Using the Context Panel with DynamicSystems
Description
Accessing the Context-Sensitive Options
Examples
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.
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.
Conversions submenu
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.
Manipulations submenu
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.
Plots submenu
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
Sine
Square
Step
Triangle
Conversion Example
1. Enter 1s+1.
1s+1
2. Select the expression. From the Context Panel, select Dynamic Systems>Conversions>Transfer Function to Differential Equation. The result will be:
ⅆⅆtx1t=−x1t−u1t,y1t=−x1t
Plotting Example
3. Enter 1s+1.
4. Select 1s+1, and from the Context Panel, select Dynamic Systems>Plots>Phase Plot.
See Also
Context-sensitive menus
DynamicSystems
Download Help Document
