| 摘要: |
| The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of
various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for
such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model
of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball
and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from
the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor
with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with
suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed
models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear,
simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is
unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID
control scheme. |
| 关键词: Ball and plate system · Correlation function · Model validation · Particle swarm optimization (PSO) · PSO PID controller |
| DOI：https://doi.org/10.1007/s11768-024-00208-8 |
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| 基金项目: |
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| Mathematical modelling of ball and plate system with experimental and correlation function-basedmodel validation |
| T. R. Dil Kumar1,S. J. Mija1 |
| (1 Department of Electrical Engineering, National Institute of Technology Calicut, Kozhikode 673601 Kerala, India) |
| Abstract: |
| The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of
various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for
such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model
of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball
and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from
the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor
with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with
suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed
models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear,
simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is
unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID
control scheme. |
| Key words: Ball and plate system · Correlation function · Model validation · Particle swarm optimization (PSO) · PSO PID controller |
