基于谐波平衡法的伺服驱动系统机电耦合混合建模及谐振抑制方法研究

The coupling of electromechanical system is a common problem in servo drive system, which brings great difficulties to the resonance suppression control of the system. In order to solve the problem of low fusion degree between mechanical system and electrical system in the process of traditional electromechanical coupling modeling, the coupling mechanism of viscoelastic macro unit mechanical dynamics model and Park electrical model is studied. A hybrid modeling method of electromechanical coupling based on harmonic balance method is proposed. Using hyperbolic wave partial differential equation to characterize the torsional motion characteristics of viscoelastic macro element section. An analytical model of the deep fusion( rotational Speed, current, Flux and load) for servo drive system is obtained by harmonic balance method. In order to solve the problem that the violent change of rotational speed and load in complex working condition requires fast suppression of system resonance, a control method based on high order sliding mode and acceleration feedback is proposed. At the same time, the adaptive control strategy of working condition interval is used. The variation of load torque is estimated according to the change of system acceleration when the sliding mode line is approaching or leaving the sliding mode line, so that the electromagnetic torque is controlled under different working conditions to follow the load change, Different control methods are adopted according to rotational speed and load change factor to achieve the purpose of rapid suppression of resonance and improvement of system robustness.This project provides an effective method for electromechanical coupling modeling and resonance suppression control of servo drive system.

机电耦合是伺服驱动系统普遍存在的问题，给系统谐振抑制控制带来很大困难。针对传统机电耦合建模过程中机械系统与电气系统融合度不高的问题，深入研究粘弹性宏单元机械动力学模型和Park电气模型的耦合机理，提出一种基于谐波平衡法的机电耦合深度混合建模方法，运用双曲型波动偏微分方程来表征粘弹性宏单元截面扭转运动特性，采用谐波平衡法获得伺服驱动系统转速—电流—磁链—负载多物理量深度融合的解析模型；为解决复杂工况下转速和负载剧烈变化要求快速抑制系统谐振的问题，提出一种基于高阶滑模和加速度反馈相结合的控制方法，结合工况区间自适应控制策略，根据趋近或离开滑模线时系统加速度的变化值估算负载转矩的变化量，从而在不同工况下控制电磁转矩跟随负载变化，依据转速和负载变化因子采取不同的控制方法，以达到对谐振快速抑制和提高系统鲁棒性的目的。本项目研究内容为伺服驱动系统机电耦合建模和谐振抑制控制提供一种有效方法。

伺服驱动系统中电机与机械传动系统呈强耦合、时变等非线性特性，是一类典型的机电耦合系统。机械、电磁参数激励作用会导致伺服驱动系统产生机电耦合振动，严重影响系统可靠性。针对传统机电耦合系统建模过程中，机械系统与电气系统融合度不高的缺点，本项目基于Park变换下驱动电机的电压、磁链和转子运动方程，齿轮传动系统的非线性时变啮合特性，构建了多维度非线性四惯量机电耦合动力学模型；采用增量谐波平衡法求解了非线性四惯量机电耦合动力学模型的解析解，并通过变步长4~5阶Runge-Kutta数值求解方法进行对比，分析了分析电磁刚度、激励频率和传动综合误差等参数的变化对所建立的四惯量机电耦合系统非线性稳定性的影响，利用混沌理论对机电耦合振动的周期运动问题进行解析计算，揭示了多参数影响下四惯量机电耦合系统振动失稳机理。为解决复杂工况下转速和负载剧烈变化要求快速抑制系统谐振的问题，基于机电耦合系统多参数输入的特点，提出一种基于模型预测控制与陷滤波器相结合的复合控制方法，有效实现了伺服驱动系统运行过程中机械谐振的快速抑制和提升系统的鲁棒性。最后，搭建了伺服驱动系统机电耦合动态特性试验台架，验证了所提出复合控制方法的有效性。本项目成果可为伺服驱动系统机电耦合传动过程中的稳定性、可控性和可靠性提供重要参考。