Linear analysis

Linear Analysis

When you select Simulation mode, by default the Temporal analysis mode button is enabled whereas the Linear analysis mode button is not.

Procedure

1. Click on the Linear analysis mode button to enter Linear analysis mode.

The Linear Analysis options are enabled. Figure 61: Linear analysis toolbar

2. Select various components in the system.

The Variable list dialog box and Contextual variables tab appear with a new field appended in the third column which name is Status. For a state variable, this field indicates free state. If you select the field, you get a menu with the following items:

free state

fixed state

state observer

Note Fixed states are eliminated from the linear analysis. A state observer is a free state that happens also to be an observer variable.

For any other sort of variable, the original field value is clear and the cycle sequence is:

clear

control

observer

3. Try changing the status of some of your variables.

4. Select Simulate > Linear analysis > LA Status.

The LA Status Fields dialog box is displayed as in figure Figure 62. Figure 62: Linear analysis field

5. Ensure that there are no fixed states, no control variables and no observer variables. Remember that if you click on an element in the LA Status Fields window, the corresponding submodel is highlighted in the sketch, which can help you in this task. If you look at the free state variables, you will find there are often two titles for the same state variable. Thus the state variable known as MECMAS21-1 velocity at port 1 in the 2-port mass is the same as SPR000A-1 velocity at port 1 as far as the spring submodel is concerned.We begin by doing a simple linearization with no control, observer or fixed states. Hence we will get only the A matrix and as the equations of the system are linear, we will always get the same A matrix.

Simple Linearization

Procedure

1. Select LA times from the Linear analysis menu to produce the dialog box shown in figure Figure 63.

Figure 63: Linearization times dialog box

2. Click on the Add button and set a value in the input box to indicate the time at which the linearization should be done.

3. Enter linearization times of 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 seconds.

You can enter as many linearization times as you like using the input box. To remove a linearization time, select it in the list of linearization times and click on the Remove button.

4. Run the simulation.

During the run, files named SimpleMassSpring_.jac0, SimpleMassSpring_.jac1, etc. will be created. Each will contain the results of the linearization i.e. the A, B, C and D matrices at a single linearization time. However, in this case B, C and D matrices are null.

Results

Note

To make full use of these matrices, Simcenter Amesim provides tools which are described in the rest of this section: Eigenvalue analysis, Bode, Nichols and Nyquist plots, Modal Shape analysis and Root Locus.