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Simplifying ADRC design with error-based framework: case study of a DC–DC buck power converter

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Abstract

In this work, the problem of designing a robust control algorithm for a DC-DC buck power converter is investigated. The applied solution is based on a recently proposed error-based version of the active disturbance rejection control (ADRC) scheme, in which the unknown higher-order terms of the reference signal are treated as additional components of the system “total disturbance”. The motivation here is to provide a practical following of a reference voltage trajectory for the buck converter in specific cases where neither the analytical form of the desired signal nor its future values are known a’priori, hence cannot be directly used for control synthesis. In this work, the application of the error-based ADRC results in a practically appealing control technique, with compact structure, simplified control rule, and intuitive tuning (inherited from the conventional output-based ADRC scheme). Theoretical, numerical, and experimental results are shown to validate the efficacy of the error-based ADRC in buck converter control, followed by a discussion about the revealed theoretical and practical limitations of this approach.

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Notes

  1. In the considered average model, it has replaced the discrete input \(\mu \in \{0,1\}\), since PWM strategy is used here to generate governing signal from an analog input signal.

  2. Note that the linear system description is valid only as long as it can be ensured that no saturation effects occur in the coil. Otherwise, the inductance L would depend on the current \(i_L\) nonlinearly.

  3. Subscript “0” represents the nominal value of the parameter.

  4. Notation of signals dependence (on time, on states, etc.) will be omitted here and throughout the paper for presentation clearance (e.g., \(v(t,x)=: v(\,\cdot \,) =: v\)) with exception of instants when specification is notably important for the considered context.

  5. Overscore will be used hereinafter to distinguish signals reconstructed by the differentiator from the ones estimated by the observer (circumflex).

  6. One could include this term also in the ESO. However, since both reference (\(v_r\)) and output (\(v_o\)) are assumed here to be available at current time, it is thus reasonable to keep proportional action \(\mu _0 = k_0 e=k_0(v_r-v_o)\) to robustify the control design in the presence of estimation errors, inevitable in practical scenarios [19].

  7. Same observer parametrization has been done in Sect. 4.1.3.

  8. This emulates a scenario where the target signal comes from an outer-loop (i.e., cascade control) or from an entirely different, outside system.

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (No. 21620335).

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Authors and Affiliations

  1. Energy Electricity Research Center, International Energy College, Jinan University, Guangzhou, Zhuhai Campus, China

    Rafal Madonski

  2. Poznań University of Technology, Poznań, Poland

    Krzysztof Łakomy

  3. Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing, China

    Jun Yang

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  1. Rafal Madonski
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  2. Krzysztof Łakomy
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Correspondence to Rafal Madonski.

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Madonski, R., Łakomy, K. & Yang, J. Simplifying ADRC design with error-based framework: case study of a DC–DC buck power converter. Control Theory Technol. 19, 94–112 (2021). https://doi.org/10.1007/s11768-021-00035-1

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