MAE 340 Lecture Notes - Lecture 7: Step Response, Damping Ratio, Settling Time

• School: University at Buffalo
• Department: Mechanical & Aerospace Engr
• Course: MAE 340
• Professor: J.Mook

Document Summary

Find the unit step response for the 2nd-order system with the lti ode. Plot the step response, and use the plot to determine the following: X + 2 x + 12x = f (t: steady-state response, maximum overshoot, peak time, 90% rise time, 2% settling time. As the problem asks for the unit step response, it is assumed that the input f (t) is the unit step input: fstep(t) = (cid:26) 0. The standard step response also assumes that all the initial conditions are zero: x(0) = x(0) = 0. This system has a natural frequency of n = 12 3. 464 rad/sec, and a damping ratio of = 0. 29, so it is underdamped and we expect some amount of overshoot. The particular solution (also the steady-state response) is just xp(t) = xss = The solution procedure for the homogeneous solution will not be shown here, but it can be shown to be xh(t) = 0. 08704e t sin (3. 3166t + 4. 4195)