# American Institute of Mathematical Sciences

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

 1 College of Electrical Engineering and Information Technology, Sichuan University, Chengdu 610065, China 2 Sichuan Institute of Aerospace Electronic Equipment, Chengdu 610100, China

*Corresponding author: Xiaodong Zeng

Received  September 2018 Revised  November 2018 Published  September 2019

Fund Project: 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)

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.

Citation: Bin Li, Xiaolong Guo, Xiaodong Zeng, Songyi Dian, Minhua Guo. An optimal pid tuning method for a single-link manipulator based on the control parametrization technique. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020107
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Performance Specifications
Manipulator angle $q(t)$
Angle velocity $\dot{q}(t)$
Torque $\tau(t)$
Manipulator angle $q(t)$ with disturbance
Angle velocity $\dot{q}(t)$ with disturbance
Torque $\tau(t)$ with disturbance
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