In The Name of Allah The Most Beneficent The Most Merciful 1

ECE4545: Control Systems Lecture: Transient Characteristics Engr. Ijlal Haider UoL, Lahore 2

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Characteristics of System Response  Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass suspended from a spring, for example.  Frictional losses damp the system and cause the oscillations to gradually decay in amplitude towards zero. 4

Natural Frequency  The natural frequency of a second-order system is the frequency of oscillation of the system without damping. 5

Damping Ratio  In engineering, the damping ratio is a measure of describing how oscillations in a system die down after a disturbance.  The damping ratio is a measure of describing how rapidly the oscillations decay from one bounce to the next. 6

Oscillation Modes  Were the spring-mass system completely lossless, the mass would oscillate indefinitely, each bounce of equal height to the last. This hypothetical case is called undamped.  If the system contained high losses, for example if the spring-mass experiment were conducted in a viscous fluid, the mass could slowly return to its rest position without ever overshooting. This case is called overdamped.  Commonly, the mass tends to overshoot its starting position, and then return, overshooting again. With each overshoot, some energy in the system is dissipated, and the oscillations die towards zero. This case is called underdamped.  Between the overdamped and underdamped cases, there exists a certain level of damping that the system will just fail to overshoot and will not make a single oscillation. This case is called critical damping. 7

General Second Order System  Poles:  Damping Ratio and Oscillation Modes 8

Transient Characteristics  Peak Time:  Settling Time:  Overshoot: 9

Transient Characteristics  Rise Time 10

Transient Characteristics and Location of Poles  For Under damped case: 11

Effect of Pole Location 12

Dominant Closed Loop Poles  Poles having a zero nearby have less effect on the transient response  Poles at a distant location from origin have less effect on transient response  Poles located near origin are dominant because they decay slowly 13

Thank You! 14