Quiz 1: System Identification Problem

Name:__Solution__

        This is the step response of a system to a step of magnitude 5.

• Given this step response, answer the following:
• Is this system first order or second order?  Why?
• The system cannot be a first order system because of the overshoot and subsequent decaying oscillations.  They are not found in first order continuous systems.
• Could it be higher than second order?  Why/Why not?
• The system could be higher than second order.  We would need more detailed information to discriminate between a second order and a higher order system.
• What is the transfer function of the system?   G(s) = _________________

(Give numerical values for the transfer function coefficients, and give numerical values for any parameters used to compute the transfer function.  In this context, numerical values means decimal values with no computations left undone.)
• To get the transfer function of the system note the following;
• Since the output settles out at 2 for an input of 5, the DC gain is 2/5 or 0.4.
• The overshoot goes to 2.65.  That's a 32.5% overshoot, and it means the damping ratio is around 0.32.
• The period of the oscillations is about (43-11) = 32 seconds.  That means that the frequency of oscillation is 6.28/32 = .196.  The correction factor for the damping ratio takes this up to .207
• That makes the transfer function, G(s) = [0.4*.043]/[s² + 2(.32)*.207)s + .043] or G(s) = .017/[s² + .1325s + .043]