}{b}}\end{array}\right$ (7)