part create equation linear_state_equation

The Linear State Equation (LSE) is designed to model a linear, time-invariant control system defined in the state space, especially to facilitate importing of controllers developed in with external software. It can be used, however, to define any arbitrary set of coupled constant-coefficient differential and algebraic equations which can be expressed in matrix notation as:

where, at least the A matrix must be non-zero. The LINEAR_STATE_EQUATION follows standard control systems terminology, where X is the state vector, Y is the output vector, U is the input vector and IC is the initial condition vector, X(t=0). In the Adams data set, each of these vectors is defined using an ARRAY. Similarly, A is the state matrix, B is the control matrix, C is the output matrix, and D is the feedforward matrix. Each of these matrices is defined using a MATRIX. All MATRIX and ARRAY sizes must be conformable as required by the above equation. ARRAYs with zero-length and zero-sized matrices should not be defined; Adams will correctly formulate the system equations based on those ARRAYs and MATRIXs which do exist.

Normally, entity names are composed of alphabetic, numeric, or '_' (underscore) characters, and start with an alphabetic or '_' character. They may be of any length. For more information, see Using Extended Names.

By enclosing the name in double quotes, you may use other printable characters, or start the name with a numeral. If a name contains characters, or starts with a numeral, you must always quote the name when entering it.

Note that you can specify the parentage of an entity (e.g. what part "owns" a marker or a geometry element) when you CREATE it by changing the name. If you enter just the entity name, then the default parent will be assigned by Adams View. If you type in the full name, then you may override the default parent. In most cases, when creating an entity, Adams View will provide a default name. The default name that Adams View provides will specify the parentage that it has assumed.

You may, of course, delete this name and use your own. The form of a full name is:

The number of levels used varies from case to case and the parentage must exist before an entity can be assigned to it.

You may also enter zero as an identifier, either explicitly or by default. The next time you write an Adams file, Adams View will replace the zero with a unique, internally-generated identifier.

Adams View will permanently store this identifier with the element just as if you had entered it yourself.

Normally, you would let all identifiers default to zero, and Adams View would generate the identifiers for you. You are never required to enter a non-zero identifier. You only need to specify it if, for some reason, you wish to control the Adams file output.

These comments must follow the title statement and be followed by the comment 'END OF MODEL COMMENTS'. This string must be uppercase.

When an Adams Solver data file is written, the comments for an object are written before the statement corresponding to the object.

When the Y_OUTPUT_ARRAY_NAME parameter is used, the user must also include a C_OUTPUT_MATRIX or D_FEEDFORWARD_MATRIX name, or both, in the LINEAR_STATE_EQUATION definition, and these matrices must have the same number of rows as there are elements in the Y_OUTPUT_ARRAY_NAME.