3. Steady State Error and Time Response Performance

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3. Steady State Error and Time Response Performance ) s ( R Final Value Theorem: Parabolic input Step input Ramp input

) s ( R E(s): Laplace transform of the error G(s): Forward path transfer function Steady state error:

System type: Roots at s=0 of the denominator of the forward path transfer function denote the sytem type. Example: System type: 1 System type: 2 System type: 0 System type: 1

Position error coefficient Step Input: Step input ) s ( R Position error coefficient System type: ess 1

Velocity error coefficient Ramp Input: ) s ( R Ramp input Velocity error coefficient System type: ess 1 2

Acceleration error coefficient Parabolic Input: Parabolic input ) s ( R Acceleration error coefficient System type: ess 1 2 3

Example 3.1 a) ) s ( R System type: 0 Stability test Final value theorem: Step Ramp Parabolic ess: Step Ramp Parabolic [cn]ss: Step Ramp Parabolic System type: 0 Stability test

Integral control improves the steady state error performance Example 3.1 b) ) s ( R ess: Step Ramp Parabolic System type: 1 Integral control improves the steady state error performance ess: Step Ramp Parabolic System type : 0 Derivative control does not change the error performance

Example 3.1 d) ) s ( R System type: 2 DcDp  s0 System type: 0 ess: Step Ramp Parabolic System type: 2 DcDp  s0 System type: 0 Overshoot DcDp  s1 System type: 1 DcDp  s2 System type: 2 DcDp  s3 System type: 3

Example 3.2: ) s ( R System type: 0 ess: Step Ramp Parabolic Stability

Integral control improves the steady state error performance Example 3.3 : ) s ( R Sistem tipi: 1 Integral control improves the steady state error performance ess: Step Ramp Parabolic

Derivative control does not change the error performance Örnek 3.4 : ) s ( R Sistem tipi: 0 ess: Step Ramp Parabolic Derivative control does not change the error performance