Analyze > Linearize generates the ABCD state-space matrices from a nonlinear system by numerically evaluating the matrix perturbation equations at the time the simulation was halted and Embed was invoked. For a general MIMO (multiple input/multiple output) system, the ABCD state-space matrices contain the following coefficients to the vector equations:
where:
A = system matrix
B = input gain matrix
C = output gain matrix
D = direct link gain matrix
state vector derivative
state vector
output vector
input vector
Analyze > Linearize uses a central differencing scheme to approximate the partial derivative terms at the specified operating point. The four resulting matrices are displayed and can be saved in an M file.
To generate and display ABCD state-space matrices
1. Prepare the system for linearization.
2. Choose Analyze > Linearize.
3. In the System Linearization dialog under Output Selection, activate Linearize To Screen Display.
4. Click OK, or press ENTER.
Four dialogs appear in succession showing each matrix.
5. Click OK, or press ENTER to close the current matrix dialog and open the next one.
To generate and write ABCD state-space matrices to an M file
1. Prepare the system for linearization.
2. Choose Analyze > Linearize.
3. In the System Linearization dialog under Output Selection, activate Linearize To MatLab File.
4. In the Result File box, specify the complete path to the M file name to which the matrices are to be written. The following defaults are used for the parts of the pathname that you omit:
Pathname |
Default |
The disk drive |
C: |
The directory name |
The directory from which you opened Embed |
The file name |
VABCD |
The file extension |
M |
5. Click OK, or press ENTER.
1. Prepare the system for linearization.
2. Choose Analyze > Linearize.
3. In the System Linearization dialog, click Select Input/Output Points.
The pointer becomes a crossbar.
4. To select an input reference point, click the output connector on the block that produces the signal with which you want to linearize.
The output connector changes color. If the connector you select is invalid, you hear a beep.
5. To select an output reference point, click the input connector on the block that consumes the signal against which you want to linearize.
The input connector changes color. If the connector you select is invalid, Embed beeps.
6. Click over empty screen to exit this mode.