Linearization parameters

When you select Linear Analysis mode , the LA Times and LA Status menu options and buttons are enabled:

Setting Linear analysis times

LA times

Linear Analysis Times setting

1. Select Simulate > Linear analysis > LA Times, or select Linear analysis > LA Times in the Simulation contextual toolbar to produce the Linearization Times dialog box.

You can enter as many linearization times as you require.

2. To remove a time, highlight the item in the list and click on Remove.

3. Click OK to validate your changes. If you click on Cancel, they are discarded.

Linear analysis status

Linear Analysis Status

LA status

We define state variable in its broadest sense to include:

• Explicit states

• Implicit states

• Constraint variables

All state variables have an LA status which is one of the following:

• Free state Free state

• Fixed state Fixed state

• State observer State observer

A fixed state is a state which is excluded from the linearization process. If a state is not fixed, it is free. If there are N states, M of which are fixed, the order of the Jacobian produced is N-M. A free state that is also an observer variable is called a state observer.

All variables other than state variables, also have an LA status which is one of the following:

• Clear Clear variable

• Control Control variable

• Observer Observer variable

No state variable can be made a control variable.

Simcenter Amesim can be used to linearize a system about an operating point producing the standard A, B, C and D matrices for the state space equations with:

where x, u and y are the state, control and observer variables respectively. Strictly speaking this is true only for classical ordinary differential equations (O.D.E.s).

It is possible to apply the linearization process to a reduced subset of state variables. To do this, the excluded states must be frozen, or fixed. These states are then set to fixed states. We can also say that their linear analysis status is set to fixed status.

Since these states are excluded from linearization, the size of the A matrix is reduced, as the number of eigenvalues.

If a state is not fixed, it is included in the linearization, at least as a free state. However, it can also be part of the observer vector by setting its status to State observer.

Here is a brief summary of the possible linear analysis status and their repercussion on the x and y vectors:

• Any state variable set to Fixed state is excluded from linearization.

• Any state variable set to Free state is included in x vector.

• Any state variable set to State observer is included in x and y vectors.

• Any variable set to Control is included in the u vector.

• Any variable set to Observer is included in the y vector.

• Any variable set to Clear will not be included in any vector.

To check the current status of variables, click on or use the LA Status menu option to produce the LA Status Fields dialog box.

Figure 300: LA Status Fields dialog box

Note

• The information is stored in 4 lists under the headings Free states, Fixed states, Control variables and Observer variables.

• If a state variable is also an observer variable it will appear in both the Free states and the Observer variables lists. This is the only occasion when a variable can appear on more than one list.

• Under each item is an output variable. If a corresponding input variable exists, this is also added prefixed by a "~".

• You cannot change anything in the dialog box. Any changes must be made as explained in the following section.