Compensation strategies based on Bode step concept for actuator rate limit effect on first-order plus time-delay systems

  • Jie YuanEmail author
  • Shumin Fei
  • YangQuan ChenEmail author
Original paper


Rate limit of system actuators is one of the major restrictions in the physical world. However, in classical and modern control design, the actuator rate limit has always been neglected. The rate limit generates amplitude attenuation and phase delay of the control signal, which will deteriorate closed-loop system performance, and may even lead to system instability. In this study, the Bode step control method was applied to the first-order plus time-delay system to achieve a better tolerance of smaller rate limit value. A rate limit compensation strategy is proposed based on the describing function and the onset frequency of the rate limiter. Both illustrative example and hardware-in-the-loop experiments are given to show the effectiveness of Bode step controller and the proposed rate limit compensation method.


Actuator rate limit Describing function Bode step First-order plus time-delay system Bode integral formula 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of AutomationSoutheast UniversityNanjingChina
  2. 2.Mechatronics, Embedded Systems and Automation LabUniversity of CaliforniaMercedUSA

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