.ModelicaTest.MultiBody.PlanarLoopWithMove

Information

This model is a combination of a multi-body system with a kinematic loop and a Move block, where symbolic transformation is difficult:

Standard symbolic transformation works in the following way if functions are present with annotation "InineAfterIndexReduction = true".

1. These functions are not inlined, the Pantelides algorithm is applied and the equations are symbolically differentiated.
2. The functions are inlined and further symbolic transformation is performed (sorting the equations, dummy derivative method etc..

The model contains the following functions that have annotation "InineAfterIndexReduction = true":

1. MultiBody.Frames.resolve1/resolve2(..) functions are used to transform the coordinates of a vector in another coordinate system. When these functions need to be differentiated in the Pantelides algorithm, then Euler's differentiation rule is applied with the angular velocity that is usually a factor of 2-3 more efficient as if direct differentiation is applied. The drawback is that the sparsity structure is more "coarse" and this lets the Pantelides algorithm fail in this example (this happens usually only in systems with kinematic loops). This means that the differentiated equation system is structurally singular, after the functions with annotation "InineAfterIndexReduction = true" are inlined.
2. The Rotational.Sources.Move block is using internally functions to express that an input u[2] is the derivative of input u[1]. In order that this is possible, the functions have the annotation "InineAfterIndexReduction = true" so that the differentiation takes place with the not inlined functions. After the Pantelides algorithm and the differentiation is applied, the functions are inlined to enhance efficiency.

The problem with (1) is that after inlining the functions with annotation "InineAfterIndexReduction = true", the equations are structurally singular, but the source of the singularity is now known. One remedy is to restart symbolic processing and to inline all functions with "InineAfterIndexReduction = true" before the Pantelides algorithm is applied. In the model, this approach is in principal successful and the model would be structurally regular. However, the Move block is no longer working correctly if the Pantelides algorithm is applied with inlining. For this reason in MSL 3.2.1 build 3, the annotation "InineAfterIndexReduction = true" in the Move block has been replaced by annotation "Inline = false". This results in slightly less efficient code, but is more robust in the situation at hand.