Relación entre polos y respuestas en sistemas de segundo orden: una revisión

Abstract

Plants at industrial level show a different behavior according to their manufacturing and calibration conditions, this behavior can be represented mathematically with linear or higher order systems. In this section we will study the behavior of the response in time and in the complex plane of plants that behave as a second order system. The parameters that allow changing the response of these systems to an input signal are the natural frequency of the Wn system, the damping factor ζ and a gain K. In order to observe the change generated by the damping factor ζ in the response from the second order system to a step input and unit step. The response over time of these systems will be mathematically deduced by varying the damping factor ζ and the poles of each system will be plotted. There are 5 types of behavior in a stable second order system, which vary when changing the value of the damping factor ζ: Sub-damped case (0 <ζ <1), Unstable case (ζ <0), Critically damped case (ζ = 1), Case not damped (ζ = 0) and Case over damped (ζ> 1).