Follow the example, represent the poles of 2nd order systems with the damping ratio ? and...

 

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Follow the example, represent the poles of 2nd order systems with the damping ratio ? and the natural frequency wn, show the poles in the s-plane for different values of and corresponding step response. Canonical form: G(s) = 3 <=0 0 <3 <1 3= 1 (>1 Pole Locations joo jos, 1 -jar s-plane Step Response Type Undamped Follow the example, represent the poles of 2nd order systems with the damping ratio ? and the natural frequency wn, show the poles in the s-plane for different values of and corresponding step response. Canonical form: G(s) = 3 <=0 0 <3 <1 3= 1 (>1 Pole Locations joo jos, 1 -jar s-plane Step Response Type Undamped

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Detailed Explanation The representation of secondorder systems in control theory involves understanding the poles of the system which are critical for analyzing system behavior The poles are determined by two parameters the damping ratio and the natural frequency n The canonical form of a secondorder system is given by the transfer function Gs n 2 s 2 2 n s n 2 Here s is the complex variable n is the natural frequency is the damping ratio The poles of the system which are the roots of the denominator polynomial can be expressed as s n j n 1 2 The damping ratio determines the type of system response underdamped critically damped or overdamped The natural frequency n affects the frequency of oscillation in the system In control systems engineering secondorder systems play a crucial role and their behavior is often characterized by the damping ratio and natural frequency n The transfer function of a secondorder system in canonical form is given by Gs n 2 s 2 2 n s n 2 The poles of this transfer function which determine ... View the full answer