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

Bin Li; Xiaolong Guo; Xiaodong Zeng; Songyi Dian; Minhua Guo

doi:10.3934/dcdss.2020107

Article Contents

2020, Volume 13, Issue 6: 1813-1823. Doi: 10.3934/dcdss.2020107

This issue Previous Article Stabilization of a discrete-time system via nonlinear impulsive control Next Article A time-scaling technique for time-delay switched systems

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
^*Corresponding author: Xiaodong Zeng

Received: September 2018

Revised: November 2018

Published: April 2020

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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Abstract

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.

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Mathematics Subject Classification: 90c30.

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Figure 1. Performance Specifications

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Figure 2. Manipulator angle $ q(t) $

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

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Figure 4. Torque $ \tau(t) $

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

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

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

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