Respuesta sistema primer orden ante escalón: ganancia, constante de tiempo (teoría).

This video details the calculation of the step response (zero initial conditions) of the system \tau\frac{dy}{dt}+y=K u , whose transfer function is G(s)=\frac{K}{\tau s+1}. For a step of amplitude A, the result is y(t)=KA\cdot (1-e^{-t/\tau}). It is verified that at t=\tau, the output is 63% of the final value, and at t=3\tau it is 95%, and at t=4\tau it is 98% of the final value KA. A graphical example on 7/(5s+1) illustrates the response using Matlab. It is noted that for G(s)=b/(s+a) we would have to use K=b/a, \tau=1/a, so all conclusions would be equivalent. The final part of the video discusses the effect of a possible delay d (it's simple: everything happens d seconds later), and also graphically verifies everything related to the simulation of 7/(5*s+1)*exp(-2.5s). The video    • Modelos primer orden + retardo: propiedade...   , a continuation/complement to this one, emphasizes the concepts associated with this last case of "first-order with delay" and provides a first example of experimental identification of this type of system. The theoretical "ramp" response of first-order systems is discussed in the video    • Respuesta sistema primer orden ante rampa ...   , a continuation of this one. ____________ More information, links, and PDF/code at http://personales.upv.es/asala/YT/V/o... ____________ Subscribe if you are interested in modeling, identification, and process control in engineering. Thank you!, Antonio Sala Polytechnic University of Valencia (UPV)