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Design PID controllers for desired time-domain or frequency-domain response.
Weidong Zhang1, Yugeng Xi, Genke Yang
1Department of Automation, Shanghai Jiaotong University, PRC. wdzhang@mail.sjtu.edu.cn
ISA Transactions
|October 26, 2002
Summary
This study presents new methods for designing Proportional-Integral-Derivative (PID) controllers for systems with time delays. The developed controllers achieve specific time-domain and frequency-domain responses for both nominal and uncertain systems.
Area of Science:
- Control Systems Engineering
- Optimal Control Theory
- Process Control
Background:
- Practical control system design often requires specific time-domain (e.g., overshoot, rise time) or frequency-domain (e.g., resonance peak, stability margin) responses.
- While many Proportional-Integral-Derivative (PID) controller design methods exist, few address quantitative time- and frequency-domain specifications simultaneously.
Purpose of the Study:
- To design suboptimal PID controllers for stable processes with time delay.
- To achieve required quantitative time-domain and frequency-domain responses for nominal and uncertain systems.
Main Methods:
- Development of an H(infinity) PID controller using optimal control theory.
- Analytical derivation of controller parameters.
- Investigation and comparison of H(infinity), H2, and Maclaurin PID controllers.
Main Results:
- An H(infinity) PID controller was designed and its parameters derived analytically.
- The properties of the H(infinity) PID controller were investigated and compared with H2 and Maclaurin PID controllers.
- All three designed controllers demonstrated the ability to meet quantitative time-domain and frequency-domain response requirements.
Conclusions:
- The developed H(infinity) PID controller, along with H2 and Maclaurin PID controllers, effectively meets specified quantitative time- and frequency-domain performance criteria for systems with time delays.
- This work provides a framework for designing PID controllers that satisfy practical engineering specifications for both nominal and uncertain process systems.