分离流动的电磁力主动控制
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摘要
主动流动控制是控制科学和流体力学交叉所产生的一个新的研究领域。主动流动控制通过向流场注入可控的能量,可抑制流动分离和转捩、提高流动稳定性,达到减少航行器在流体中的阻力、减少压力脉动、降低辐射噪声等效果。与被动控制方式相比,主动流动控制具有更高的效率和鲁棒性,因而具有广阔的应用前景,但也面临着更加复杂的理论和实际应用问题。
利用海水的弱导电性,通过电磁力来改变局部流场,是一种新兴的主动流动控制方式。本文以电磁力作用下圆柱绕流和大功角翼型绕流两种分离流动为控制对象,研究了有关的模型降阶、控制器设计和分析问题。
一般主动流动控制分为基于模型和不依赖模型两类方式,本文对两类控制方式都进行了研究。首先,在模型降阶研究中,利用有限体积法得到的流场分析数据,基于快照式本征正交分解和Galerkin投影方法,建立了电磁力作用下圆柱绕流的降阶模型,并利用改进的粒子群优化算法进行模型参数的校准,提高了降阶模型的精度。在降阶模型的基础上,应用非线性系统的耗散性理论设计了控制器。利用POD分解证明了当圆柱绕流处于稳定的振荡状态时,圆柱所受升力的频率与流场中任一点速.度振荡的频率相同,因此可以利用升力的测量信号来估计流场的状态。该控制器以布置在圆柱表面的电极和磁极作为作动器,将升力作为传感器反馈信号。通过改变圆柱壁面上的电极电压来耗散尾流中的脉动能量,设计的控制器能有效地减少圆柱绕流的振荡幅度。
其次,在不依赖于模型的主动流动控制策略研究中,提出了基于粒子群优化的极值搜索控制算法(PSOESC)。该算法可通过在线测量和寻优,使得控制器工作在最佳状态附近；为提高该算法的实用性,针对粒子群优化的随机性、群体性特点,提出状态序列的重排算法,以减少控制过程中的振荡和增益过大现象；还针对粒子群优化和分离流动的极限环振荡周期性特点,提出了PSOESC加速收敛算法。
最后,利用随机差分方程理论分析了PSOESC在噪声环境中的稳定性,给出了测量噪声干扰下保证粒子群优化算法收敛的充分条件,并分析了目标函数性态和噪声强度对寻优精度的影响。证明了有界测量噪声干扰的作用下标准PSO算法产生的序列所满足的动态方程的稳定性判据与无干扰时的一致。当标准PSO的参数满足条件时,噪声不会影响标准PSO算法是否收敛。该结论也可推广到时变参数PSO算法中去。但是,噪声会影响标准PSO寻优的准确性,即在噪声干扰下,PSO将只是收敛到真最优值的附近,其误差限的大小与目标函数的性态和噪声的强度有关。
数值分析和模型实验表明,本文提出的两种主动流动控制策略均可达到较好的控制效果。采用闭环控制可提高主动流动控制的效率,减少功率消耗、电化学腐蚀等不利影响。利用提出的模型降阶方法得到的电磁力作用下分离流动的低阶模型,可精确地描述流动的主要特征,并且具有较高的鲁棒性；基于低阶模型设计的控制策略可有效地抑制流动分离,从而减少圆柱绕流所产生的横向振荡力和阻力,或提高翼型的升阻比。提出的不依赖于模型的PSOESC控制策略可以得到相近的控制效果,并且鲁棒性更好。
Active flow control (AFC) is a new, interdisciplinary study area that crosses control sci-ence and fluid mechanics. By injecting energy into the flow, AFC can control the separation and transition, and reduce the drags of vehicles by improving the flow stability, or reduce the pressure fluctuations, or reduce the radiation noises and other effects. Compared with the passive control, active flow control is more efficient and robust, and thus has broad ap-plication prospects. However, AFC also faces with more complex theocratical and practical problems than passive flow control.
Applying electromagnetic force to to change the local flow field of weak electrical conductivity media, is a new active flow control approach. In this dissertation, two separated flow pattern, cylinder wake and high-attack-angle hydrofoil, controlled by the Lorentz force are studied. To fill the gap between theory and engineering, the model reduction, controller design and analysis issues are studied.
Active flow control can be classified into two types, model-based and model-independent. Both types of AFC are studied in this dissertation. First, the model reduction study, obtained using the finite volume method of data flow analysis, based on the snapshot-style proper orthogonal decomposition and Galerkin projection method, the electromagnetic force was established under the reduced-order model for flow around a cylinder. We apply the improved particle swarm optimization algorithm for model parameter calibration, to improve the accuracy of the model reduction. Based on the reduced order model, and by applying nonlinear system theory, a dissipative controller is designed.
Second, in the study of the model-independent control method, we propose a novel swarm-intelligent based control algorithm-particle swarm optimisation based extremum seeking control algorithm (PSOESC). The proposed PSOESC algorithm can steer the sys-tem state to the vicinity of the best point through online measurement and optimization. Furthermore, to enhance the practicality of the algorithm, we propose a state sequence re-arrangements algorithm to handle the random, swarm characteristics of the PSO. In the proposed algorithm, the control process is smoothed by reshuffle-then-insertion procedure to reduce the oscillation and to avoid large control gains. We also propose an accelerat-ing algorithm for PSOESC to accelerate the convergence rate of PSOESC for limit cycle control, by employing the periodical nature of the limit cycle and the characteristics of PSO.
Finally, we conduct a theoretical analysis of the stability of PSOESC in a noisy environ- ment by stochastic differential equations theory. Sufficient condition is given to guarantee the convergence of PSO in noisy environment. We also analyse the influence of the objective function and the noise intensity on the optimisation accuracy.
Numerical analysis and model experiments show that the proposed control strategies of the two studied active flow control method can both achieve better results than literatures. Closed-loop control can improve the efficiency and reduce the electrochemical corrosion. Using the proposed model reduction method, the flow separations are controlled by the electromagnetic force. The obtained reduced order model can accurately describe the main flow characteristics, and has high robustness. The control law designed based on the reduced order model can effectively reduce the flow separation, thereby reducing the resulting flow around a cylinder oscillating transverse force and resistance, or increase the airfoil lift-drag ratio. The proposed PSOESC can obtain similar results, but more robust.
利用海水的弱导电性,通过电磁力来改变局部流场,是一种新兴的主动流动控制方式。本文以电磁力作用下圆柱绕流和大功角翼型绕流两种分离流动为控制对象,研究了有关的模型降阶、控制器设计和分析问题。
一般主动流动控制分为基于模型和不依赖模型两类方式,本文对两类控制方式都进行了研究。首先,在模型降阶研究中,利用有限体积法得到的流场分析数据,基于快照式本征正交分解和Galerkin投影方法,建立了电磁力作用下圆柱绕流的降阶模型,并利用改进的粒子群优化算法进行模型参数的校准,提高了降阶模型的精度。在降阶模型的基础上,应用非线性系统的耗散性理论设计了控制器。利用POD分解证明了当圆柱绕流处于稳定的振荡状态时,圆柱所受升力的频率与流场中任一点速.度振荡的频率相同,因此可以利用升力的测量信号来估计流场的状态。该控制器以布置在圆柱表面的电极和磁极作为作动器,将升力作为传感器反馈信号。通过改变圆柱壁面上的电极电压来耗散尾流中的脉动能量,设计的控制器能有效地减少圆柱绕流的振荡幅度。
其次,在不依赖于模型的主动流动控制策略研究中,提出了基于粒子群优化的极值搜索控制算法(PSOESC)。该算法可通过在线测量和寻优,使得控制器工作在最佳状态附近；为提高该算法的实用性,针对粒子群优化的随机性、群体性特点,提出状态序列的重排算法,以减少控制过程中的振荡和增益过大现象；还针对粒子群优化和分离流动的极限环振荡周期性特点,提出了PSOESC加速收敛算法。
最后,利用随机差分方程理论分析了PSOESC在噪声环境中的稳定性,给出了测量噪声干扰下保证粒子群优化算法收敛的充分条件,并分析了目标函数性态和噪声强度对寻优精度的影响。证明了有界测量噪声干扰的作用下标准PSO算法产生的序列所满足的动态方程的稳定性判据与无干扰时的一致。当标准PSO的参数满足条件时,噪声不会影响标准PSO算法是否收敛。该结论也可推广到时变参数PSO算法中去。但是,噪声会影响标准PSO寻优的准确性,即在噪声干扰下,PSO将只是收敛到真最优值的附近,其误差限的大小与目标函数的性态和噪声的强度有关。
数值分析和模型实验表明,本文提出的两种主动流动控制策略均可达到较好的控制效果。采用闭环控制可提高主动流动控制的效率,减少功率消耗、电化学腐蚀等不利影响。利用提出的模型降阶方法得到的电磁力作用下分离流动的低阶模型,可精确地描述流动的主要特征,并且具有较高的鲁棒性；基于低阶模型设计的控制策略可有效地抑制流动分离,从而减少圆柱绕流所产生的横向振荡力和阻力,或提高翼型的升阻比。提出的不依赖于模型的PSOESC控制策略可以得到相近的控制效果,并且鲁棒性更好。
Active flow control (AFC) is a new, interdisciplinary study area that crosses control sci-ence and fluid mechanics. By injecting energy into the flow, AFC can control the separation and transition, and reduce the drags of vehicles by improving the flow stability, or reduce the pressure fluctuations, or reduce the radiation noises and other effects. Compared with the passive control, active flow control is more efficient and robust, and thus has broad ap-plication prospects. However, AFC also faces with more complex theocratical and practical problems than passive flow control.
Applying electromagnetic force to to change the local flow field of weak electrical conductivity media, is a new active flow control approach. In this dissertation, two separated flow pattern, cylinder wake and high-attack-angle hydrofoil, controlled by the Lorentz force are studied. To fill the gap between theory and engineering, the model reduction, controller design and analysis issues are studied.
Active flow control can be classified into two types, model-based and model-independent. Both types of AFC are studied in this dissertation. First, the model reduction study, obtained using the finite volume method of data flow analysis, based on the snapshot-style proper orthogonal decomposition and Galerkin projection method, the electromagnetic force was established under the reduced-order model for flow around a cylinder. We apply the improved particle swarm optimization algorithm for model parameter calibration, to improve the accuracy of the model reduction. Based on the reduced order model, and by applying nonlinear system theory, a dissipative controller is designed.
Second, in the study of the model-independent control method, we propose a novel swarm-intelligent based control algorithm-particle swarm optimisation based extremum seeking control algorithm (PSOESC). The proposed PSOESC algorithm can steer the sys-tem state to the vicinity of the best point through online measurement and optimization. Furthermore, to enhance the practicality of the algorithm, we propose a state sequence re-arrangements algorithm to handle the random, swarm characteristics of the PSO. In the proposed algorithm, the control process is smoothed by reshuffle-then-insertion procedure to reduce the oscillation and to avoid large control gains. We also propose an accelerat-ing algorithm for PSOESC to accelerate the convergence rate of PSOESC for limit cycle control, by employing the periodical nature of the limit cycle and the characteristics of PSO.
Finally, we conduct a theoretical analysis of the stability of PSOESC in a noisy environ- ment by stochastic differential equations theory. Sufficient condition is given to guarantee the convergence of PSO in noisy environment. We also analyse the influence of the objective function and the noise intensity on the optimisation accuracy.
Numerical analysis and model experiments show that the proposed control strategies of the two studied active flow control method can both achieve better results than literatures. Closed-loop control can improve the efficiency and reduce the electrochemical corrosion. Using the proposed model reduction method, the flow separations are controlled by the electromagnetic force. The obtained reduced order model can accurately describe the main flow characteristics, and has high robustness. The control law designed based on the reduced order model can effectively reduce the flow separation, thereby reducing the resulting flow around a cylinder oscillating transverse force and resistance, or increase the airfoil lift-drag ratio. The proposed PSOESC can obtain similar results, but more robust.
引文
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