outputtype = tf, coeff, zpk, ss, or de

Specifies the subtype of the returned system object.  The default return type is based on the type of the system objects specified in the systems parameter. See the Description section for more details on the return type.

parameters = set(name = complexcons) or list(name = complexcons)

Specifies numeric values for parameters in sys. These values override those specified by the parameters field of the system object, which in turn override the settings in in SystemOptions(parameters). The numeric value on the right-hand side of each equation is substituted for the name on the left-hand side in the expressions that define the model. No checking is done during the substitution to determine whether the substituted value is valid. For example, a complex value can be substituted for the coefficient of a polynomial. If the complex value had been originally assigned to the model at creation, a warning would be generated.

The ScaleOutputs command  creates a system that scales the outputs of sys by the coefficients in the coefficients list.

The type of the system object ScaleOutputs returns is determined by the type of the system object specified in the sys parameter unless an option is specified.

If the sys parameter is an algebraic equation (ae) and no option is specified, the ScaleOutputs command returns a system object in state space form by default. If the algebraic equation system does not have a state space representation, an error is returned. For details on algebraic equation object support by the DynamicSystems package, see DynamicSystems[AlgEquation].

$\mathrm{with}\left(\mathrm{DynamicSystems}\right)\:$

$\mathrm{sys1}≔\mathrm{StateSpace}\left(\frac{s}{s^3+5s^2+7s+6}\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys1}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s);\; 3\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ \mathrm{-6}& \mathrm{-7}& \mathrm{-5}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{ccc}0& 1& 0\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{c}0\end{array}\right]\end{array}\right.$

$\mathrm{co}≔\left[\mathrm{k1}\right]$

$\mathrm{co}≔\left[\mathrm{k1}\right]$

$\mathrm{sys1a}≔\mathrm{ScaleOutputs}\left(\mathrm{sys1}\,\mathrm{co}\,\mathrm{parameters}=\left[\mathrm{k1}=1\right]\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys1a}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s);\; 3\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(t\right)\,\mathrm{x2}\left(t\right)\,\mathrm{x3}\left(t\right)\right]\\ \mathrm{a}\=\left[\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ \mathrm{-6}& \mathrm{-7}& \mathrm{-5}\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{ccc}0& \frac{1}{\mathrm{k1}}& 0\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{c}0\end{array}\right]\end{array}\right.$

$\mathrm{sys1b}≔\mathrm{ScaleOutputs}\left(\mathrm{sys1}\,\mathrm{co}\,\mathrm{outputtype}=\mathrm{de}\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys1b}\right)$

$\left[\begin{array}{l}\mathbf{Diff.\; Equation}\\ \mathrm{continuous}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(t\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(t\right)\right]\\ \mathrm{de}\=\{\begin{array}{l}\[\frac{\ⅆ}{\ⅆt}\mathrm{x1}\left(t\right)\=\mathrm{x2}\left(t\right),\\ \frac{\ⅆ}{\ⅆt}\mathrm{x2}\left(t\right)\=\mathrm{x3}\left(t\right),\\ \frac{\ⅆ}{\ⅆt}\mathrm{x3}\left(t\right)\=-6\mathrm{x1}\left(t\right)-7\mathrm{x2}\left(t\right)-5\mathrm{x3}\left(t\right)+\mathrm{u1}\left(t\right),\\ \mathrm{y1}\left(t\right)\=\frac{\mathrm{x2}\left(t\right)}{\mathrm{k1}}\]\end{array}\end{array}\right.$

$\mathrm{ss\_a}≔\mathrm{Matrix}\left(\left[\left[1\,2\right]\,\left[0\,4\right]\right]\right)\:$

$\mathrm{ss\_b}≔\mathrm{Matrix}\left(\left[\left[3\,7\right]\,\left[9\,6\right]\right]\right)\:$

$\mathrm{ss\_c}≔\mathrm{Matrix}\left(\left[\left[5\,6\right]\,\left[5\,2\right]\right]\right)\:$

$\mathrm{ss\_d}≔\mathrm{Matrix}\left(\left[\left[0\,1\right]\,\left[0\,0\right]\right]\right)\:$

$\mathrm{sys2}≔\mathrm{StateSpace}\left(\mathrm{ss\_a}\,\mathrm{ss\_b}\,\mathrm{ss\_c}\,\mathrm{ss\_d}\,\mathrm{discrete}\,\mathrm{sampletime}=0.001\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys2}\right)$

$\left[\begin{array}{l}\mathbf{State\; Space}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{2\; output(s);\; 2\; input(s);\; 2\; state(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(q\right)\,\mathrm{u2}\left(q\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(q\right)\,\mathrm{y2}\left(q\right)\right]\\ \mathrm{statevariable}\=\left[\mathrm{x1}\left(q\right)\,\mathrm{x2}\left(q\right)\right]\\ \mathrm{a}\=\left[\begin{array}{cc}1& 2\\ 0& 4\end{array}\right]\\ \mathrm{b}\=\left[\begin{array}{cc}3& 7\\ 9& 6\end{array}\right]\\ \mathrm{c}\=\left[\begin{array}{cc}5& 6\\ 5& 2\end{array}\right]\\ \mathrm{d}\=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\end{array}\right.$

$\mathrm{PrintSystem}\left(\mathrm{TransferFunction}\left(\mathrm{sys2}\right)\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{2\; output(s);\; 2\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\,\mathrm{u2}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\,\mathrm{y2}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{69z-24}{z^2-5z+4}\\ {\mathrm{tf}}_{2,1}\=\frac{33z+12}{z^2-5z+4}\\ {\mathrm{tf}}_{1,2}\=\frac{z^2+66z-112}{z^2-5z+4}\\ {\mathrm{tf}}_{2,2}\=\frac{47z-92}{z^2-5z+4}\end{array}\right.$

$\mathrm{cf}≔\left[a\,\frac{1}{2}\right]$

$\mathrm{cf}≔\left[a\,\frac{1}{2}\right]$

$\mathrm{sys2a}≔\mathrm{ScaleOutputs}\left(\mathrm{sys2}\,\mathrm{cf}\,\mathrm{outputtype}=\mathrm{tf}\right)\:$

$\mathrm{PrintSystem}\left(\mathrm{sys2a}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{2\; output(s);\; 2\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\,\mathrm{u2}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\,\mathrm{y2}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{69z-24}{a{z}^2-5az+4a}\\ {\mathrm{tf}}_{2,1}\=\frac{66z+24}{z^2-5z+4}\\ {\mathrm{tf}}_{1,2}\=\frac{z^2+66z-112}{a{z}^2-5az+4a}\\ {\mathrm{tf}}_{2,2}\=\frac{94z-184}{z^2-5z+4}\end{array}\right.$

The DynamicSystems[ScaleOutputs] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.