Using Context-Sensitive Menus for DynamicSystems - Maple Programming Help

Description

 • The DynamicSystems Context Menus gives you the ability to access almost all of the commands in the DynamicSystems package with the click of a mouse. The DynamicSystems Context Menus will be automatically activated when the DynamicSystems package is loaded into the workspace.
 • The DynamicSystems context-sensitive menu consists of four submenus: System Creation, Conversion, Manipulation and Plotting. Using these submenus, you can create DynamicSystems System Objects, convert between different DynamicSystems equation and matrix representations, analyze the dynamics of a system, and obtain plots of the frequency, impulse and system response characteristics to a wide variety of inputs.

 • To use this feature, you must load the DynamicSystems package by executing with(DynamicSystems).
 • You can access the context-sensitive menu for any of the following four inputs: continuous and discrete differential equations, state space Matrices, continuous and discrete transfer functions, and zero-pole-gain Matrices. The inputs must be defined in the following manner to access the context-sensitive menu:

 Differential Equations: list of equation(s) State Space Matrices: sequence of 4 Matrices Transfer Functions: Matrix of one or several rational polynomials Zero-Pole-Gain Matrices: sequence of 3 Matrices

 • Right-click on one of these objects and from the context-sensitive menu, select DynamicSystems. There are four submenus.

System Creation

 • The System Creation submenu allows you to create DynamicSystems System Objects from the different DynamicSystems representations. Once created, the System Objects can be used with any of the commands found within the DynamicSystems package.

 • The Conversions submenu provides you with a mechanism to convert between the four DynamicSystems representations mentioned above, namely Differential Equation, State Space Matrices, Transfer Function, and Zero-Pole-Gain Matrices.

 • The Manipulations submenu permits you to conduct analysis operations on all the DynamicSystems representations.
 • The following analysis operations are available from the context-sensitive menu:

 Characteristic Polynomial Controllability Matrix Controllable Grammians Gain Margin Phase Margin Observability Matrix Observable

 • Note: The majority of these commands are only available for State Space inputs.

 • The Plots submenu enables you to explore the underlying system dynamics using different plotting commands.
 • The plotting operations that are available from the context-sensitive menu are listed below:

 Bode Plot Impulse Response Plot Magnitude Plot Phase Plot Nichols Plot Nyquist Plot Response Plot Root Contour Plot Root Locus Plot Zero Pole Plot

 • When creating a Response Plot, you can select from the following input signals:

 Chirp Ramp Sinc Sine Square Step Triangle

Examples

1. To begin, load the DynamicSystems package.

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

Conversion Example

2. Enter $\frac{1}{s+1}$.

 > $\frac{1}{s+1}$
 $\frac{{1}}{{s}{+}{1}}$ (1)

3. Right-click (Control-click on Macintosh) on the expression. From the context menu, select DynamicSystems>Conversions>Transfer Function to Differential Equation The result will be:

$\left[\frac{ⅆ}{ⅆt}\mathrm{x1}\left(t\right)=-\mathrm{x1}\left(t\right)+\mathrm{u1}\left(t\right),\mathrm{y1}\left(t\right)=\mathrm{x1}\left(t\right)\right]$

Plotting Example

4. Enter $\frac{1}{s+1}$.

 > $\frac{1}{s+1}$
 $\frac{{1}}{{s}{+}{1}}$ (2)

5. Right-click on $\frac{1}{s+1}$, and from the context menu, select DynamicSystems>Plots>Phase Plot.