Characteristic Equation of Second Order System
We know in the Second order System, the open loop transfer function is [Tex]\frac{\omega^2_n}{S(S+2\delta \omega_n)}[/Tex]
Second Order System
The Transfer function is given as
[Tex]\frac{C(s)}{R(s)}=\frac{G(s)}{1+G(s)}[/Tex]
now putting the value [Tex]\frac{\omega^2_n}{S(S+2\delta \omega_n)}[/Tex] in the transfer function
we get transfer function as
[Tex]\frac{C(s)}{R(s)}=\frac{\omega^2_n}{s^2+2\delta \omega_ns+\omega^2_n}[/Tex]
now the root characteristics can be found as
[Tex]s=-\delta \omega_n ± \omega_n \sqrt{\delta^2-1}[/Tex]
Now C(s) can be written as
C(s)=[Tex]C(s)=\frac{\omega^2_n}{s^2+2\delta \omega_ns+\omega^2_n}R(s)[/Tex]
Where,
C(s)=Laplace transform of output signal
R(s)=Laplace transform of Input signal
[Tex]\omega_n[/Tex]=natural frequency
[Tex]\delta [/Tex]=damping ratio
Response of Second Order System
Control systems play a critical position in regulating and keeping the conduct of dynamic structures, making sure of balance and desired overall performance. One common form of machine encountered in the control idea is the second one-order system. The reaction of such structures is essential to understand for engineers and researchers operating in various fields. Now let’s move on to the concepts of pole and zero and the transient response to the second order system.
In contrast to the simplicity of first-order systems, second-order systems have many answers that need to be analyzed and explained. Changing first-order parameters only changes the response rate, while changing second-order parameters can change the response. For example, the second order may show similar behavior to the first order, or it may show temporary responses, either negative or weak, depending on the value of the product. In this article, we delve into the traits, analysis, and importance of the response of the second-order system on top of things theory.
Table of Content
- Second Order System
- Characteristics
- Step Response
- Transient Response Specification
- Types
- Mathematical Formula
- Importance