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An optimal pid tuning method for a single-link manipulator based on the control parametrization technique

  • *Corresponding author: Xiaodong Zeng

    *Corresponding author: Xiaodong Zeng 

This work was partially supported by a grant from National Natural Science Foundation of China under number 61701124, a grant from Science and Technology on Space Intelligent Control Laboratory, No. KGJZDSYS-2018-03, a grant from Sichuan Science and Technology Program under number 2019YJ0105, and a grant from Fundamental Research Funds for the Central Universities (China)

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  • A control parametrization based optimal PID tuning scheme for a single-link manipulator is developed in this paper. The performance specifications of the control system are formulated as continuous state inequality constraints. Then, the PID optimal tuning problem of the single-link manipulator can be formulated as an optimal parameter selection problem subject to continuous inequality constraints. These continuous inequality constraints are handled by the constraint transcription method together with a local smoothing technique. In such a way, the transformed problem becomes an optimal parameter selection problem in a canonical form, which can be solved efficiently by control parametrization method. Since approach is using the gradient-based method, the corresponding gradient formulas for the cost function and the constraints are derived, respectively. The effectiveness of the proposed method is demonstrated by numerical simulations.

    Mathematics Subject Classification: 90c30.


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  • Figure 1.  Performance Specifications

    Figure 2.  Manipulator angle $ q(t) $

    Figure 3.  Angle velocity $ \dot{q}(t) $

    Figure 4.  Torque $ \tau(t) $

    Figure 5.  Manipulator angle $ q(t) $ with disturbance

    Figure 6.  Angle velocity $ \dot{q}(t) $ with disturbance

    Figure 7.  Torque $ \tau(t) $ with disturbance

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