滚珠丝杠式电动舵机非线性分析及控制策略研究
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摘要
电动舵机是导弹控制系统中重要的控制子系统，电动舵机根据自动驾驶仪控制指令进行偏转，改变导弹的飞行姿态，其性能直接影响导弹的性能。受到制造工艺、安装精度制约，电动舵机存在间隙、摩擦等非线性因素，同时随着电动舵机日趋向高带宽、轻量化方向发展，电动舵机组件的弹性变形直接影响了系统的运动性能，因此，研究间隙、摩擦、弹性变形等非线性因素对电动舵机伺服系统动态特性的影响，并选择合适的方法来减弱、抑制或消除这些因素影响相当重要。本文以滚珠丝杠式电动舵机为研究对象，对电动舵机中的非线性因素进行理论分析和仿真分析，并以此为基础展开相应的控制理论与方法研究，且进行了实验验证。论文主要包括以下五个方面的内容：
(1)依据系统总体指标，对电动舵机进行负载匹配、元件选型。同时根据第二类拉格朗日方程建立了电动舵机结构动力学模型，基于ANSYS对电动舵机进行模态及谐响应分析，得到舵机系统的固有频率和振型，并设计完成了满足要求的舵机结构。
(2)考虑到间隙、摩擦、弹性变形等非线性因素，采用笛卡尔坐标法建立舵机的多体动力学模型，并通过ADAMS仿真分析了非线性因素对舵机性能的影响。结果表明非线性因素对舵机性能具有严重影响。
(3)针对电动舵机系统的非线性、快时变等特点，设计改进自抗扰控制器，该控制器去除原有的跟踪微分器，采用线性误差反馈控制律和线性扩张状态观测器，引入Fal函数滤波系统。同时证明了系统的稳定性，提出了控制器参数的选择方法，基于NSGA-II算法对改进自抗扰控制器进行参数整定，通过ADAMS和MATLAB/Simulink构造机械和控制联合仿真平台，将建立的非线性舵机模型和改进自抗扰控制器进行联合仿真分析。通过不同条件下的输入输出分析，表明采用优化后的控制器，舵机系统动态和静态性能得到了改进。
(4)为了探索基于观测器设计非线性控制器，本文分别设计了基于扰动观测器的电动舵机非线性PID控制器与基于降维观测器的电动舵机PID_LQR控制器，通过仿真分析，验证了改进控制器的可行性。结论表明改进的控制器具有很好的动态特性和抗扰性。
(5)搭建半实物仿真平台，分别采用PI、自抗扰控制器和改进自抗扰控制器对滚珠丝杠式电动舵机进行控制，验证控制策略的可行性。实验结果表明跟踪±1°~±18°阶跃信号时，改进自抗扰控制器下系统上升时间为8~17ms，超调量为0~8.25%，稳态均方差为0.0094~0.0129；跟踪15sin(5πt)正弦信号时，改进自抗扰控制器能够消除位置平顶和速度死区，相位滞后0.06543rad，性能明显优于常规自抗扰控制器和PI控制器。该控制器减少了设计参数，位置跟踪超调量小，响应时间快，稳态均方差小，改善了舵机系统的动态和稳态性能。
本文充分考虑了舵机系统中的间隙、摩擦、弹性变形等非线性因素，提供了一种综合考虑刚柔-非线性-机电耦合作用的电动舵机系统性能研究方法。该方法为电动舵机的研究提供了新思路，对今后进一步研究具有重要的参考价值。
Electromechanical actuator (EMA) is an important sub-system in the control ofmissile. It is steerred by the signal stemming from autopilot, and changes the flightattitude of missile, thus it directly affects the capability of missile. Influenced bymanufacturing technology, assembly precision, EMA contains many nonlinearfactors, such as clearance and friction. Meanwhile, with the design of EMA tends tohigh bandwidth and lightweight design, the elastic deformation of EMA componentshave a serious effect on the performance of EMA. For these reasons, it is urgent tocarry out the research on influence of clearance, friction and elastic deformation ondynamic characteristics of EMA, and adopt efficient methods to lessen, inhibite orremove the adverse factors. This paper focuses on an EMA with ball screw drive.Firstly the theoretical analysis and simulation on nonlinear factors were presented.Then, control theory of EMA was studied based on above analysis. At last,experiments were performed. This paper is organized as follows.
(1)Firstly, according to the system indicators of EMA, load matching,component selecting of EMA were implemented. Secondly, structural dynamicmodel of EMA were established based on the Lagrange's equations of the secondkind. Finally, modal analysis and harmonic analysis of EMA were simulated byANSYS software, which obtained natural frequency and mode shape of EMA. As aresult, the structure meeting the requirements of system indicators was designed.
(2)Considering the influences of clearance, friction and elastic deformation onEMA, a simple model for EMA in the framework of multibody systems formulationwas presented by cartesian coordinates. Then, numerical simulation of nonlinearEMA was performed using ADAMS soft. The simulation results show that nonlinearfactors can significantly affect the dynamic response of EMA.
(3)Because electromechanical actuator (EMA) is a nonlinear, time-varyingservo system, the method of improved Active Disturbance Rejection Controller(ADRC) was proposed to improve the tracking performance of EMA. The newcontroller was established by removing nonlinear tracking-differentiator, andemploying linear state error feedback, linear extended state observer and Falfunction filter system. Simultaneously, the stability of the controller was proved andselection principle of the controller parameters were presented based on ModernControl Theory. In order to further improve controller performances, improvedADRC parameters were optimized by NSGA-II algorithm. United simulationincluding the model of nonlinear EMA and improved ADRC was established byADAMS and MATLAB/Simulink respectively. The feasibility of this controller wasdemonstrated through simulation under different input conditions. It is exactly toprove conclusively that the system static and dynamic performance is improved byoptimized controller.
(4)For the purpose of designing nonlinear controller based on the observer,nonlinear PID controller based on disturbance observer and PID_LQR Controllerbased on reduced-order observer were designed respectively in the paper. Throughsimulation, the validity of these methods was testified. Simulation results show thatboth improved controllers have good following performance and robustness.
(5)Semi-physical simulation system platform was builded. The performance ofPI controller, ADRC, improved ADRC were compared on EMA. Experimentalresults of improved ADRC indicate that rise time, overshoot and the steady statemean square deviation of EMA are8~17ms,0~8.25%,0.0094~0.0129respectivelywhen±1°~±18°angle are tracked. When the tracked angle is15sin(5πt), the phase error is0.06543rad, and there is no position flat crest and velocity dead space,whichhave the advantage over PI controller and traditional ADRC. It can be concludedthat the improved ADRC has a fast response, slight overshoot and high accuracy instability, as well as strong anti-disturbance and robustness. Thus, dynamicperformance and steady precision of the system are both improved.
The paper taked into account nonlinear factors in EMA, and presented rigidflexible, nonlinearity, electromechanical coupled research technique on EMA bycomprehensive analysis. In a word, the research comes up with a new study concepton EMA and has a certain reference value to the further study of EMA with ballscrew drive in the future work.
(1)依据系统总体指标，对电动舵机进行负载匹配、元件选型。同时根据第二类拉格朗日方程建立了电动舵机结构动力学模型，基于ANSYS对电动舵机进行模态及谐响应分析，得到舵机系统的固有频率和振型，并设计完成了满足要求的舵机结构。
(2)考虑到间隙、摩擦、弹性变形等非线性因素，采用笛卡尔坐标法建立舵机的多体动力学模型，并通过ADAMS仿真分析了非线性因素对舵机性能的影响。结果表明非线性因素对舵机性能具有严重影响。
(3)针对电动舵机系统的非线性、快时变等特点，设计改进自抗扰控制器，该控制器去除原有的跟踪微分器，采用线性误差反馈控制律和线性扩张状态观测器，引入Fal函数滤波系统。同时证明了系统的稳定性，提出了控制器参数的选择方法，基于NSGA-II算法对改进自抗扰控制器进行参数整定，通过ADAMS和MATLAB/Simulink构造机械和控制联合仿真平台，将建立的非线性舵机模型和改进自抗扰控制器进行联合仿真分析。通过不同条件下的输入输出分析，表明采用优化后的控制器，舵机系统动态和静态性能得到了改进。
(4)为了探索基于观测器设计非线性控制器，本文分别设计了基于扰动观测器的电动舵机非线性PID控制器与基于降维观测器的电动舵机PID_LQR控制器，通过仿真分析，验证了改进控制器的可行性。结论表明改进的控制器具有很好的动态特性和抗扰性。
(5)搭建半实物仿真平台，分别采用PI、自抗扰控制器和改进自抗扰控制器对滚珠丝杠式电动舵机进行控制，验证控制策略的可行性。实验结果表明跟踪±1°~±18°阶跃信号时，改进自抗扰控制器下系统上升时间为8~17ms，超调量为0~8.25%，稳态均方差为0.0094~0.0129；跟踪15sin(5πt)正弦信号时，改进自抗扰控制器能够消除位置平顶和速度死区，相位滞后0.06543rad，性能明显优于常规自抗扰控制器和PI控制器。该控制器减少了设计参数，位置跟踪超调量小，响应时间快，稳态均方差小，改善了舵机系统的动态和稳态性能。
本文充分考虑了舵机系统中的间隙、摩擦、弹性变形等非线性因素，提供了一种综合考虑刚柔-非线性-机电耦合作用的电动舵机系统性能研究方法。该方法为电动舵机的研究提供了新思路，对今后进一步研究具有重要的参考价值。
Electromechanical actuator (EMA) is an important sub-system in the control ofmissile. It is steerred by the signal stemming from autopilot, and changes the flightattitude of missile, thus it directly affects the capability of missile. Influenced bymanufacturing technology, assembly precision, EMA contains many nonlinearfactors, such as clearance and friction. Meanwhile, with the design of EMA tends tohigh bandwidth and lightweight design, the elastic deformation of EMA componentshave a serious effect on the performance of EMA. For these reasons, it is urgent tocarry out the research on influence of clearance, friction and elastic deformation ondynamic characteristics of EMA, and adopt efficient methods to lessen, inhibite orremove the adverse factors. This paper focuses on an EMA with ball screw drive.Firstly the theoretical analysis and simulation on nonlinear factors were presented.Then, control theory of EMA was studied based on above analysis. At last,experiments were performed. This paper is organized as follows.
(1)Firstly, according to the system indicators of EMA, load matching,component selecting of EMA were implemented. Secondly, structural dynamicmodel of EMA were established based on the Lagrange's equations of the secondkind. Finally, modal analysis and harmonic analysis of EMA were simulated byANSYS software, which obtained natural frequency and mode shape of EMA. As aresult, the structure meeting the requirements of system indicators was designed.
(2)Considering the influences of clearance, friction and elastic deformation onEMA, a simple model for EMA in the framework of multibody systems formulationwas presented by cartesian coordinates. Then, numerical simulation of nonlinearEMA was performed using ADAMS soft. The simulation results show that nonlinearfactors can significantly affect the dynamic response of EMA.
(3)Because electromechanical actuator (EMA) is a nonlinear, time-varyingservo system, the method of improved Active Disturbance Rejection Controller(ADRC) was proposed to improve the tracking performance of EMA. The newcontroller was established by removing nonlinear tracking-differentiator, andemploying linear state error feedback, linear extended state observer and Falfunction filter system. Simultaneously, the stability of the controller was proved andselection principle of the controller parameters were presented based on ModernControl Theory. In order to further improve controller performances, improvedADRC parameters were optimized by NSGA-II algorithm. United simulationincluding the model of nonlinear EMA and improved ADRC was established byADAMS and MATLAB/Simulink respectively. The feasibility of this controller wasdemonstrated through simulation under different input conditions. It is exactly toprove conclusively that the system static and dynamic performance is improved byoptimized controller.
(4)For the purpose of designing nonlinear controller based on the observer,nonlinear PID controller based on disturbance observer and PID_LQR Controllerbased on reduced-order observer were designed respectively in the paper. Throughsimulation, the validity of these methods was testified. Simulation results show thatboth improved controllers have good following performance and robustness.
(5)Semi-physical simulation system platform was builded. The performance ofPI controller, ADRC, improved ADRC were compared on EMA. Experimentalresults of improved ADRC indicate that rise time, overshoot and the steady statemean square deviation of EMA are8~17ms,0~8.25%,0.0094~0.0129respectivelywhen±1°~±18°angle are tracked. When the tracked angle is15sin(5πt), the phase error is0.06543rad, and there is no position flat crest and velocity dead space,whichhave the advantage over PI controller and traditional ADRC. It can be concludedthat the improved ADRC has a fast response, slight overshoot and high accuracy instability, as well as strong anti-disturbance and robustness. Thus, dynamicperformance and steady precision of the system are both improved.
The paper taked into account nonlinear factors in EMA, and presented rigidflexible, nonlinearity, electromechanical coupled research technique on EMA bycomprehensive analysis. In a word, the research comes up with a new study concepton EMA and has a certain reference value to the further study of EMA with ballscrew drive in the future work.
引文
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