Physical Model Reduction of a Parallel and Hybrid Manipulator Using Eigenvalue Sensitivity Method

Abstract

The multi-energy domain dynamic systems are of utmost importance; a number of researchers have carried out their modelling by taking advantage of this concept. The dynamic systems are very complex in nature as the time required for simulation is large and their computations become difficult. Therefore, the model reduction is done such that the dynamics of the systems are preserved and accuracy is maintained. With this, the simulation time and number of calculations are reduced considerably. The contribution of this paper is that modelling of a parallel and hybrid manipulator is done using bond graph modelling technique, and then, their dynamic models are reduced with the eigenvalue sensitivity method for model reduction. This paper attempts to achieve this by mathematically finding the redundant elements, which do not add to the dynamics of the system but increase the calculation time by increasing the complexity of the system. The redundant elements could be neglected, and hence, the complexity reduced without compromising the accuracy. The eigenvalues are calculated from the system matrix, and effect matrices are formed. The row and column based on eigenvalues can be reduced to form a reduced model. The trajectory tracking is done for both the manipulators, and results are presented in this paper for full and reduced models. The comparisons of results for full and reduced models are also given in the form of absolute and percentage errors.