Control Systems (CS) Lecture (supplementary Slides)

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Presentation transcript:

Control Systems (CS) Lecture-14-15 (supplementary Slides) Time Domain Analysis of 2nd Order Systems Dr. Imtiaz Hussain Associate Professor Mehran University of Engineering & Technology Jamshoro, Pakistan email: imtiaz.hussain@faculty.muet.edu.pk URL :http://imtiazhussainkalwar.weebly.com/

Time Domain Specifications of Underdamped system

Time Domain Specifications (Rise Time)

Time Domain Specifications (Rise Time)

Time Domain Specifications (Rise Time)

Time Domain Specifications (Peak Time) In order to find peak time let us differentiate above equation w.r.t t.

Time Domain Specifications (Peak Time)

Time Domain Specifications (Peak Time) Since for underdamped stable systems first peak is maximum peak therefore,

Time Domain Specifications (Maximum Overshoot)

Time Domain Specifications (Maximum Overshoot)

Time Domain Specifications (Settling Time) Real Part Imaginary Part

Time Domain Specifications (Settling Time) Settling time (2%) criterion Time consumed in exponential decay up to 98% of the input. Settling time (5%) criterion Time consumed in exponential decay up to 95% of the input.