Sensitivity Function with Applications to Analyze Frequency Characteristics under Conditions of System Parameter Varying

Shuo ZHANG, Sheng-guo ZHANG, Yu-xuan TANG, Chun-lan LUO


This paper focuses on analyzing the sensitivity of frequency characteristics of closed-loop system under reference input and external disturbance. In the first place, the sensitivity function of linear time-invariant control system is defined. Then the sensitivity functions of frequency characteristics including plant and controller parameters are derived in accordance with the closed-loop transfer functions and error transfer functions of closed-loop systems. And then the sensitivity of amplitude-frequency characteristics, while plant parameter and controller parameter are varying, is analyzed. Application results indicate the effects, which the plant parameter and controller parameter exert on the frequency characteristics of closed-loop systems, can be analyzed directly by sensitivity function. The analysis method about frequency characteristics facilitates the plant parameter design and the controller parameter determination for closed-loop systems.


Sensitivity function, Transfer function, Frequency characteristic, Parameter varying


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