# ELE 302 Lecture Notes - Lecture 38: Damping Ratio, Settling Time, Matlab

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## Document Summary

The following more detailed answers will help you understand better the properties of the pid controllers in these two examples. The conjugate poles were at: 4 j 5. 46. The damping ratio was 0. 59, as required, and the frequency = 6. 77 rad/seconds. As expected, the stepeval check confirms that the specs were met: We can identify the value of integral controller gain by looking up the numerator expression in the derived transfer function: 40. 78 s k . The larger the integral gain is, the stronger integral action is. Control reduces gain margin, hence for the same value of proportional gain (here, k = 40. 78), the system will be more oscillatory. =0. 3, will correspond to the least oscillatory trace, trace # 3, and the largest. Integral gain, k =2, will correspond to the most oscillatory trace, trace # 1. Which integrator gain value, and which transfer function, result in a response that meets the transient specifications from question 1, i. e. po =

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