Second Order Underdamped System Identification

[@Stat1onary]

Ive never heard someone say the rise time is when it crosses the steady state number before but rather x at 90-95% of steady state value = t_r

[@apm]

That is a good alternative definition, especially when you have a first order or an overdamped or critically damped 2nd order (or higher) system. I use this definition for graphically fitting 2nd order underdamped systems as shown here: apmonitor.com/pdc/index.php/Main/SecondOrderGraphical The rise time (as I have it defined), is needed to relate to \tau_s and \zeta.

[@fl6365]

How to obtain the estimate of the damping and the natural frequency by means of a graphical survey of the step response? Having only the x-axis (time) and the y-axis (meters) available. Thanks

[@apm]

Check out this page: apmonitor.com/pdc/index.php/Main/SecondOrderGraphical

[@Debraj1978]

Can we use real time scipy optimizer to identify the underdamped system, like what you have done for overdamped system in other videos?

[@apm]

Yes, see Scipy and Gekko code here: apmonitor.com/pdc/index.php/Main/SecondOrderOptimization There is also a TCLab exercise at the course: apmonitor.com/do

[@apm]

Gekko is particularly good for real-time systems

[@vithiyananthanesanmanuelje3772]

WELL EXPLAINED SIR THANK YOU SIR

[@mohammedalsaeedi9417]

what if you only have poles not the graph

[@apm]

If you have the poles in the Laplace domain such as s=-3, s=-2 then you can reconstruct the transfer function also using the gain information: 4/((s+3)(s+2)). You can then give it a step input (1/s) and then calculate an inverse Laplace transform to get the analytic solution. More information is here: apmonitor.com/pdc/index.php/Main/TransferFunctions