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This guide explores the impact of system types and control strategies on steady-state error and time response performance, focusing on the Parabolic Input and Final Value Theorem. It covers Stability tests, examples, and integral control's role in error reduction. The text details various system types and their implications through Step, Ramp, and Parabolic inputs, helping readers grasp key concepts for optimizing control system effectiveness.
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Parabolic Input: R(t) t (s) (Parabolic input error coefficient)
3. Steady State Error and Time Response Performance R ( s ) Step input Ramp input Parabolicinput Final Value Theorem:
R ( s ) Parabolic Step Ramp Final value theorem: Step Ramp Parabolic ess: Step Ramp Parabolic [cn]ss: Example 3.1 a) System type: 0 Stability test
R ( s ) Step Ramp Parabolic ess: Step Ramp Parabolic ess: Example 3.1 b) System type: 1 Integral control improves the steady state error performance System type : 0 Derivative control does not change the error performance
R ( s ) Overshoot Step Ramp Parabolic ess: Example 3.1 d) System type: 2 DcDp s0 System type: 0 DcDp s1 System type: 1 DcDp s2 System type: 2 DcDp s3 System type: 3
