Second Order SystemSnapshot of the front panel of the simulator:
Description of the system to be simulatedIn this lab the step response of a general or standard second order system is simulated (that is, the time response on the output of the system is calculated numerically). The mathematical model of the second order system which is simulated in this lab, is the differential equation
where
An alternative way of representing this model is by Laplace transforming the differential equation, and taking the ratio of output to input (in the Laplace domain), to get the transfer function from input u to output y:
AimTo develop a qualitative understanding of how the following (standard) parameters influate the step respons of a second order system: Gain K, relative damping factor z, natural (or undamped) resonance frequency w_{0}, and the step input height U. MotivationSecond order systems - as first order systems - constitute an important class of dynamic systems: There are many physical systems which behave (approximately) as second first order systems, e.g. stirred liquid tanks with thermal capacities in the liquid and in the heating element, DC-motors with armature dynamics and electro-mechanical dynamics, feedback control systems (e.g. process control systems and servomechanisms), sensors, and second order lowpass filters. TasksThe equality sign "=" in the following text can be regarded as "approximately equal to" (so that you do not have to enter exact numeric values). In several taskes below you are to give a value for the response-time, T_{r}. It is a convenient parameter to characterize how quick is a dynamic system with respect to it's step response. T_{r} is defined as the time it takes the step response to reach 63% of it's stationary (final) value. (For first order systems the response-time is equal to the time-constant.) It can be shown that for second order systems T_{r} is approximately equal to 1.5/w_{0} (it actually varies somewhat with z).
Updated 17. January 2008. Developed by Finn Haugen. E-mail: finn@techteach.no. |