Author : Abhilash V Nair and Kannan Madhavan

This paper introduces an easiest method for modeling mechanical systems, which will be helpful for control engineers dealing with higher order mechanical systems because the method is more beneficial for higher order systems. This method is a continuation of inspection method of network solution based on KCL. The method is perfectly fit for SISO systems. Even though it can be used for modeling MIMO systems by considering one input and one output at a time. In this method, entire system static parameters and dynamic parameters have to be transformed into Laplace domain such that complete system will be represented in transformed domain. Transfer function Matrix can be derived from the transformed system by considering each mass as independent nodes. Transfer function matrix of the system relates all inputs and all outputs of the system and selecting proper combination of input and output any one can find the corresponding transfer function by using Crammers’ Rule. In this way, the obtained transfer function will be exactly same as differential equation method. One limitation is the method is not suitable for such systems with nonlinear nature and system states and state trajectory are to be taken into consideration.

Keywords: KCL-Kirchhoff’s Current Law, SISO-Single input single output systems, MIMO-Multi input multi output systems, Transfer Function, System states, Crammer’s Rule, Transfer function matrix.