10-11-2012, 03:59 PM
LAG AND LEAD Compensation Techniques
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Compensation Techniques
• Performance specifications for the closed-loop system
• Stability
• Transient response Ts, Ms (settling time, overshoot)
or phase and gain margins
• Steady-state response ess (steady state error)
• Trial and error approach to design
Frequency response approach to compensator design
Information about the performance of the closed-loop system,
obtained from the open-loop frequency response:
• Low frequency region indicates the steady-state behavior.
• Medium frequency (around -1 in polar plot, around gain
and phase crossover frequencies in Bode plots) indicates
relative stability.
• High frequency region indicates complexity.
Requirements on open-loop frequency response
• The gain at low frequency should be large enough to give
a high value for error constants.
• At medium frequencies the phase and gain margins should
be large enough.
• At high frequencies, the gain should be attenuated as
rapidly as possible to minimize noise effects.
Compensators
• lead:improves the transient response.
• lag: improves the steady-state performance at the expense
of slower settling time.
• lead-lag: combines both
Lag compensation based on the frequency response
Procedure:
1. Determine the compensator gain Kcβ to satisfy the
requirement for the given error constant.
2. Find the frequency point where the phase of the gain
adjusted open-loop system (KcβG(s)) is equal to -180° +
the required phase margin + 5°~ 12°.
This will be the new gain crossover frequency c.
3. Choose the zero of the
octave to 1 decade below c .
4. Determine the attenuation necessary to bring the
magnitude curve down to 0dB at the new gain crossover
frequency