سیستمهای کنترل خطی پاییز 1389 بسم ا... الرحمن الرحيم دکتر حسين بلندي - دکتر سید مجید اسما عیل زاده

Design Controller Via Root Locus

Design Via Root Locus: We follow the following approaches to study the root locus based design. 1. cascade compensators to improve the steady state error : PI Controller and (Phase) Lag Compensator 2. cascade compensators to improve the transient response: PD Controller and (Phase) Lead Compensator 3. cascade compensators to improve the steady state error and transient response: PID Controller and (Phase) Lag-Lead Compensator, Notch Filter

1- PI (Proportional and Integral) Controller, adding an integrator and a zero

Example: PI controller

15 Example: PI controller

16 Example: PI controller

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18 Example: PI controller

2- Phase Lag Compensator, adding a pole and a zero

Example: Phase Lag compensator

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34 Example: Phase Lag compensator

35 Example: Phase Lag compensator

36 Example: Phase Lag compensator

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3- PD Compensator, adding a zero

Example: PD controller

4- Phase Lead Compensator, adding a pole and a zero

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55 Example: Phase Lead compensator

56 Example: Phase Lead compensator

57 Example: Phase Lead compensator

58 Example: Phase Lead compensator

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60 Example: Phase Lead compensator

61 Example: Phase Lead compensator