基于滑动模态的永磁直线同步电动机鲁棒速度控制
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摘要
本文以国家自然科学基金项目和辽宁省教育厅基金项目为背景,以现代高档数控机床用永磁直线同步电动机(PMLSM)伺服进给系统为研究对象,针对其直接驱动的特点和鲁棒性及跟踪性能的双重要求,在滑模控制的基础上,结合反馈线性化、高阶滑模和奇异摄动等理论和方法,对变量间具有非线性耦合及存在参数变化、端部效应和负载扰动等诸多不确定性的PMLSM伺服系统的鲁棒速度控制问题进行研究。主要研究内容包括如下几个部分:
针对PMLSM的机电耦合问题,提出用非线性坐标变换和非线性状态反馈将系统解耦成相互独立的线性的电流和速度子系统。针对线性速度子系统设计速度跟踪控制器。并设计扩张滑模观测器来鲁棒观测反馈线性化所需要的动子加速度和负载扰动信号。利用Lyapunov稳定性理论对由反馈线性化、速度跟踪控制器和扩张滑模观测器所构成的非线性闭环系统的稳定性进行分析。
在考虑参数和负载扰动不确定性的情况下,提出用二阶滑模控制实现PMLSM伺服系统的速度和电流之间以及直、交轴电流之间的动态鲁棒解耦。分别独立设计速度控制器和直轴电流控制器的滑模面,采用二阶滑模控制的螺旋算法来实现鲁棒控制律的设计。并利用超螺旋算法来设计鲁棒微分器,对加速度信号进行鲁棒观测。该策略可较好地实现PMLSM伺服系统变量间的动态解耦,对负载和参数的变化具有很强的鲁棒性,同时可有效地削弱抖振。
针对PMLSM伺服系统的高阶非线性耦合模型,基于机电变量间的双时标特征,提出利用奇异摄动理论的块对角化法将模型分解成两个不同时标下的快变和慢变子系统。并采用超螺旋算法分别设计快变和慢变子系统的控制律,再统一时标,合成得到复合控制,以实现PMLSM伺服系统的高响应鲁棒速度控制。
以TMS320 LF2407A为核心构建PMLSM实验系统平台,采用双直线电动机对拖的加载实验方案,其中加载用PMLSM控制系统采用速度开环、电流闭环控制方式以模拟突加负载。分别在空载、负载及动子质量变化情况下,针对基于PI控制的矢量控制方法、二阶滑模控制方法和基于奇异摄动的二阶滑模控制方法进行对比实验研究,验证了控制策略的理论研究及仿真结果的有效性。
Taking the project supported by National Natural Science Foundation of China and by Education Office Foundation of Liaoning Province as background, this dissertation researches on the permanent-magnet linear synchronous motor(PMLSM) servo feeding system used in modern advanced NC machine tool. And based on sliding mode control, for the characteristic of direct drive and the double requirements of robustness and tracking performance, several theories and methods, such as feedback linearization, high-order sliding mode and singularly perturbation, are combined to solve the robust speed control problem of PMLSM servo system with some uncertainties such as nonlinear coupling between variables, parameters variations, end-effects and load disturbances. The main contents are as follows:
For the electromechanical coupling problem of PMLSM, the nonlinear coordinates transform and nonlinear state feedback are employed to decouple the servo system into two independent subsystems, that is, linear current and speed subsystems. Then, a speed tracking controller is designed for the linear speed subsystem. The mover acceleration and load disturbance signals needed by feedback linearization are observed robustly through an extended sliding mode observer. The stability of nonlinear closed-loop system composed of feedback linearization, speed tracking controller and sliding mode extended observer is analyzed by Lyapunov stability theory.
The second-order sliding mode control is employed to realize the dynamic robust decoupling between speed and currents, and between direct and quadrature axis currents of PMLSM servo system in the existence of parameters and load disturbances uncertainties. The sliding surfaces of speed controller and direct axis current controller are independently designed. The robust control laws are designed by twisting algorithm of second-order sliding mode control. And a robust differentiator is designed to observing the acceleration signal robustly based on the super twisting algorithm. This strategy preferably achieves the dynamic decoupling between variables of PMLSM servo system, has good robustness to load and parameters variations, and simultaneously weakens the chattering effectively.
For the high-order nonlinear coupling model of PMLSM servo system, the block-diagonalization method of singularly perturbation theory is used to decouple PMLSM servo system into fast and slow subsystems with two different time scales. The controllers of fast and slow subsystem are designed by sup-twisting algorithm of second-order sliding mode control respectively. Then the time scales are uniformed and the control signals are synthesized to obtain the composited control, to implement the high response robust speed control for PMLSM servo system.
The PMLSM experiment system is established using TMS320 LF2407A. A dual-linear motor system added load experiment scheme is employed, in which one of the two linear motor control system adopts speed open-loop and current closed-loop to simulate the suddenly added load. Vector control based on PI control, second-order sliding mode control and second-order sliding mode control based on singularly perturbation are experimentally compared and studied with no-load, load and mover quality variations respectively, which verify the feasibility of the theory studies and simulation results of the proposed control methods.
针对PMLSM的机电耦合问题,提出用非线性坐标变换和非线性状态反馈将系统解耦成相互独立的线性的电流和速度子系统。针对线性速度子系统设计速度跟踪控制器。并设计扩张滑模观测器来鲁棒观测反馈线性化所需要的动子加速度和负载扰动信号。利用Lyapunov稳定性理论对由反馈线性化、速度跟踪控制器和扩张滑模观测器所构成的非线性闭环系统的稳定性进行分析。
在考虑参数和负载扰动不确定性的情况下,提出用二阶滑模控制实现PMLSM伺服系统的速度和电流之间以及直、交轴电流之间的动态鲁棒解耦。分别独立设计速度控制器和直轴电流控制器的滑模面,采用二阶滑模控制的螺旋算法来实现鲁棒控制律的设计。并利用超螺旋算法来设计鲁棒微分器,对加速度信号进行鲁棒观测。该策略可较好地实现PMLSM伺服系统变量间的动态解耦,对负载和参数的变化具有很强的鲁棒性,同时可有效地削弱抖振。
针对PMLSM伺服系统的高阶非线性耦合模型,基于机电变量间的双时标特征,提出利用奇异摄动理论的块对角化法将模型分解成两个不同时标下的快变和慢变子系统。并采用超螺旋算法分别设计快变和慢变子系统的控制律,再统一时标,合成得到复合控制,以实现PMLSM伺服系统的高响应鲁棒速度控制。
以TMS320 LF2407A为核心构建PMLSM实验系统平台,采用双直线电动机对拖的加载实验方案,其中加载用PMLSM控制系统采用速度开环、电流闭环控制方式以模拟突加负载。分别在空载、负载及动子质量变化情况下,针对基于PI控制的矢量控制方法、二阶滑模控制方法和基于奇异摄动的二阶滑模控制方法进行对比实验研究,验证了控制策略的理论研究及仿真结果的有效性。
Taking the project supported by National Natural Science Foundation of China and by Education Office Foundation of Liaoning Province as background, this dissertation researches on the permanent-magnet linear synchronous motor(PMLSM) servo feeding system used in modern advanced NC machine tool. And based on sliding mode control, for the characteristic of direct drive and the double requirements of robustness and tracking performance, several theories and methods, such as feedback linearization, high-order sliding mode and singularly perturbation, are combined to solve the robust speed control problem of PMLSM servo system with some uncertainties such as nonlinear coupling between variables, parameters variations, end-effects and load disturbances. The main contents are as follows:
For the electromechanical coupling problem of PMLSM, the nonlinear coordinates transform and nonlinear state feedback are employed to decouple the servo system into two independent subsystems, that is, linear current and speed subsystems. Then, a speed tracking controller is designed for the linear speed subsystem. The mover acceleration and load disturbance signals needed by feedback linearization are observed robustly through an extended sliding mode observer. The stability of nonlinear closed-loop system composed of feedback linearization, speed tracking controller and sliding mode extended observer is analyzed by Lyapunov stability theory.
The second-order sliding mode control is employed to realize the dynamic robust decoupling between speed and currents, and between direct and quadrature axis currents of PMLSM servo system in the existence of parameters and load disturbances uncertainties. The sliding surfaces of speed controller and direct axis current controller are independently designed. The robust control laws are designed by twisting algorithm of second-order sliding mode control. And a robust differentiator is designed to observing the acceleration signal robustly based on the super twisting algorithm. This strategy preferably achieves the dynamic decoupling between variables of PMLSM servo system, has good robustness to load and parameters variations, and simultaneously weakens the chattering effectively.
For the high-order nonlinear coupling model of PMLSM servo system, the block-diagonalization method of singularly perturbation theory is used to decouple PMLSM servo system into fast and slow subsystems with two different time scales. The controllers of fast and slow subsystem are designed by sup-twisting algorithm of second-order sliding mode control respectively. Then the time scales are uniformed and the control signals are synthesized to obtain the composited control, to implement the high response robust speed control for PMLSM servo system.
The PMLSM experiment system is established using TMS320 LF2407A. A dual-linear motor system added load experiment scheme is employed, in which one of the two linear motor control system adopts speed open-loop and current closed-loop to simulate the suddenly added load. Vector control based on PI control, second-order sliding mode control and second-order sliding mode control based on singularly perturbation are experimentally compared and studied with no-load, load and mover quality variations respectively, which verify the feasibility of the theory studies and simulation results of the proposed control methods.
引文
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