<p>Based on the theory of viscoelasticity, a nonlinear dynamic model of the long-distance belt conveyor system is established considering PMSMs (Permanent Magnet Synchronous Motors). Then, a constraint following robust control is designed to accurately control the start and stop of the belt conveyor. The analysis then examines the speed, tension, and other parameters at critical positions during the startup phases with different desired speed curves. The braking phase is also investigated by dividing into four cases including unloaded free braking, fully loaded free braking, unloaded emergency braking, and fully loaded emergency braking. On this basis, four temperature conditions are set to study the slip ratio for the braking process: room temperature, extremely low temperature, monthly low temperature, and monthly high temperature. The main contributions of this study are threefold. First, a discrete dynamic model of the long-distance belt conveyor system is established using the Udwadia-Kalaba approach, incorporating external disturbances, belt viscoelasticity, and PMSM dynamics. Second, a robust constraint-following controller is designed for the underactuated system, addressing both matched and mismatched uncertainties. Third, a comprehensive dynamic analysis is conducted under various operating conditions, including different starting/stopping times, load states, and temperature environments. Comparative results with a traditional PID controller show that the proposed controller reduces the speed fluctuation rate from 3.57 to 1.42%, decreases the total system tension from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$0.757\times 10^6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.757</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$0.479\times 10^6{\textrm{N}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.479</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> <mtext>N</mtext> </mrow> </math></EquationSource> </InlineEquation>, and lowers the average slip ratio from 0.503 to 0.233, confirming its effectiveness in enhancing dynamic performance and operational safety.</p>

Dynamic analysis of nonlinear models for long-distance belt conveyors with multi motor drives

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发表日期：

2026年4月15日

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Yuan Zhang,
Qiying Li,
Xianghui Jia,
Dan Zhou,
Daoxian Zhang,
Dongyue Zhang,
Chenming Li

摘要

Based on the theory of viscoelasticity, a nonlinear dynamic model of the long-distance belt conveyor system is established considering PMSMs (Permanent Magnet Synchronous Motors). Then, a constraint following robust control is designed to accurately control the start and stop of the belt conveyor. The analysis then examines the speed, tension, and other parameters at critical positions during the startup phases with different desired speed curves. The braking phase is also investigated by dividing into four cases including unloaded free braking, fully loaded free braking, unloaded emergency braking, and fully loaded emergency braking. On this basis, four temperature conditions are set to study the slip ratio for the braking process: room temperature, extremely low temperature, monthly low temperature, and monthly high temperature. The main contributions of this study are threefold. First, a discrete dynamic model of the long-distance belt conveyor system is established using the Udwadia-Kalaba approach, incorporating external disturbances, belt viscoelasticity, and PMSM dynamics. Second, a robust constraint-following controller is designed for the underactuated system, addressing both matched and mismatched uncertainties. Third, a comprehensive dynamic analysis is conducted under various operating conditions, including different starting/stopping times, load states, and temperature environments. Comparative results with a traditional PID controller show that the proposed controller reduces the speed fluctuation rate from 3.57 to 1.42%, decreases the total system tension from $0.757\times 10^6$ $0.757 \times 10^{6}$ to $0.479\times 10^6{\textrm{N}}$ $0.479 \times 10^{6} N$ , and lowers the average slip ratio from 0.503 to 0.233, confirming its effectiveness in enhancing dynamic performance and operational safety.