About Defining General State Equations |
A general state equation (GSE) can be mathematically represented as shown below. It is especially useful for importing nonlinear control laws developed manually or with an independent software package.
A GSE consists of continuous states, xc, and discrete states, xd. The continuous states xc are defined in Equations 1 as explicit, first-order, ordinary differential equations. fc() is specified in a user-written subroutine, and is assumed to be continuous everywhere. Integrators in ADAMS/Solver evaluate fc() as needed.
The discrete states, xd, are defined in Equations 2 by the
function fd(). fd() is specified in a second user-written subroutine.
Equations 2 are difference equations. A sampling period is associated
with Equations 2, and integrators only evaluate Equations 2 at the sample
times. The discrete states, xd, are assumed to be constant between sampling
periods. In Equations 2, 
is the short form for 
.
The output, y, is sampled continuously, and is defined by g(). g() is specified in a third user-written subroutine. It may be discontinuous in nature. If the output is to be fed back into the mechanical system through a force element, then it is customary to eliminate the discontinuities in y, by passing it through a low-pass filter before feeding the signal into the force element. You can use the transfer function to define a low-pass filter. Failure to eliminate discontinuities in y will cause significant integration difficulties.
If Equations 1 are not present, the GSE is classified as a purely discrete GSE. If Equations 2 are not present, the GSE is classified as being purely continuous. If both Equations 1 and 2 are present, the GSE is classified as a sampled system. When neither Equations 1 nor 2 are present, the GSE does not contain any internal states.
The GSE allows you to implement four different kinds of system states:
None (Feed-Forward Only System)