 AlgEquation - Maple Help

DynamicSystems

 AlgEquation
 create an algebraic equation system object Calling Sequence AlgEquation(ae, invars, outvars, opts) Parameters

 ae - equation or list(equation); algebraic-equations invars - (optional) name, anyfunc(name) or list of same; input variables outvars - (optional) name, anyfunc(name) or list of same; output variables Options

 • discrete = truefalse
 True means the system is discrete, false means the system is continuous. The default value is assigned by DynamicSystems[SystemOptions].
 • sampletime = realcons
 The sampling time of a discrete system. The default value is assigned by DynamicSystems[SystemOptions].
 • systemname = string
 The name of the system. The default is the empty string.
 • inputvariable = list of names or functions of time
 The names of the inputs to the system. A name, say u, is converted to a function u(t), where t is the independent variable of the system, only if the ae equations specified do not contain the independent variable. See DynamicSystems/SystemObject. The default value is assigned by DynamicSystems[SystemOptions].
 • outputvariable = list of names or functions of time
 The names of the outputs of the system. A name, say y, is converted to a function y(t), where t is the independent variable of the system, only if the ae equations specified do not contain the independent variable. The default value is assigned by DynamicSystems[SystemOptions].
 • parameters = list of name=complexcons
 Specifies values for symbolic parameters. These are used in operations that require numeric evaluation, such as plotting. Description

 • The AlgEquation command creates an algebraic-equation (AE) system object, that is, a system whose input/output equations are given by non-differential algebraic equations. It is provided to permit code generation of algebraic-equation blocks. This object cannot be used by many of the commands in the DynamicSystems package.
 • The ae parameter specifies the equation or equations. It may be a single equation, or a list of equations.
 • The optional parameters invars and outvars specify the input and output variables of the algebraic 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.
 • The variables of the equations are explicit functions of the time-variable (usually t for a continuous system, q for a discrete system).  Only input or output variables are allowed in the equations.  If invars and/or outvars are specified as names, rather than functions of time, the corresponding names in the equations are converted to functions of time. Examples

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{sys1}≔\mathrm{AlgEquation}\left(y=\mathrm{sin}\left(x\right),x,y\right):$
 > $\mathrm{PrintSystem}\left(\mathrm{sys1}\right)$
 $\left[\begin{array}{l}{\mathbf{Algebraic Equation}}\\ {\mathrm{continuous}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{x}{}\left({t}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{y}{}\left({t}\right)\right]\\ {\mathrm{ae}}{=}\left[{y}{}\left({t}\right){=}{\mathrm{sin}}{}\left({x}{}\left({t}\right)\right)\right]\end{array}\right$ (1)
 > $\mathrm{sys2}≔\mathrm{AlgEquation}\left(y=\mathrm{sin}\left(x\right),x,y,\mathrm{discrete}=\mathrm{true},\mathrm{sampletime}=0.01\right):$
 > $\mathrm{PrintSystem}\left(\mathrm{sys2}\right)$
 $\left[\begin{array}{l}{\mathbf{Algebraic Equation}}\\ {\mathrm{discrete; sampletime = .1e-1}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{x}{}\left({q}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{y}{}\left({q}\right)\right]\\ {\mathrm{ae}}{=}\left[{y}{}\left({q}\right){=}{\mathrm{sin}}{}\left({x}{}\left({q}\right)\right)\right]\end{array}\right$ (2)
 > $\mathrm{ListEqn}≔\left[\mathrm{x1}\left(t\right)=r\left(t\right)\mathrm{cos}\left(\mathrm{\theta }\left(t\right)\right),\mathrm{y1}\left(t\right)=r\left(t\right)\mathrm{sin}\left(\mathrm{\theta }\left(t\right)\right)\right]:$
 > $\mathrm{InputVar}≔\left[r\left(t\right),\mathrm{\theta }\left(t\right)\right]:$
 > $\mathrm{OutputVar}≔\left[\mathrm{x1}\left(t\right),\mathrm{y1}\left(t\right)\right]:$
 > $\mathrm{sys3}≔\mathrm{AlgEquation}\left(\mathrm{ListEqn},\mathrm{InputVar},\mathrm{OutputVar}\right):$
 > $\mathrm{PrintSystem}\left(\mathrm{sys3}\right)$
 $\left[\begin{array}{l}{\mathbf{Algebraic Equation}}\\ {\mathrm{continuous}}\\ {\mathrm{2 output\left(s\right); 2 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{r}{}\left({t}\right){,}{\mathrm{\theta }}{}\left({t}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{x1}}{}\left({t}\right){,}{\mathrm{y1}}{}\left({t}\right)\right]\\ {\mathrm{ae}}{=}\left[{\mathrm{x1}}{}\left({t}\right){=}{r}{}\left({t}\right){}{\mathrm{cos}}{}\left({\mathrm{\theta }}{}\left({t}\right)\right){,}{\mathrm{y1}}{}\left({t}\right){=}{r}{}\left({t}\right){}{\mathrm{sin}}{}\left({\mathrm{\theta }}{}\left({t}\right)\right)\right]\end{array}\right$ (3)
 > $\mathrm{ListEqn}≔\left[\mathrm{x1}\left(q\right)=r\left(q\right)\mathrm{cos}\left(\mathrm{\theta }\left(q\right)\right),\mathrm{y1}\left(q\right)=r\left(q\right)\mathrm{sin}\left(\mathrm{\theta }\left(q\right)\right)\right]:$
 > $\mathrm{InputVar}≔\left[r\left(q\right),\mathrm{\theta }\left(q\right)\right]:$
 > $\mathrm{OutputVar}≔\left[\mathrm{x1}\left(q\right),\mathrm{y1}\left(q\right)\right]:$
 > $\mathrm{sys4}≔\mathrm{AlgEquation}\left(\mathrm{ListEqn},\mathrm{InputVar},\mathrm{OutputVar},\mathrm{discrete}=\mathrm{true},\mathrm{sampletime}=0.01\right):$
 > $\mathrm{PrintSystem}\left(\mathrm{sys4}\right)$
 $\left[\begin{array}{l}{\mathbf{Algebraic Equation}}\\ {\mathrm{discrete; sampletime = .1e-1}}\\ {\mathrm{2 output\left(s\right); 2 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{r}{}\left({q}\right){,}{\mathrm{\theta }}{}\left({q}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{x1}}{}\left({q}\right){,}{\mathrm{y1}}{}\left({q}\right)\right]\\ {\mathrm{ae}}{=}\left[{\mathrm{x1}}{}\left({q}\right){=}{r}{}\left({q}\right){}{\mathrm{cos}}{}\left({\mathrm{\theta }}{}\left({q}\right)\right){,}{\mathrm{y1}}{}\left({q}\right){=}{r}{}\left({q}\right){}{\mathrm{sin}}{}\left({\mathrm{\theta }}{}\left({q}\right)\right)\right]\end{array}\right$ (4) Compatibility

 • The DynamicSystems[AlgEquation] command was updated in Maple 18.
 • The parameters option was introduced in Maple 18.
 • For more information on Maple 18 changes, see Updates in Maple 18.