Using the Context Panel with DynamicSystems - Maple Programming Help

Using the Context Panel with DynamicSystems

Description

 • The DynamicSystems context-sensitive options in the Context Panel give you the ability to access almost all of the commands in the DynamicSystems package with the click of a mouse.
 • The DynamicSystems menu in the Context Panel 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.

Accessing the Context-Sensitive Options

 • You can access the context-sensitive options 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 options:
 – 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
 • From the Context Panel for one of these items, select Dynamic Systems. There are four submenus.

System Creation

 • Use the System Creation submenu to create DynamicSystems System Objects from the different DynamicSystems representations. After the System Objects are created, they can be used with any of the commands found within the DynamicSystems package.

 • Use the Conversions submenu to convert between the four DynamicSystems representations mentioned above, namely Differential Equation, State Space Matrices, Transfer Function, and Zero-Pole-Gain Matrices.

 • Use the Manipulations submenu to conduct analysis operations on all the DynamicSystems representations.
 • The following analysis operations are available from the Context Panel:

 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.

 • Use the Plots submenu to explore the underlying system dynamics using different plotting commands.
 • The plotting operations available through the context-sensitive options 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

Conversion Example

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

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

2. Select the expression. From the Context Panel, select Dynamic Systems>Conversions>Transfer Function to Differential Equation. The result will be:

$\left[\frac{ⅆ}{ⅆt}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}\mathrm{x1}\left(t\right)=-\mathrm{x1}\left(t\right)-\mathrm{u1}\left(t\right),\mathrm{y1}\left(t\right)=-\mathrm{x1}\left(t\right)\right]$

Plotting Example

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

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

4. Select $\frac{1}{s+1}$, and from the Context Panel, select Dynamic Systems>Plots>Phase Plot.