Cse ppt 39,38,29 (1)
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This document summarizes key aspects of a second-order control system's time domain response. It defines a general second-order transfer function and explains that systems can be overdamped, underdamped, undamped, or critically damped depending on the damping ratio ζ. The natural frequency ωn and damping ratio ζ are described. For an underdamped second-order system with 0< ζ <1 and ωn > 0, the document examines the system's response to a unit step input, focusing on the transient and steady state responses. Poles are described as complex if ζ< 1 and the system is parameterized by ζ and ωn.
Cse ppt 39,38,29 (1)
- 1. Time domain response of 2nd order control system By:- • Dharit Unadkat - 130870111039 • Jenish Thumar -130870111038 • Shivam Rai -130870111029 Guided By:- • Prof. Vishal Shah • Prof. Haresh Suthar Class:- EC-4th Sem, Parul Institute Of Technology, Limda.
- 2. Second – Order System • A general second-order system is characterized by the following transfer function: • We can re-write the above transfer function in the following form (closed loop transfer function):
- 3. • According the value of ζ, a second-order system can be set into one of the four categories: 1. Overdamped - when the system has two real distinct poles (ζ >1). 2. Underdamped - when the system has two complex conjugate poles (0 <ζ <1) 3. Undamped - when the system has two imaginary poles (ζ = 0). 4. Critically damped - when the system has two real but equal poles (ζ = 1).
- 4. - referred to as the un-damped natural frequency of the second order system, which is the frequency of oscillation of the system without damping. - referred to as the damping ratio of the order system, which is a measure of the degree of resistance to change in the system output. second o Poles; Poles are complex if ζ< 1
- 5. Time-Domain Specification Time-Domain Specification 22 2 2)( )( )( nn n sssR sC sT The system (2nd order system) is parameterized by ς and ωn For 0< ς <1 and ωn > 0, we like to investigate its response due to a unit step input Two types of responses that are of interest: (A) Transient response (B) Steady state response
- 6. 22 2 2)( )( )( nn n sssR sC sT Mapping the poles into s-plane
- 13. Thank You