Robust control of uncertain cylinder wake flows based on robust reduced order models

A technique for the construction of robust orthogonal flow bases, to be used for model reduction and flow control, is proposed. The construction accounts for the dependence of the flow structures with the control and variability in the flow conditions. Numerical examples, for the two-dimensional flow around a circular cylinder in laminar regime, are provided to demonstrate the robust character of the resulting reduced basis. The control of the flow is then considered with the objective of reducing the body drag in a full information framework, by blowing/suction at the cylinder surface. Different control strategies are considered, some being also robust in the sense that they incorporate variability in the flow conditions (Reynolds number). The improvements brought by the robust basis and robust control strategies is evidenced for the control of the reduced model and, more important, when the control laws determined for the reduced model are applied to the fully detailed flow model (DNS).     

End-wall effects on vortex shedding in planar shear flow over a circular cylinder

A prevailing controversy regarding the suppression of periodic vortex shedding from a circular cylinder embedded in a planar shear flow has been addressed. Three-dimensional computer simulations utilizing the advanced MGLET software [11] demonstrated the importance of the end-wall conditions. Earlier results from two-dimensional simulations at Re = 100 were reproduced only with free-slip conditions. With no-slip conditions imposed at one or both end-walls, the vortex shedding was suppressed near the no-slip boundary and the shedding pattern was substantially affected even at mid-span. The Strouhal number decreased when the shear-rate parameter was increased from 0.1 to 0.2, irrespective of the choice of boundary conditions.     

Output Feedback Boundary Control of a Ginzburg–Landau Model of Vortex Shedding

An exponentially convergent observer is designed for a linearized Ginzburg-Landau model of vortex shedding in viscous flow past a bluff body. Measurements are restricted to be taken collocated with the actuation which is applied on the cylinder surface. The observer is used in conjuction with a state feedback boundary controller designed in previous work to attenuate vortex shedding. While the theoretical results apply to the linearized system under sufficiently smooth initial data that satisfy the boundary conditions, simulations demonstrate the performance of the linear output feedback scheme on the nonlinear plant model     

Integrated direct/indirect adaptive robust motion trajectory tracking control of pneumatic cylinders

This paper studies the precision motion trajectory tracking control of a pneumatic cylinder driven by a proportional-directional control valve. An integrated direct/indirect adaptive robust controller is proposed. The controller employs a physical model based indirect-type parameter estimation to obtain reliable estimates of unknown model parameters, and utilises a robust control method with dynamic compensation type fast adaptation to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. Due to the use of projection mapping, the robust control law and the parameter adaption algorithm can be designed separately. Since the system model uncertainties are unmatched, the recursive backstepping technology is adopted to design the robust control law. Extensive comparative experimental results are presented to illustrate the effectiveness of the proposed controller and its performance robustness to parameter variations and sudden disturbances.     

A new analytical study of MHD stagnation-point flow in porous media with heat transfer

The similarity solution for the MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium gives a system of nonlinear partial differential equations. These equations are solved analytically by using a novel analytical method (DTM-Padé technique which is a combination of the differential transform method and the Padé approximation). This method is applied to give solutions of nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the Prandtl number, permeability parameter, Hartmann number and suction/blowing parameter on the velocity and temperature profiles.     

On the use of incomplete sensitivities for feedback control of laminar vortex shedding

A feedback control method based on incomplete sensitivities and gradient evaluation by complex variable method is proposed and applied to the problem of the control of the laminar vortex shedding past a circular cylinder. This procedure results in a low-cost control algorithm, which does not require to compute the gradient of the Navier–Stokes solution with respect to the controllers. For the sake of usability for practical applications, realistic sensors and actuators are used. Validation simulations aiming at controlling the drag of the cylinder are presented and compared with previous published results, proving the efficiency of the proposed method. Application to the control of the cylinder lift is also shown.     

自由时间最优控制问题的一种控制向量参数化方法

针对自由时间最优控制问题,提出一种控制向量参数化（CVP）方法.通过引入时间尺度因子,将自由时间最优控制问题转化为固定时间问题,并将终端时刻作为优化参数.基于CVP方法,最优控制问题被转化为一个非线性规划（NLP）问题.建立目标和约束函数的Hamiltonian函数,通过求解伴随方程获得目标和约束函数的梯度,采用序列二次规划（SQP）方法获得问题的数值解.对于控制有切换结构的优化问题,给出了一种网格精细化策略,以提高控制质量.补料分批反应器最优控制问题的仿真实验验证了所提出方法的有效性.     

DNS for flow separation control around an airfoil by pulsed jets

Direct numerical simulation (DNS) for flow separation and transition around a NACA-0012 airfoil with an attack angle of 4° and Reynolds number of 100,000 has been reported in our previous paper. The details of flow separation, formation of the detached shear layer, Kelvin-Helmholtz instability (inviscid shear layer instability) and vortex shedding, interaction of nonlinear waves, breakdown, and re-attachment are obtained and analyzed. The power spectral density of pressure shows the low frequency of vortex shedding caused by the Kelvin-Helmholtz instability still dominates from the leading edge to trailing edge. Based on our understanding on the flow separation mechanism, we try to reveal the mechanism of the flow separation control using blowing jets and then optimize the jets. DNS simulations for flow separation control by blowing jets (pulsed and pitched and skewed jets) are reported and analyzed. The effects of different unsteady blowing jets on the surface at the location just before the separation points are studied. The length of separation bubble is significantly reduced (almost removed) after unsteady blowing technology is applied. The mechanism of early transition caused by the blowing jets was found. A blowing jet with K-H frequency, sharp shape function (very small mass blowing), pitching and skewing obtained the best efficiency based on the increase of the ratio of lift over drag and decrease of blowing mass flow. In this work, a DNS code with high-order accuracy and high-resolution developed by the computational fluid dynamics group at University of Texas at Arlington is applied.     

Implementation of a transient adaptive sub-cell module for the parallel-DSMC code using unstructured grids

A method of transient adaptive sub-cells (TAS) suitable for unstructured grids that is modified from the existing one for the structured grids of DSMC is introduced. The TAS algorithm is implemented within the framework of a parallelized DSMC code (PDSC). Benchmarking tests are conducted for steady driven cavity flow, steady hypersonic flow over a two-dimensional cylinder, steady hypersonic flow over a cylinder/flare and the unsteady vortex shedding behind a two-dimensional cylinder. The use of TAS enables a reduction in the computational expense of the simulation since larger sampling cells and less simulation particles can be employed. Furthermore, the collision quality of the simulation is maintained or improved and the preservation of property gradients and vorticity at the scale of the sub-cells enables correct unsteady vortex shedding frequencies to be predicted. The use of TAS in a parallel-DSMC code allows simulations of unsteady processes at a level to be carried out efficiently, accurately and with acceptable computational time.     

分布参数系统边界控制的Haar小波算法

由于分布参数系统通常由偏微分方程描述,采用解析法求解分布参数系统最优边界控制问题,是非常难以解决的.正交函数逼近的方法在分布参数系统控制方面,已经取得了较好的效果.Haar小波作为正交基函数,利用小波的一些运算及变换矩阵,将分布参数系统转化为集总参数系统,再求其逼近解.仿真示例验证了所提出的算法是非常有效的.该方法为分布参数系统的控制算法提出了一条新的解决方案.     

Robust stochastic moment control via genetic-pole placement in communication network parameter setting

In this paper, the problems of stochastic robust approximate covariance assignment and robust covariance feedback stabilization, which are applied to variable parameters of additive increase/multiplicative decrease (AIMD) networks, are considered. The main idea of the developed algorithm is to use the parameter settings of an AIMD network congestion control scheme, where parameters may assign the desired network’s window covariance, with respect to the current network conditions. The aim is to search for the optimal AIMD parameters of a feedback gain matrix such that the objective functions defined via appropriate robustness measures and covariance assignment constraints can be optimized using an adaptive genetic algorithm (AGA). It is shown that the results can be used to develop tools for analyzing the behavior of AIMD communication networks. Quality of service (QoS) and other performance measures of the network have been improved by using the proposed congestion control. The accuracy of the controller is demonstrated by using MATLAB and NS software programs.     

Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers

Transient wake flow patterns and dynamic forces acting on a rotating spherical particle with non-uniform surface blowing are studied numerically for Reynolds numbers up to 300 and dimensionless angular velocities up to Ω=1. This range of Reynolds numbers includes the three distinct wake regimes i.e., the steady axisymmetric, the steady non-symmetrical and the unsteady with vortex shedding. The Navier–Stokes equations for an incompressible viscous flow are solved by a finite volume method in a three-dimensional, time accurate manner. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that unsteady three-dimensional wake flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects and thus, vortex shedding occurs even at Re=200. Global properties, such as the lift and drag coefficients, and the Strouhal number are also significantly affected. It is shown that the present data for the average lift and drag coefficients correlate well with:

C_L/(1+Ω)^3.6=0.11

C_D(1+20V_S)^0.2/(1+Ω)^Re/1000=24(1+Re^2/3/6)/Re

where V_S is the average surface blowing velocity normalized by the free stream velocity.     

Optimal control problems with multiple characteristic time points in the objective and constraints

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved.     

离散时滞系统的近似最优扰动抑制

研究了状态变量合有时滞的离散系统在外部扰动下的最优控制问题．通过引入一个灵敏度参数,将原系统的最优扰动抑制问题转化为一族不含超前项和时滞项的两点边值问题,并由此导出了最优扰动抑制控制器的这代近似设计方法．得到的最优扰动抑制控制律由解析的前馈一反馈项和伴随向量级数和形式的补偿项组成,截取伴随向量级数的有限和得到原系统的次优扰动抑制控制律．数值仿真表明该近似最优控制器对外部持续扰动具有良好的鲁棒性。     

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations

A numerical simulation of the flow past a circular cylinder which is able to oscillate transversely to the incident stream is presented in this paper for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved by a finite volume method with an industrial CFD code in which a coupling procedure has been implemented in order to obtain the cylinder displacement. A preliminary work is first conducted for a fixed cylinder to check the wake characteristics for Reynolds numbers smaller than 150 in the laminar regime. The Strouhal frequency f_S and the aerodynamic coefficients are thus controlled among other parameters. Simulations are then performed with forced oscillations characterized by the frequency ratio F = f₀/f_S, where f₀ is the forced oscillation frequency, and by the adimensional amplitude A. The wake characteristics are analyzed using the time series of the fluctuating aerodynamic coefficients and their power spectral densities (PSD). The frequency content is then linked to the shape of the phase portraits and to the vortex shedding mode. By choosing interesting couples (A, F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map. A second batch of simulations involving free vibrations (so-called vortex-induced vibrations or VIV) is finally carried out. Oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the time integration of the motion is realized by an explicit staggered algorithm which provides the cylinder displacement according to the aerodynamic charges exerted on the cylinder wall. Amplitude and frequency response of the cylinder are thus investigated over a wide range of reduced velocities to observe the different phenomena at stake. In particular, the vortex shedding modes have also been related to the frequency response observed and our results at Re = 100 show a very good agreement with other studies using different numerical approaches.     

The extended homotopy perturbation method and boundary layer flow due to condensation and natural convection on a porous vertical plate

The extended homotopy perturbation method (EHPM), which is an extension to the well-known homotopy perturbation method (HPM) due to He, is applied to derive the analytical solution of the boundary layer flow of falling vapour due to the condensation on a cold, porous vertical plate. The EHPM calculates the solution automatically by adjusting the scaling factor of the independent similarity variable normal to the plate. The results obtained by the EHPM are in excellent agreement with the exact numerical solution. Also an asymptotic solution, valid for a large suction parameter is developed which matches very well with the exact solution even for moderate values of the suction velocity. Finally, it is shown that the EHPM solution is also applicable to the moderate values of blowing across the plate.     

基于微分算子小波显式表示的分布参数系统最优逼近控制

基于微分算子在紧支撑正交小波基下的精确显式表示，给出了一种分布参数系统最优控制的逼近计算方法．将微分算子投影到小波空间，利用其矩阵表示形式，将分布参数系统的最优控制转化为集中参数系统最优控制问题．该方法不需要为边界条件重新构造基函数，在将偏微分方程转化为其常微分方程近似形式的过程中，不需要考虑边界条件的影响，因此计算方便、适用范围广，同时具有很高的精度和计算效率,可以对计算误差进行预测．利用该方法进行了基于Daubechies (db1)小波的仿真计算，并对计算结果进行了验证．     

Spectral simulations of an unsteady compressible flow past a circular cylinder

An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.     

有界扰动下约束非线性系统鲁棒经济模型预测控制EI北大核心CSCD

针对未知但有界扰动下约束非线性系统,提出一种新的鲁棒经济模型预测控制(Economic model predictive control,EMPC)策略,保证闭环系统对扰动输入具有输入到状态稳定性(Input-to-state stability,ISS).基于微分对策原理,分别优化经济目标函数和关于最优经济平衡点的鲁棒稳定性目标函数,其中经济最优性与鲁棒稳定性是具有冲突的两个控制目标.利用鲁棒稳定性目标最优值函数构造EMPC优化的隐式收缩约束,建立鲁棒EMPC的递推可行性和闭环系统关于最优经济平衡点相对于有界扰动输入到状态稳定性结果.最后以连续搅拌反应器为例,对比仿真验证本文策略的有效性.     

Behavior of micro-polar flow due to linear stretching of porous sheet with injection and suction

The boundary layer flow of a micro-polar fluid due to a linearly stretching sheet is investigated. The influence of various flow parameters like ‘suction and injection velocity through the porous surface’, ‘viscosity parameter causing the coupling of the micro-rotation field and the velocity field’ and ‘vortex viscosity parameter’ on ‘shear stress at the surface’, ‘fluid velocity’ and ‘micro-rotation’ are studied. The governing equations of the transformed boundary layer are solved analytically using homotopy analysis method (HAM). The convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. Comparison between the HAM and numerical solutions showed excellent agreement.