Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (6): 1982-1989.doi: 10.13229/j.cnki.jdxbgxb20200600

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Moving horizon linear quadratic regulator control for ball and plate system with input constraints

Guang-xin HAN1(),Ju-le ZHAO2,Yun-feng HU3   

  1. 1.College of Information and Control Engineering，Jilin Institute of Chemical Technology，Jilin 132022，China
    2.College of Electrical Engineering，Northeast Electric Power University，Jilin 132011，China
    3.College of Communication Engineering，Jilin University，Changchun 130022，China
  • Received:2020-08-10 Online:2021-11-01 Published:2021-11-15

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Abstract:

This paper studies the trajectory tracking control of ball and plate system with actuator dynamic being considered. To realize precise trajectory tracking control, three steps are included as following. Firstly, according to the target trajectory, the feedforward control and target state are obtained using differential flatness technology. Secondly, tracking error system is established according to the target state and then a moving horizon Linear-Quadratic Regulator (LQR) controller is designed based on one of three fundamental principles of model predictive control. Thirdly, considering the practical constraints of control inputs, the target controller is achieved by solving Linear Matrix Inequalities（LMIs） under the condition of variable elliptic domain limits. Simulation results show that the closed-loop system has good trajectory tracking performance, steady state performance and robust performance under input constraints.

Key words: automatic control technology, ball and plate system, input constraints, differential flat, moving horizon linear quadratic regulator （LQR） control, variable elliptic domain limits

CLC Number: 

  • TP273

Fig.1

Quanser ball & plate experiment equipment"

Fig.2

Principle figure of direct servo system"

Fig.3

Comparing results before andafter model simplification"

Fig.4

Tracking of plum-type trajectory"

Fig.5

Trajectory tracking error"

Fig.6

Deviation of track tracking after amplification"

Fig.7

Control input of Moving horizon LQR"

Fig.8

Trajectory tracking under internal disturbance"

Fig.9

Trajectory tracking under external disturbance"

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