Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.     

Stability analysis of supersonic entropy layers including shock effects

The prediction of the laminar/turbulent transition location in supersonic boundary layers plays an important role to accurately compute aerodynamic forces and heating rates for the aerodynamic design and control of hypersonic vehicles. The stability characteristics of supersonic boundary layers depend e.g. on nose bluntness, transverse curvature, wall temperature, shock waves, etc. Most parameters can be theoretically investigated by performing conventional stability calculations with vanishing or asymptotic perturbation conditions at the far field. In this approach the formation of a shock in front of the leading edge of a blunt body is ignored. However, to improve the understanding of the interaction between instability waves originating inside supersonic boundary layer with those coming from the inviscid entropy layer, the presence of the shock has to be taken into account. This paper presents a method, how shock effects can be physically consistently included in stability calculations. The outer free‐stream boundary conditions are replaced by appropriate shock conditions. The required perturbation equations can be derived from the linearized unsteady Rankine‐Hugoniot equations, accounting for the effect of shock oscillations due to perturbated waves which originate from the flow field windward of the shock.     

The torsion of a viscoelastic plate in an unsteady flow

The stability of the equilibrium position of a viscoelastic plate, subjected to torsional strain and effect of the free airflow is investigated. The unsteadiness of the flow is taken into account by introducing integral terms into the moments of the aerodynamic forces acting on the plate. In a neighbourhood of the equilibrium position, a general solution of a Volterra-type integro-differential equation with partial derivatives is constructed in the form of a Fourier series, as a function of the longitudinal coordinate of the plate with coefficients that are the power series in the small parameters introduced. The stability of the plate equilibrium in the unstrained state is analysed in the case when there are small perturbations (possibly, discontinuous) of the flow velocity. The stability under persistent perturbations of the equilibrium of the strained plate with respect to non-linear perturbing forces and perturbations of its shape at the instant of time preceding the specified initial instant is also investigated.     

Numerical study of helicopter blade–vortex mechanism of interaction using the potential flow theory

The blade–vortex interaction (BVI) phenomenon plays a key role in the rotorcraft aerodynamics. Numerical investigations of BVI using classical CFD approaches are computationally expensive. In the present research we propose a numerical approach, based on the potential flow theory, for the numerical investigation of helicopter blade–vortex mechanism of interaction. This approach overcomes the computational expenses posed by the CFD techniques. The influence of vertical miss distance, angle of attack, airfoil camber, and vortex strength on the helicopter blade–vortex mechanism of interaction is subject of investigation. The study reveals that the magnitude of the aerodynamic coefficients decreases with the increase of vertical miss distance and angle of attack, and the decrease of vortex strength and core size.     

基于BP网络和RBF网络的模糊系统建模

Ｗｈｅｎａｐｐｌｙｉｎｇａｆｕｚｚｙｃｏｎｔｒｏｌｍｅｔｈｏｄｏｒａｎｉｎｔｅｌｌｉｇｅｎｃｅｃｏｎｔｒｏｌｍｅｔｈｏｄｔｏａｎｅｆｆｅｃｔｉｖｅｃｏｎｔｒｏｌｏｖｅｒａｃｏｍｐｌｅｘｓｙｓｔｅｍ,ｉｔｉｓｓｏｍｅｔｉｍｅｓｎｅｃｅｓｓａｒｙｔｏｉｄｅｎｔｉｆｙｓｙｓｔｅｍａｔｉｃｓｔｒｕｃｔｕｒｅａｎｄｐａｒａｍｅｔｅｒｓ．Ｍａｔｈｅｍａｔｉｃａｌｌｙ,ｉｔｉｓｊｕｓｔｔｈｅｐｒｏｂｌｅｍｓｏｆｕｎｉｖｅｒｓａｌｆｕｎｃｔｉｏｎａｌａｐｐｒｏｘｉｍａｔｉｏｎａｎｄｆｕｎｃｔｉｏｎａｐｐｒｏｘｉ…     

Modeling and control of parafoils based on computational fluid dynamics

The determination of aerodynamic parameters of parafoil canopies has been a crucial issue because it affects the model precision. To calculate the aerodynamic coefficients of a canopy, the lifting-line theory has been used in the traditional method. However, because of the existence of leading-edge incisions, there are some restrictive assumptions in lifting-line theory when one is calculating the aerodynamic coefficients of a canopy. Therefore in this article we calculate the aerodynamic coefficients on the basis of computational fluid dynamics. As an improvement, the effects of a leading-edge incision and trailing-edge deflection are considered. Firstly, lift and drag coefficients are obtained by use of computational fluid dynamics. Then the least-squares method is used to identify incision and deflection factors. Furthermore, an eight-degrees-of-freedom mathematical model of a parafoil system is established on the basis of the parameters obtained. Finally, a novel control algorithm, generalized predictive control based on a characteristic model, is applied to the system. The precision of the model established and the effectiveness of the proposed control method are validated by simulation and airdrop testing.     

A new correlation method for the aerodynamic service loads determination of a rigid wing based on CFD analysis

A new correlation method for the aerodynamic service loads determination of a rigid wing based on CFD analysis is presented. All flight conditions can be handled by the proposed method. The derived correlation equations are achieved by considering a training fighter aircraft as a prototype. Each wing of aircraft is divided into thirty three parts in the span wise direction. Extensive numerical solutions have been attempted by varying a number of parameters that directly affect the wings aerodynamic loads, such as Mach numbers, angle of attack, control surfaces deflections and etc. For each set of input parameters, the corresponding aerodynamic loads applied to different wing parts are calculated. The resulted loads and the corresponding input parameters are incorporated into a linear regression method in order to develop the appropriate correlation equations. The outputs of the developed equations are the aerodynamic loads at each part of the wing based on the independent variables, which are the above mentioned input parameters. The validity of the developed equations is shown by comparing the loads obtained from the latter equations with the corresponding ones calculated through numerical analysis for different flight conditions. The correlation equations can now be used to calculate the aerodynamic loads at each part for any set of arbitrary values assigned to the input parameters.     

Nonlinear Dynamic Modelling of a Gas Engine Using an RBF-Network

A Radial Basis Function network (RBFN) is used to obtain a model of a gas engine, an unstable two-input/single-output system (MISO-system), to be used for the design of the speed control system. The RBFN-centers are chosen using the stepwise orthogonalization algorithm, and an input space compression which helps to avoid sparse data sets is presented. The influence of noisy data is investigated in a nonlinear system example, in order to find the cause of the model errors in the case of the gas engine model. The quality of the nonlinear RBFN-model is demonstrated by comparing measured and simulated data.     

柔长结构气固耦合的线性与非线性气动力理论

针对柔性结构与风在三方向相互作用的特点,在合理的结构节段力学模型的基础上,建立了新的气动力模型,即三分力系数C_i=C_i(β(t),θ),(#em/em#=D,L,M)不仅是瞬时攻角的函数,而且也是转速的函数,并依据“片条理论”与改进的“准静态理论”,提出了推导结构节段模型与风相互作用的线性与非线性气动力项的方法,从而将土木工程中柔性结构与风的相互作用的线性与非线性理论集中到一个模型中.对于线性气动力部分,给出了与经典气动力公式中相对应的颤振导数的半解析表达式.对于非线性气动力部分,给出了扭转气动耦合的非线性气动力表达式,并给出了Tacoma大桥扭转非线性运动的控制方程,其形式与结果与V.F.B-m的相吻合.     

Betrachtungen zu den Hauptproblemen der mathematischen Aussenballistik

Summary The paper provides a short survey of the actual state of the theoretical exterior ballistics. In particular the fundammental equations defining the motion of a rotating projectile are given in a form suitable for numerical calculation. Then, using the argument that a projectile possesses full rotational and also mirror summetry, the explicit development of the force and moment components is given in terms of the linear and angular velocities. Finally this development is compared with the experimentally known aerodynamic coefficients and stability derivatives.     

Identification and adaptive control: An application to flight control systems

This paper presents the first results obtained in the application of stochastic control theory to flight control problems. It involves identification and adaptive control of an aircraft which operates over a wide range of environmental conditions that affect its dynamic characteristics. The bulk of the paper deals with theidentification problem of estimating stability derivatives in the presence of turbulence. Simulation results are presented both for identification and control (windgust alleviation and desired response to pilot input). While no practical implementation is reported, the implications for such implementation appear to be promising.The author is indebted to Mr. K. Iliff for all the simulation results using the IBM 360-91 at UCLA. The many helpful discussions with Dr. H. Rediess are gratefully acknowledged. Thanks are also due to Mr. Jiri Ruzicka for lending a helping hand throughout.     

Stability of Markovian jump neural networks with impulse control and time varying delays

This paper is concerned with the stability of delayed recurrent neural networks with impulse control and Markovian jump parameters. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. By applying the Lyapunov stability theory, Dynkin’s formula and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the exponential stability of the equilibrium point. Moreover, three numerical examples and their simulations are given to show the less conservatism and effectiveness of the obtained results. In particular, the traditional assumptions on the differentiability of the time varying delays and the boundedness of their derivatives are removed since the time varying delays considered in this paper may not be differentiable, even not continuous.     

High-order sliding mode controller with backstepping design for aeroelastic systems

A nonlinear system for controlling flutter in an aeroelastic system is proposed. The dynamic model describes the plunge and pitch motion of a wing. Interacting nonlinear forces such as structural and aerodynamic forces cause destabilizing phenomena such as flutter and limit cycle oscillation on the wing. Aeroelastic models have a wing section with only a single trailing-edge control surface for suppressing limit cycle oscillation. When modeling a single control surface, the controller design can achieve trajectory control of either plunge displacement or pitch angle, but not both, and internal dynamics describe the residual motion in closed-loop systems. Internal dynamics of aeroelasticity depend on model parameters such as freestream velocity and spring constant. Since single control surfaces have limited effectiveness, this study used leading- and trailing-edge control surfaces to improve control of limit-cycle oscillation. Moreover, two control surfaces were used to provide sufficient flexibility to shape both the plunge and the pitch responses. In this study, high order sliding mode control (HOSMC) with backstepping design achieved system stability and eliminated limit cycle phenomenon. Compared to the conventional sliding mode control design, the proposed control law not only preserves system robustness, but also avoids chatter phenomenon. Simulation results show that the proposed controller effectively regulate the response to origin in state space even under saturated controller input.     

Supersonic flow past triangular wings with ribs on their surface PMM vol. 31, no. 6, 1967, pp. 1050–1056

Various types of partitions are a common feature of lifting surfaces. These partitions can take the form of stiffening ribs, deflectors for preventing secondary flows or flow separation, etc. The presence of partitions has a marked effect on the character of flow and on the values of the aerodynamic parameters. Flow past such wings cannot be computed in the general case. Wings of a special type are amenable to simple solution, however, and this will be considered below. One special case of interaction between a partition and an infinite wing is also considered in [1].     

Risk assessment for crosswind stability of vehicles on exposed sites

The main purpose of this paper is to provide a reliable evaluation for the crosswind stability of different road vehicles in a realistic physical scenario. Unlike existing approaches, we analyze the wind-vehicle system by probabilistic methods. The aerodynamic coefficients together with the gust parameters are considered as random variables. In addition, on-site measured wind data are used to calibrate the gust model. As the excitation of the vehicle is a stochastic process, risk analyses have to be carried out and failure probabilities are computed. Based on the failure probabilities, guidelines for speed limitations or traffic restrictions can be developed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of optimal filter higher-order derivatives

In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter first-order derivatives, the parameter can be estimated online. To analyze the asymptotic behavior of such methods, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. These properties are studied here. Under regularity conditions, we show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the same derivatives are geometrically ergodic.     

Nonlinear feedback control of chaotic pendulum in presence of saturation effect

In present paper, a feedback linearization control is applied to control a chaotic pendulum system. Tracking the desired periodic orbits such as period-one, period-two, and period-four orbits is efficiently achieved. Due to the presence of saturation in real world control signals, the stability of controller is investigated in presence of saturation and sufficient stability conditions are obtained. At first feedback linearization control law is designed, then to avoid the singularity condition, a saturating constraint is applied to the control signal. The stability conditions are obtained analytically. These conditions must be investigated for each specific case numerically. Simulation results show the effectiveness and robustness of proposed controller. A major advantage of this method is its shorter chaotic transient time in compare to other methods such as OGY and Pyragas controllers.     

Aeromechanical stability of rotorcraft with advanced geometry blades

An improved aeroelastic formulation for the advanced geometry blades, involving variable sweep, droop, pretwist, and planform, is presented. The blade is modeled as a series of arbitrarily-oriented elastic segments with each segment divided into finite elements. Inter-element compatibility relations governing non-Eulerian moderate rotations of the finite elements are also presented. Fuselage dynamic interaction with the advanced geometry blades is included in the formulation. The nonlinear partial differential equations of motion are discretized in space and time using Hamilton's principle. Selective results are presented in hover and forward flight. Results indicate that sweep, and droop in particular, can have a strong influence on both the rotor aeroelastic stability and the rotorcraft aeromechanical stability. Droop can be considerably stabilizing. Sweep increases the blade torsional loads, but is not detrimental to flap and lag vibratory loads.¹     

Modeling and dynamics of a two-line kite

A mathematical model of a kite connected to the ground by two straight tethers of varying lengths is presented and used to study the traction force generated by kites flying in cross-wind conditions. The equations of motion are obtained by using a Lagrangian formulation, which yields a low-order system of ordinary differential equations free of constraint forces. Two parameters are chosen for the analysis. The first parameter is the wind velocity. The second parameter is one of the stability derivatives of the aerodynamic model: the roll response to the sideslip angle, known also as effective dihedral. This parameter affects significantly the lateral dynamics of the kite. It has been found that when the effective dihedral is below a certain threshold, the kite follows stable periodic trajectories, and naturally flies in cross-wind conditions while generating a high tension along both tethers. This result indicates that kite-based propulsion systems could operate without controlling tether lengths if kite design, including the dihedral and sweep angles, is done appropriately. If both tether lengths are varied out-of-phase and periodically, then kite dynamics can be very complex. The trajectories are chaotic and intermittent for values of the effective dihedral below a certain negative threshold. It is found that tether tensions can be very similar with and without tether length modulation if the parameters of the model are well-chosen. The use of the model for pure traction applications of kites is discussed.     

A Generalized Smoother for Linear Ordinary Differential Equations

Ordinary differential equations (ODEs) are equalities involving a function and its derivatives that define the evolution of the function over a prespecified domain. The applications of ODEs range from simulation and prediction to control and diagnosis in diverse fields such as engineering, physics, medicine, and finance. Parameter estimation is often required to calibrate these theoretical models to data. While there are many methods for estimating ODE parameters from partially observed data, they are invariably subject to several problems including high computational cost, complex estimation procedures, biased estimates, and large sampling variance. We propose a method that overcomes these issues and produces estimates of the ODE parameters that have less bias, a smaller sampling variance, and a 10-fold improvement in computational efficiency. The package GenPen containing the Matlab code to perform the methods described in this article is available online.