Transfer Functions and Mathematical Modeling of Dynamic Systems with MATLAB

Abstract

This study introduces the mechanical elements that are the main components in the dynamic modeling of mechanical systems. It discusses the electrical elements of voltage and current source, resistor, capacitor, inductor, and operational amplifier. We derive mathematical models for electrical systems. The transfer function, enables connecting the input to the output of a dynamic system into the Laplace domain for single-input, single output, multiple-input and multiple output systems. It is shown that how to derive the transfer function for SISO systems and the transfer function matrix for MIMO systems by starting from the system time-domain mathematical model or using complex impedances. The transfer function is further utilized to determine the free and forced time responses with zero initial conditions of mechanical and electrical. The concept of state space is an approach that can be used to model and determine the response of dynamic systems in the time domain. Using a vector-matrix formulation, the state space procedure is an alternate method of characterizing mostly MIMO systems defined by a large number of coordinates (DOFs). Different state space algorithms are applied, depending on whether the input has time derivatives or no time derivatives. Methods of conversion between state space and transfer function. MATLAB is quite useful to transform the system model from transfer function to state space, and vice versa. We also used the partial-fraction expansion of the ratio of two polynomials, block diagram algebra