Equations for State Matrix

 

RecurDyn model includes the plant model, the plant inputs and the plant outputs as Figure 1.   

 

Figure 1  Multi Body System

 

RecurDyn/Linear carries out linearization of plant model.  

The linearized equation of plant model become

 

img54.gif                            (1)

 

We define states as

 

img56.gif  and  img57.gif                        (2)

 

From equation (1), the A matrix and B matrix can be derived as below equation

 

img58.gif

 

 

img60.gif                                      (3)

 

Plant outputs are defined the function of img61.gif,  img62.gif and U.

 

img63.gif                                          (4)

 

Conclusively, in State Matrix the linearized RecurDyn model is represented as:

 

img64.gif                                         (5)

 

Where:

img64.gif represents the state variables of the plant.

U represents the plant inputs.

Y represents the plant outputs.

A, B, C and D are state matrices.

 

You can define the plant inputs and plant outputs. RecurDyn/Solver automatically determines the states. But if you want to make arbitrary coordinate states, you change states by modeling plant input force in the arbitrary coordinate.