Iso-damping: Difference between revisions
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Iso-damping is a desirable system property refering to a state, where the phase [[Bode plot]] is flat, i.e., the phase derivative with respect to the frequency is zero, at a given frequency called the "tangent frequency" , <math>{\omega}_c</math>. At the "tangent frequency" the [[Nyquist plot|Nyquist curve]] tangentially touches the sensitivity circle and the phase Bode is locally flat which implies that the system will be more robust to gain variations. For systems that exhibit iso-damping property, the [[Overshoot (signal)|overshoots]] of [[Step response|step responses]] will remain almost constant for different values of the controller gain. This will ensure that the closed-loop system is robust to gain variations. <ref>YQ. Chen, C. Hu and K. L. Moore, "Relay Feedback Tuning of Robust PID Controllers With Iso-Damping Property," Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, Hawaii USA, December 2003.</ref> |
Iso-damping is a desirable system property refering to a state, where the phase [[Bode plot]] is flat, i.e., the phase derivative with respect to the frequency is zero, at a given frequency called the "tangent frequency" , <math>{\omega}_c</math>. At the "tangent frequency" the [[Nyquist plot|Nyquist curve]] tangentially touches the sensitivity circle and the phase Bode is locally flat which implies that the system will be more robust to gain variations. For systems that exhibit iso-damping property, the [[Overshoot (signal)|overshoots]] of [[Step response|step responses]] will remain almost constant for different values of the controller gain. This will ensure that the closed-loop system is robust to gain variations. <ref>YQ. Chen, C. Hu and K. L. Moore, "Relay Feedback Tuning of Robust PID Controllers With Iso-Damping Property," Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, Hawaii USA, December 2003.</ref> |
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The iso-damping property can be expressed as <math>\frac{d \angle G(s)}{ds}{|}_{s = {j\omega}_{c}} = 0</math> , or equivalently: |
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<math>\angle \frac{dG(s)}{ds}{|}_{s = {j\omega}_{c}} = \angle G(s){|}_{s = {j\omega}}</math> , |
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where <math>{\omega}_c</math> is the tangent frequency and <math>G(s)</math> is the open-loop system transfer function. |
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Revision as of 17:39, 7 March 2010
Iso-damping is a desirable system property refering to a state, where the phase Bode plot is flat, i.e., the phase derivative with respect to the frequency is zero, at a given frequency called the "tangent frequency" , . At the "tangent frequency" the Nyquist curve tangentially touches the sensitivity circle and the phase Bode is locally flat which implies that the system will be more robust to gain variations. For systems that exhibit iso-damping property, the overshoots of step responses will remain almost constant for different values of the controller gain. This will ensure that the closed-loop system is robust to gain variations. [1]
The iso-damping property can be expressed as , or equivalently:
,
where is the tangent frequency and is the open-loop system transfer function.
- ^ YQ. Chen, C. Hu and K. L. Moore, "Relay Feedback Tuning of Robust PID Controllers With Iso-Damping Property," Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, Hawaii USA, December 2003.