Steady State Error
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This document discusses steady state error in control systems. It defines steady state error as the difference between the input and output of a system as time approaches infinity. The steady state error depends on the type of input signal (step, ramp, or parabolic) and the system type (type 0, 1, or 2). The document provides equations to calculate steady state error for different system types and input signals. For example, a type 0 system has a steady state error of A/(1+Kp) for a step input, where Kp is the system gain and A is the input amplitude.
Steady State Error
- 1. GREEN UNIVERSITY OF BANGLADESH Department: EEE (Eve) Prepared By: Md. Sahed Dewan ID# 143010021 Prepared For: Md. Joynal Abedin Lecturer, GUB Course Title: Control System
- 3. Introduction Control system analysis focus on three specifications: i) transient response, ii) stability & iii) steady-state errors. Steady state error is the difference between the input and output for a prescribed test input as t ∞ The steady-state error will depend on the type of input (step, ramp & parabolic) as well as the system type (0, I & II).
- 4. Test waveforms for evaluating steady state errors of position control system.
- 6. E(s) = R(s) – H(s) C(s) ∑ R(s) C(s) E(s) G(s) H(s) - + C(s) = E(s) G(s) C(s) = (R(s) – H(s) C(s)) G(s) C(s) + H(s) C(s) G(s) = R(s) G(s) C(s) (1 + H(s) G(s) ) = R(s) G(s) = C(s) R(s) G(s) 1 + H(s) G(s) Again, E(s) = R(s) – C(s) = R(s) – So, E(s) = G(s) R(s) 1 + G(s) R(s) 1 + G(s) For feedback, H(s) = 1 So, = C(s) = ● R(s) G(s) 1 + G(s) G(s) 1 + G(s) C(s) R(s)
- 7. Type 0: Step Input: Kp = G(s) lim s 0 Type 1: Ramp Input: Kv = s G(s)lim s 0 Type 2: Parabolic Input: Ka = s G(s) lim s 0 2
- 8. Steady State Error Type Step Ramp Parabolic 0 A (1+Kp) ∞ ∞ I 0 A Kv ∞ II 0 0 A Ka
- 9. Thank you