Mathematical Expression For Calculating The Steady State Error
Steady State error can be calculated using final Value theorem
We know the transfer function of the unity negative feedback closed loop control system as,
C(s)/R(s)=G(s)/1+G(s)
⇒C(s)=R(s)*G(s)/1+G(s)……………(1)
The output of the summing point is
ess = lim t→ 0 e(t) = lim s→0 s*E(s)
e(t) = r(t) – c(t)
or, Taking Laplace Transform : E(s)=R(s)−C(s)…………(2)
Substituting equation 1 in 2, we get
E(s) = R(s) – [ R(s)*G(s)/1+G(s)]
ess = lim s→0 s*R(s) [ 1- G(s)/1+G(s)]
ess = lim s→0 [ s*R(s)/1+G(s)]
Steady State Errors for Unity Feedback Systems
In this Article, We will be going through Steady State Errors for Unity Feedback Systems in control systems, First, we will start our Article with an introduction to Steady State Errors, then we will through its two types, and then we will see mathematical Expression for calculating the Steady-State Error, At last, we will conclude our Article with its Advantages, Disadvantages, Applications and Some FAQs.
Table of Content
- What is Steady State Errors?
- Types of Steady State Errors For a Unity Feedback System
- Expression for Position, Velocity and Acceleration Error Constants
- Applications
- Advantages
- Disadvantages
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