柔性多体系统建模与控制
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摘要
随着航天、机器人和高速机车等领域相关技术的发展,轻质柔性材料在工程系统中获得广泛应用。系统运行速度的不断加快和精度要求的不断提高,使传统的基于多刚体动力学的建模与控制理论难以满足实践需求,需充分考虑柔性部件的存在对系统动力学特性的影响,将系统建模为柔性多体系统。以现代柔性航天器和柔性机械臂为主要实际背景,柔性多体系统的建模与控制研究是当前一个热点问题。柔性多体系统具有非线性、强耦合、分布参数和时变等特点,对建模与控制提出了较高的要求。因此开展柔性多体系统建模与控制研究具有重要的现实意义和较高的理论价值。
本文主要研究了柔性多体系统的建模与控制问题。基于柔性多体系统动力学研究进展,以具有hub-beam构型的柔性多体系统为例,研究了传统混合坐标模型、一次近似耦合模型和近似线性化模型的精度和使用范围,基于近似线性化模型、一次近似耦合模型分别研究了线性控制方法和非线性控制方法,构建了仿真实验系统,在此基础上对柔性多体系统的实验建模进行了研究。
柔性多体系统刚性大范围运动与柔性变形之间的耦合本质上是非线性的。混合坐标法是目前应用范围最广的建模方法,但是无法解释系统高速运行时观测到的动力刚化现象,相应地最近提出了一次近似耦合建模理论。本文首先研究了动力学理论建模问题。以hub-beam构型的柔性多体系统为例,对传统混合坐标法、动力刚化和一次近似耦合建模方法分别进行了论述,推导给出了三类模型的统一形式。研究比较了三类模型的模态特性和典型激励下的响应,对三类模型的精度和应用范围进行了讨论。
对于运行速度较低的柔性多体系统,忽略耦合非线性得到的线性化模型具有令人满意的精度。本文第三章研究了以动量轮为执行机构的hub-beam构型系统的线性控制问题。基于线性化耦合模型推导了动量轮驱动的hub-beam系统动力学模型,以此为基础提出了H_∞减振跟踪控制方案,并转化为H_∞标准问题框架进行求解。在引入了柔性结构振动控制致动器后,提出了自学习组合控制方案,对组合控制律和自学习律分别进行了证明。在考虑剩余模态影响的条件下,通过数值算例对两类线性控制方案进行了验证。
当柔性多体系统运行速度较高时,耦合非线性特征较显著。本文第四章研究了柔性多体系统的非线性控制问题。首先针对一类非线性系统提出了反馈LPV化方法,给出了详细讨论和证明。随后以运动速度较高时的hub-beam系统为例,基于一次近似耦合模型采用反馈LPV化方法,进一步对得到的LPV系统设计线性状态反馈控制律实现区域极点配置,并转化为线性矩阵不等式约束下的凸优化问题进行求解。针对引入了压电致动器的hub-beam系统,发展了一次近似耦合模型,并以此为基础设计了滑模变结构控制律,考虑了剩余模态的影响,对压电致动器最优配置进行了讨论。在考虑剩余模态影响的条件下,通过数值算例对两类非线性控制方案进行了验证。
动力学理论建模并根据实验进行修正的建模方法在许多情形下是可行的。对于不能用理论方法进行建模的情形,根据系统输入输出实验数据通过辨识得到数学模型是较好的选择。本文第五章研究了实验建模问题。首先构建了实验系统,对各部分原理和设计进行说明。采用频率域子空间连续系统辨识方法进行模型辨识,给出了多正弦激励信号的幅频整形设计方法。最后通过控制实验验证了辨识模型的有效性。
Along with the advances in the area of aerospace,robotics and high-speed vehicles, light-weight flexible material has been widely applied in engineering plants.Traditional modeling and control theory based on rigid multibody dynamics couldn't meet the practical demand of high-speed and high-precision operation.It's necessary to model such plants to be flexible multibody systems,so as to account for the effects of flexible appendages on system dynamics.Modeling and control of flexible multibody systems is one of the hot research topics currently,for which modern flexible spacecrafts and flexible manipulators are practical examples.Flexible multibody systems are characterized with nonlinearity,serious coupling,distributed-parameter and time-varying property.Consequently modeling and controller design is a challenging problem.The research in this field has intensive background in practice and prominent importance in theory.
In view of recent advances in the field of multibody system dynamics,this dissertation investigates modeling and control of flexible multibody systems. Throughout the dissertation,flexible multibody systems with the typical hub-beam configuration are selected as an example.The traditional hybrid co-ordinates model, first order approximation coupling(FOAC)model,and the approximately linearized model are investigated and compared.The accuracy and application slope of every model is discussed.Linear control schemes and nonlinear control schemes are proposed, based on the approximately linearized model and the FOAC model respectively.An experimental platform is built,and the designing procedure is given in detail.Finally experimental modeling study is performed on the platform.
The coupling between the large rigid motion and the flexible displacement is essentially nonlinear.Currently the hybrid co-ordinates method is the most widely used modeling method,but fails to accord with the "dynamic stiffening" phenomena in experiments when the motion speed is high.Accordingly,the first order approximation modeling theory was proposed recently.Theoretical modeling problem is discussed first in this dissertation.Taking the hub-beam system as an example,traditional co-ordinates method,dynamic stiffening and FOAC modeling theory are depicted respectively.The uniform simplified formulation of the three models is derived.Then modal characteristics and responses to typical excitations are investigated and compared.The accuracy and application slope are discussed.
For systems operating at low speed,ignoring the coupling nonlinearities will preserve satisfying accuracy.In Chapter Three linear control schemes are investigated based on the hub-beam system driven by a momentum wheel.Linear dynamic equation is derived,and a H_∞vibration-suppressing tracking scheme is proposed and transformed into a standard H_∞controller synthesis problem.Self-learning assembling control scheme is proposed with actuators introduced for vibration control purpose.The assembling control law and self-learning law are proved.The two schemes are verified through numerical simulations with the presence of residual modes.
For systems operating at high speed,coupling nonlinearities is not neglectable.In Chapter Four nonlinear control schemes are investigated.An approach to transforming a class of nonlinear systems into LPV systems by nonlinear state feedback is proposed first.The approach is proved and discussed in detail.The approach is then applied to an FOAC model of hub-beam systems,and linear state feedback is designed for the resultant LPV system.The regionally poles placement problem is converted into a convex optimization problem.with LMI constraints.The FOAC model is revised for the hub-beam system with piezoelectric actuators introduced.Then sliding mode variable structure control law is designed accounting for residual modes.Optimal placement of actuators is discussed.The two schemes are verified through numerical simulations with the presence of residual modes.
Theoretical modeling with some modifications according to experimental results is feasible for many cases.If not,identifying the mathematical model from experimental input and output data is an alternative approach.In Chapter Five experimental modeling is investigated.An experimental platform is built first.The designing principles and procedure are given in details.Frequency domain subspace identification for continuous systems is employed,and the preshaping method in multisine signal design stage is proposed.The identified model is validated by control performance.
本文主要研究了柔性多体系统的建模与控制问题。基于柔性多体系统动力学研究进展,以具有hub-beam构型的柔性多体系统为例,研究了传统混合坐标模型、一次近似耦合模型和近似线性化模型的精度和使用范围,基于近似线性化模型、一次近似耦合模型分别研究了线性控制方法和非线性控制方法,构建了仿真实验系统,在此基础上对柔性多体系统的实验建模进行了研究。
柔性多体系统刚性大范围运动与柔性变形之间的耦合本质上是非线性的。混合坐标法是目前应用范围最广的建模方法,但是无法解释系统高速运行时观测到的动力刚化现象,相应地最近提出了一次近似耦合建模理论。本文首先研究了动力学理论建模问题。以hub-beam构型的柔性多体系统为例,对传统混合坐标法、动力刚化和一次近似耦合建模方法分别进行了论述,推导给出了三类模型的统一形式。研究比较了三类模型的模态特性和典型激励下的响应,对三类模型的精度和应用范围进行了讨论。
对于运行速度较低的柔性多体系统,忽略耦合非线性得到的线性化模型具有令人满意的精度。本文第三章研究了以动量轮为执行机构的hub-beam构型系统的线性控制问题。基于线性化耦合模型推导了动量轮驱动的hub-beam系统动力学模型,以此为基础提出了H_∞减振跟踪控制方案,并转化为H_∞标准问题框架进行求解。在引入了柔性结构振动控制致动器后,提出了自学习组合控制方案,对组合控制律和自学习律分别进行了证明。在考虑剩余模态影响的条件下,通过数值算例对两类线性控制方案进行了验证。
当柔性多体系统运行速度较高时,耦合非线性特征较显著。本文第四章研究了柔性多体系统的非线性控制问题。首先针对一类非线性系统提出了反馈LPV化方法,给出了详细讨论和证明。随后以运动速度较高时的hub-beam系统为例,基于一次近似耦合模型采用反馈LPV化方法,进一步对得到的LPV系统设计线性状态反馈控制律实现区域极点配置,并转化为线性矩阵不等式约束下的凸优化问题进行求解。针对引入了压电致动器的hub-beam系统,发展了一次近似耦合模型,并以此为基础设计了滑模变结构控制律,考虑了剩余模态的影响,对压电致动器最优配置进行了讨论。在考虑剩余模态影响的条件下,通过数值算例对两类非线性控制方案进行了验证。
动力学理论建模并根据实验进行修正的建模方法在许多情形下是可行的。对于不能用理论方法进行建模的情形,根据系统输入输出实验数据通过辨识得到数学模型是较好的选择。本文第五章研究了实验建模问题。首先构建了实验系统,对各部分原理和设计进行说明。采用频率域子空间连续系统辨识方法进行模型辨识,给出了多正弦激励信号的幅频整形设计方法。最后通过控制实验验证了辨识模型的有效性。
Along with the advances in the area of aerospace,robotics and high-speed vehicles, light-weight flexible material has been widely applied in engineering plants.Traditional modeling and control theory based on rigid multibody dynamics couldn't meet the practical demand of high-speed and high-precision operation.It's necessary to model such plants to be flexible multibody systems,so as to account for the effects of flexible appendages on system dynamics.Modeling and control of flexible multibody systems is one of the hot research topics currently,for which modern flexible spacecrafts and flexible manipulators are practical examples.Flexible multibody systems are characterized with nonlinearity,serious coupling,distributed-parameter and time-varying property.Consequently modeling and controller design is a challenging problem.The research in this field has intensive background in practice and prominent importance in theory.
In view of recent advances in the field of multibody system dynamics,this dissertation investigates modeling and control of flexible multibody systems. Throughout the dissertation,flexible multibody systems with the typical hub-beam configuration are selected as an example.The traditional hybrid co-ordinates model, first order approximation coupling(FOAC)model,and the approximately linearized model are investigated and compared.The accuracy and application slope of every model is discussed.Linear control schemes and nonlinear control schemes are proposed, based on the approximately linearized model and the FOAC model respectively.An experimental platform is built,and the designing procedure is given in detail.Finally experimental modeling study is performed on the platform.
The coupling between the large rigid motion and the flexible displacement is essentially nonlinear.Currently the hybrid co-ordinates method is the most widely used modeling method,but fails to accord with the "dynamic stiffening" phenomena in experiments when the motion speed is high.Accordingly,the first order approximation modeling theory was proposed recently.Theoretical modeling problem is discussed first in this dissertation.Taking the hub-beam system as an example,traditional co-ordinates method,dynamic stiffening and FOAC modeling theory are depicted respectively.The uniform simplified formulation of the three models is derived.Then modal characteristics and responses to typical excitations are investigated and compared.The accuracy and application slope are discussed.
For systems operating at low speed,ignoring the coupling nonlinearities will preserve satisfying accuracy.In Chapter Three linear control schemes are investigated based on the hub-beam system driven by a momentum wheel.Linear dynamic equation is derived,and a H_∞vibration-suppressing tracking scheme is proposed and transformed into a standard H_∞controller synthesis problem.Self-learning assembling control scheme is proposed with actuators introduced for vibration control purpose.The assembling control law and self-learning law are proved.The two schemes are verified through numerical simulations with the presence of residual modes.
For systems operating at high speed,coupling nonlinearities is not neglectable.In Chapter Four nonlinear control schemes are investigated.An approach to transforming a class of nonlinear systems into LPV systems by nonlinear state feedback is proposed first.The approach is proved and discussed in detail.The approach is then applied to an FOAC model of hub-beam systems,and linear state feedback is designed for the resultant LPV system.The regionally poles placement problem is converted into a convex optimization problem.with LMI constraints.The FOAC model is revised for the hub-beam system with piezoelectric actuators introduced.Then sliding mode variable structure control law is designed accounting for residual modes.Optimal placement of actuators is discussed.The two schemes are verified through numerical simulations with the presence of residual modes.
Theoretical modeling with some modifications according to experimental results is feasible for many cases.If not,identifying the mathematical model from experimental input and output data is an alternative approach.In Chapter Five experimental modeling is investigated.An experimental platform is built first.The designing principles and procedure are given in details.Frequency domain subspace identification for continuous systems is employed,and the preshaping method in multisine signal design stage is proposed.The identified model is validated by control performance.
引文
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