Order & Poles: Basics of Control Engineering

[dhruv.tara]

Homework Statement

In control engg. we define the order of the system as (or atleast as far as I have understood as) Nu/s^m*(s+a)(s+b)...

I cannot understand the base for such classification? Why are we classifying systems based on the number of poles they have on origin?

Homework Equations

The Attempt at a Solution

 

[CEL]

No, the order of the system is the number of poles (at the origin and elsewhere).

 

[Ecthelion]

CEL is correct.

Something to add however is the way you have written the transfer function - it's done for a purpose. In controls seeing how many poles are at the origin, you're s^m part of the denomenator, has many ramifications that can be crucial when interpreting a system response or designing for one. So in seeing, and perhaps formatting a transfer function in this fashion, it is an aesthetic move but can make things easier.

 

[dhruv.tara]

thanks guys I was confusing myself with the order and type of the system... good I could get that clear just in time :)

 

[DeeNos]

The order of a system in control engineering is determined by the number of poles it has on the origin. This classification is based on the mathematical representation of the system, specifically the transfer function, which is used to describe the relationship between the input and output of a system. The poles of a system are the values of s that make the denominator of the transfer function equal to zero, and the order is determined by the highest power of s in the denominator.

The reason for classifying systems based on the number of poles on the origin is because it provides important information about the behavior and stability of the system. Systems with more poles on the origin tend to have slower responses and are more difficult to control. On the other hand, systems with fewer poles on the origin have faster responses and are easier to control.

Additionally, the order of a system also affects the complexity of its design and control. Higher order systems require more complex control strategies, while lower order systems can often be controlled with simpler methods. Therefore, understanding the order of a system is important in determining the appropriate control approach.

In summary, the classification of systems based on their order and poles is a fundamental concept in control engineering, as it provides valuable information about the behavior, stability, and complexity of a system. It is a useful tool for engineers to design and control systems effectively.