splane4

splane4 - Root locus techniques j 5 K=50 4 3 2 1 K=0 K=25 5...

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Root locus techniques K s(s+10) E(s) C(s) R(s) - + 1 j ϖ K=50 K=50 K=25 -5 K=0 K=0 σ σ 5 0 4 3 2 The root locus show the changes in the tran- sient response as the gain , K , is varied. K< 25 real poles, overdamped K = 25 multiple poles, critically damped K> 25 Complex poles, underdamped 1
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Looking at the underdamped poles ( K> 25), the real parts of the complex poles stay the same. The setting time is inversely propor- tional to the real parts for this second order system so we can say that the settling time will remain constant for underdamped responses regardless of the value of K . Also, as we increase the gain, the damping ratio diminishes, and the percent overshoot in- creases. The damped frequency of oscillator, equal to the imaginary part of the poles, also increases with the gain, resulting in a reduction of the peak time. Finally, since the root locaus never passes into the right half plane, the system is always sta- ble, regardless of the value of K , the gain. 2
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splane4 - Root locus techniques j 5 K=50 4 3 2 1 K=0 K=25 5...

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