Trim Conditions Research Articles

Tailored Dynamic Gain-Scheduled Control

This paper advances the theoretical basis and application of dynamic gain-scheduled control, a novel method for the control of nonlinear systems, to an aircraft model. Extensions of this method involving multivariable gain scheduling and continuation tailoring are developed. The idea behind this method is to schedule the control law gains with a fast-varying state rather than with a slow-varying state or an input parameter. This approach is advantageous because it is then possible to schedule the gains with a state that is dominant in the mode that we are most interested in controlling. The use of this type of gain scheduling is shown to improve the transient response of the aircraft model when stepping between trim conditions and to reduce control surface movement, thus reducing the potential for saturation problems. Hidden coupling terms that introduce unwanted dynamics when scheduling gains with a fast state (rather than the input design parameter) are eliminated directly by applying a transformation to the classical parameter-scheduled gain distributions that are calculated using optimal control theory. A highly nonlinear unmanned combat air vehicle model is used to demonstrate the design process.

A study on trimming of aluminum autobody sheet and development of a new robust process eliminating burrs and slivers

Small pieces of metal are generated during trimming of automotive body panels. Commonly referred to as slivers, these pieces can be imprinted into the surface of stamped panels. This may require metalfinish of every stamped exterior panel. The objective of the paper is to study the influence of trimming conditions on quality of trimmed surface and to modify the trimming process to eliminate slivers and burrs from trimmed surface. This objective is being accomplished through numerical simulation of the blank fracture and experimental study of trimmed surface formation. Suggested solution includes two measures: (1) building an elastic support of the offal eliminating bending of the part of the blank being trimmed off; (2) creating the preference of crack propagation from the lower shearing edge by machining a small radius on the upper shearing edge.

Pathogenesis and treatment of spontaneous quarter cracks - quantifying vertical mobility of the hoof capsule at the heels

Summary Spontaneous quarter cracks (Q.C) are defined as cracks, parallel to the horn tubules, originating at the coronary band, in the region of the quarters-heels of the hoof, due to internal trauma as opposed to external trauma (wire cuts e.g.). They consist in a fracture of the hoof wall, from the inside out, proximal to distal, and occur when the ipsilateral ungular cartilage (U.C.), expanding outwards in the loaded limb meets an excessively upwardly shunted hoof wall in the quarter-heel region (Sheared heel) as shown with resected hooves under load. Palpation and measurement of the free margin of the ipislateral, U.C. above the proximal border of the hoof capsule (H.C.) is clinically important in the evaluation and treatment of spontaneous Q.C. Feet with spontaneous Q.C. have a free U.C. margin of less than 15mm depending on the hoof’s size. Increasing the free margin of the U.C. is fundamental in the treatment of spontaneous Q.C. as the lesion originates from the inside out and no amount of crack debridement and fixation by itself will allow for free lateral expansion of the ipsilateral U.C. without it traumatising the coronary band. Lowering of an upwardly shunted heel/quarter can be achieved by special trimming and shoeing methods and /or by a full-wall depth sub-coronary grooving. The first allows for an average of ±7mm of instant hoof wall lowering at the affected heel relative to the ipsilateral U.C. and distal phalanx (D.P.). Finally the author studied the opposite effect; the amount of instant upward displacement of the hoof wall at the heels, relative to the distal phalanx, on the loaded foot with a 20mm heel raise. This was done in vivo by radiological means under standardised trimming and exposure conditions. Average, instant vertical displacement on 18 limbs amounted to 4,3 mm. These results call into question the effectiveness of some raised heel shoeing techniques which aim to change the phalangeal alignment between the D.P. and the proximal phalanges.

Dynamic gain-scheduled control of the ICE 101-TV

AbstractThis paper shows the theoretical development and application of dynamic gain scheduled control – a novel method for the control of nonlinear systems – to an aircraft model. The idea behind this method is to schedule the control law gains with a fast varying state variable rather than with a slow varying state or an input parameter. This is advantageous as it is then possible to schedule the gains with a state variable that is dominant in the mode that we are most interested in controlling. The use of this type of gain scheduling is shown to improve the transient response of the aircraft model when stepping between trim conditions and to overcome some of the problems associated with conventional gain scheduled controllers (such as control surface position limit saturation). ‘Hidden coupling terms’ that introduce unwanted dynamics when scheduling gains with a fast state (rather than the input design parameter) are eliminated directly by applying a transformation to the classical parameter-scheduled gain distributions which are calculated using eigenstructure assignment. A second order longitudinal model and a 5th order longitudinal/lateral model of the ICE 101-TV tailless delta-wing aircraft configuration are used to demonstrate the design process.

Aircraft Spin Recovery, with and without Thrust Vectoring, Using Nonlinear Dynamic Inversion

The present paper addresses the problem of spin recovery of an aircraft as a nonlinear inverse dynamics problem of determining the control inputs that need to be applied to transfer the aircraft from a spin state to a level trim flight condition. A stable, oscillatory, flat, left spin state is first identified from a standard bifurcation analysis of the aircraft model considered, and this is chosen as the starting point for all recovery attempts. Three different symmetric, level-flight trim states, representative of high, moderate, and low-angle-of-attack trims for the chosen aircraft model, are computed by using an extended-bifurcation-analysis procedure. A standard form of the nonlinear dynamic inversion algorithm is implemented to recover the aircraft from the oscillatory spin state to each of the selected level trims. The required control inputs in each case, obtained by solving the inverse problem, are compared against each other and with the standard recovery procedure for a modern, low-aspect-ratio, fuselage heavy configuration. The spin recovery procedure is seen to be restricted because of limitations in control surface deflections and rates and because of loss of control effectiveness at high angles of attack. In particular, these restrictions adversely affect attempts at recovery directly from high-angle-of-attack oscillatory spins to low-angleof-attack trims using only aerodynamic controls. Further, two different control strategies are examined in an effort to overcome difficulties in spin recovery because of these restrictions. The first strategy uses an indirect, two-step recovery procedure in which the airplane is first recovered to a high- or moderate-angle-of-attack level-flight trim condition, followed by a second step where the airplane is then transitioned to the desired low-angle-of-attack trim. The second strategy involves the use of thrust-vectoring controls in addition to the standard aerodynamic control surfaces to directly recover the aircraft from high-angle-of-attack oscillatory spin to a low-angle-of-attack level-flight trim state. Our studies reveal that both strategies are successful, highlighting the importance of effective thrust management in conjunction with suitable use of all of the aerodynamic control surfaces for spin recovery strategies.

축소형 회전익 항공기의 간략화된 동적 모델링

모형헬리콥터를 이용한 무인항공기 설계를 위해 비선형 형태의 수학적 모델이 선행되어야 한다. 모형헬리콥터는 실기 헬리콥터에 비해 회전수가 훨씬 높으며 따라서 동특성도 실물기에 비해 훨씬 빠르다는 차이점이 있다. 본 논문에서는 축소형 헬리콥터의 수학적 모델링에 필요한 정식화과정으로서 복잡성을 최소화하면서도 실제의 동특성에 잘 부합하도록 각 구성요소별로 계산한 후 전체로 합산하는 방법을 제시하였다. 제자리 비행과 전진비행에서 수치계산을 통해 트림 값들을 계산하고 제자리 비행조건에서 선형 시스템을 해석하여 모형헬리콥터의 비행모드를 분석하였다. 계산결과 일반적인 경향은 몇 가지 작은 부분 이외에는 대체로 다른 연구결과와 비슷하였다. 이 과정을 검증하기 위해서 비행시험을 수행하여 시스템식별에 의한 결과와 비교하는 연구가 후속 수행될 예정이다. It is prerequisite that we have to fomulate the nonlinear mathematical modeling to design the guidance and control system of rotorcraft-based unmanned aerial vehicle using a small-scaled commercial helicopter. The small-scaled helicopters are very different from the full-scale helicopters in dynamic behavior such as high rotation speed and high frequency dynamic characteristics. In this paper, the formulation of the mathematical model of the small-scaled helicopter to minimize the complexity is presented by component and source build-up approach. It is linearized at the trim condition of hovering and forward flight and analyzed the flight modes. The results of this approach have general trends but a little difference. To verify this approach, it is necessary to compare this theoretical model with experimental results by system identification using flight test as a next research topic.

Advances in the Modelling of Motorcycle Dynamics

Starting from an existing advanced motorcycle dynamics model, which allows simulation of reasonably general motions and stability, modal and response computations for small perturbations from any trim condition, improvements are described. These concern (a) tyre/road contact geometry, (b) tyre shear force and moment descriptions, as functions of load, slip and camber, (c) tyre relax- ation properties, (d) a new analytic treatment of the monoshock rear suspension mechanism with sample results, (e) parameter values describing a contemporary high performance machine and rider, (f) steady-state equilibrium and power checking and (g) steering control. In particular, the Magic Formula motorcycle tyre model is utilised and complete sets of parameter values for contemporary tyres are derived by identification methods. The new model is used for steady turning, stability, design parameter sensitivity and response to road forcing calculations. The results show the predictions of the model to be in general agreement with observations of motorcycle behaviour from the field and they suggest that frame flexibility remains an important design and analysis area, despite improvements in frame designs over recent years. Motorcycle rider parameters have significant influences on the behaviour, with results consistent with a commonly held view, that lightweight riders are more likely to suffer oscillation problems than heavyweight ones.

Development of Linear-Parameter-Varying Models for Aircraft

This paper presents a comparative study of three linear-parameter-varying (LPV) modeling approaches and their application to the longitudinal motion of a Boeing 747 series 100/200. The three approaches used to obtain the quasi-LPV models are Jacobian linearization, state transformation, and function substitution. Development of linear parameter varying models are a key step in applying LPV control synthesis. The models are obtained for the up-and-away flight envelope of the Boeing 747-100/200. Comparisons of the three models in terms of their advantages, drawbacks, and modeling difficulty are presented. Open-loop time responses show the three quasi-LPV models matching the behavior of the nonlinear model when in the trim region. Differences between the models are more apparent as the response of the aircraft deviates from the nominal trim conditions. ¯

Nonlinear Response of Aeroservoelastic Systems Using Discrete State-Space Approach

A generalized direct simulation method using a discrete time-domain state-space approach for transient response of both open- and closed-loop nonlinear aeroelastic systems is developed. Based on a nonlinear parameter scheme that divides the nonlinear system into sublinear systems, the method first assembles a set of discrete time-domain state-space equations and then computes the transient response by switching the time-integration procedure between this set of state-space equations. In so doing, various nonlinearities in structures, aerodynamics and/or control systems can be included. The method is validated by correlating the transient response of a three-degree-of-freedom airfoil section in freeplay with the experimental and numerical results obtained by Conner et al. The stability of a strut-braced wing with buckling effects at two trim conditions is also studied, which shows that the aeroelastic stability of the present strut-braced wing is trim-condition dependent. Such results clearly could not be obtained if using a linear aeroelastic analysis.

Observer/Kalman Filter Identification for Online System Identification of Aircraft

The observer/Kalman filter identification method is applied to the problem of online system identification of accurate, locally linear, aircraft dynamic models of nonlinear aircraft. It is a time-domain technique that identifies a discrete input-output mapping from known input and output data samples, without user imposed a priori assumptions about model structure or model order. The basic formulation of observer/Kalman filter identification specific to the aircraft problem is developed and implemented in a nonlinear, six-degree-of-freedom simulation of an AV-8B Harrier. A similar simulation of a generic uninhabited combat aerial vehicle is also used. Numerical examples are presented, consisting of longitudinal and lateral/directional successive online identifications at different nonperfect trim conditions, identification with sensor noise on multiple channels, and identification with discrete gusts. Accuracy of the identified linear system models to the nonlinear plant is quantified with comparison of eigenvalues, the Vinnicombe gap metric, and time history matching. Results demonstrate that the observer/Kalman filter identification method is suitable for aircraft online identification of locally linear aircraft models and is generally insensitive to moderate intensity Gaussian white sensor noise and for light to moderate intensity discrete gusts.

고정밀 레이저 가공 기술을 이용한 PRT 제작 및 특성 분석

In this paper, we fabricated PRT(platinum resistance thermometers) with the trimming technology using high fine laser system. U. V.(wavelength： 355nm) laser was mainly used for adjusting Pt thin films resistors to 100Ω at 0<TEX>$^{\circ}C$</TEX>. Internationally, the accepted A-class tolerance of temperature sensor is <TEX>${\pm}$</TEX>0.06Ω at 0<TEX>$^{\circ}C$</TEX>. according to DIN EN 60751. The width of trimmed lines was about 10<TEX>$\mu\textrm{m}$</TEX> and the best trimming conditions of Pt thin films were power : 37mW, frequency : 200Hz and bite size：1.5<TEX>$\mu\textrm{m}$</TEX>. And 96 resistors, fabricated by photolithography and etching process, have 79∼90Ω and 91∼102Ω as the proportion of 45.7% and 57.3%, respectively. As result of sitting Pt thin films resistors to the target value(109.73Ω at 25<TEX>$^{\circ}C$</TEX>), 82.3% of all resistors had the tolerance within <TEX>${\pm}$</TEX>0.03Ω and the others(17.7％) were within <TEX>${\pm}$</TEX>0.06Ω of A-class tolerance. The PRTs which wore fabricated in this research had excellent characteristics as follows； high accuracy, international standard TCR(temperature coefficient of resistance) value, long-term stability, wide temperature range, good linearity and repeatability, rapid response time, etc.

Sensitivity of Hydrocarbon Combustion Modeling for Hypersonic Missile Design

Aspects relating to the aerodynamic and propulsive design and analysis of missile-class, waverider-based hypersonic vehicles are explored in this paper. A quasi-one-dimensional engine model, including the effects of fuel injection, mixing, chemical production rates, heat transfer, and viscous losses, is developed and utilized to assess the effects of finite rate, hydrocarbon chemistry on optimized missile configurations. Resultant optimized single-and double-engine missile designs are shown for changes in fuel mixing length, fuel mixing efficiency, fuel-injector location, and assumed fuel mass fraction. The effects of these different design conditions on the cruise range are explored, as well as perturbations around these design points for optimized vehicles. Missiles are optimized for steady-state trim conditions at the beginning of cruise flight using parallelized genetic algorithm optimization software developed for this study. All missile designs are assumed to reach cruising altitude and velocity through the use of an external rocket booster. The missile is geometrically constrained to fit within the 0.61 x 0.61 × 4.27 m box limits for a naval vertical launch tube and has a desired cruise range of 750 km at Mach 8. Results show that the optimized combustor designs were extremely sensitive to small design perturbations. Two engine configurations are shown to be more robust than single-engine models for engine design perturbations.

항공기 제어면/구동장치 고장에 대한 진단규명 및 보완 제어시스템 설계에 관한 연구

본 논문에서는 항공기의 제어면 혹은 구동장치가 고장이 났을 때 이를 신속하게 진단규명하고 안정한 상태로 되돌리기 위한 고장보완제어시스템을 설계한다. 제어시스템 설계에는 수렴 속도가 빠른 확장 역전파 알고리즘을 적용한 신경회로망을 이용한다. 제어대상으로는 비선형 운동방정식으로 표현된 F-4 항공기이며 수평미익이나 에일러런의 고장이 발생할 경우에 대하여 제어시스템을 설계하고 시뮬레이션을 통하여 성능을 검증한다. In this study a control surface/actuator fault detection, identification, and accommodation system for aircraft is designed. This fault tolerant control system tries to return aircraft to its stable trim condition in a short time. The control system is designed using neural networks with Extended Back Propagation Algorithm which shows fast convergence. F-4 aircraft with possible stabilator or aileron failure/stuck is simulated with the proposed scheme.

Resist trimming in high-density CF4/O2 plasmas for sub-0.1 μm device fabrication

Resist trimming using a CF4/O2 plasma generated by an inductively coupled high-density plasma source is investigated. Results show that the resist trimming process is applicable for the fabrication of a sub-0.1 μm polysilicon gate electrode with conventional 248 nm lithography. The trim rate depends strongly on gas composition, temperature, rf source power, bias voltage, reactor pressure and total gas flow. The trim rate increases with increasing temperature, rf source power and reactor pressure but decreases with higher bias voltage. For a typical trimming condition at gas composition of CF4 and O2 with a ratio of 3.3:1, the resist trim rates are 1.0 and 1.2 nm/s for dense and isolated lines, respectively. By examining the effect of various process parameters, it is found that the trimming process is dominated by the neutral reactant species. Angle-resolved x-ray photoelectron spectroscopy shows that a fluorinated carbon oxyfluoride polymer is deposited on the sidewall of photoresist. The degree of carbon fluorination of the film is influenced by the process parameters. A more fluorinated film, obtained at lower bias voltage and higher source power, gives more trimming.

Phugoid Damping Control

Abstract : A novel phugoid damping control design methodology is developed, based on the use of wind axes and a point-mass aircraft model. The state variables are air speed, flight path angle, and heading angle, the control variables are thrust setting, angle of attack, bank angle, and sideslip angle, and the command signals are airspeed, flight path angle, and heading angle or heading rate. All the variables and parameters are nondimensionalized. A multivariable set point controller is developed which consists of: (1) a trim calculation-based nonlinear feed-forward control computer; thus, given a commanded new trim state (air speed, flight path angle, and yaw rate), the required trim thrust setting and trim angle of attack, bank angle, and sideslip angle inputs are determined, and (2) a small signal linear feedback regulator; the equations of motion linearized about the trim condition of wings level, and constant altitude flight, which simplifies the dynamics to allow separation between the lateral and longitudinal control channels, are used, and a small-signal linear multivariable regulator is designed. The linear compensator also entails integral action. Thus, the controller consists of a strongly nonlinear feed-forward module and a linear small signal compensator. The novel proposed multi variable nonlinear set point controller encompasses full three-axes autopilot functions. Moreover, this controller is used as a tracking controller, a.k.a. a 'phugoid damping' controller, provided that the bandwidth of the command signal is substantially less than the bandwidth of the closed loop flight control system. The phugoid damping controller's performance is examined in extensive simulations and its wide operational envelope is demonstrated.

Predicting Aerodynamic Rotor-Fuselage Interactions by Using Unstructured Meshes

A numerical method has been developed for the analysis of interactional aerodynamics between helicopter rotor and fuselage in forward flight. A 3-D steady compressible Euler solver is used to compute time-averaged interactional effects between the rotor and the fuselage. The rotor is modeled as an actuator disk with zero thickness carrying pressure jump across it. Collective and cyclic pitch angles are calculated to satisfy the rotor trim condition. Unstructured meshes are used to model complex rotor-fuselage configurations. Calculations are performed for two generic helicopter fuselage geometries. The results are compared with available experimental data for validation.

Critical Design Issues for Airbreathing Hypersonic Waverider Missiles

Tradeoffs involved in the design of a hydrocarbon-fueled, hypersonic waverider-based missile were explored. The problem of providing acceptable vehicle performance in a volume-constrained package was addressed. The speciŽ c case of amissile constrained to Ž t within a 0:61 £ £ 0:61 £ £ 4:27m navalvertical launch tubewas examined, and a parametric study was performed to determine the probabilistic boundaries of designing a Mach 6 missile to satisfy the desired mission goal of a 750-km cruising range. All missile designs were assumed to reach cruising altitude and velocity through the use of an external rocket booster. The key design elements investigated are fuel volume fraction, engine inlet pressure, the number of scramjet engines, and the effects of changing the engine mixing and burning efŽ ciencies. Missile designs were optimized for steady-state trim conditions at the beginning of cruise using genetic algorithmsoftware. The sensitivities of the modeling assumptionson the performance of the Ž nal optimized designs are explained. The overall contribution of the optimized designs along with the predicted change in performance expected with increased modeling accuracy allows upper performance and range limits to be established. Double-engine designs are shown to be more promising than single-engine designs for achieving the desired 750-km range, as well as allowing for increased payload.

Computation of Flight Mechanics Parameters Using Continuation Techniques

A new approach is presented for the computation of continuation diagrams. It differs in principle from the usual approach of continuing the equilibrium points by considering one or more of the controls as continuation parameters and with the other controls held fixed. The novel approach addresses the problem of Light dynamics from the pilot point of view by allowing all the controls to be freely determined. At the same time some of the states are so constrained that along the continuation curve a particular pilot trim condition is maintained.

Attitude Control System Design for Return of the Kistler K1 Orbital Vehicle

An attitude control system design is presented that provides the maneuver capability and aerodynamic angle maintenancenecessary fortheatmosphericreentryand return tolaunchsiteofanunmannedreusablelaunch vehicle. The primary functions are categorized into those that perform bank maneuvers about the air-relative velocity vector and those that are responsible for the tracking and control of the vehicle aerodynamic trim conditions. The control system is supported by an onboard aerodynamic estimation function. The estimator uses measurements of vehicle states from navigation in combination with analytic models in a gain-scheduled e lter environment to provide control with current trim angle information. The control system uses this information to minimize actual vehicle deviations from the trim. Also, control is provided with bank commands from a guidance function. As this paperis concerned only with the control and estimation functions, the guidance strategies are discussed only to the extent that is necessary to justify/clarify control or estimator designs. The algorithms developed here are applied to the Kistler K1 Orbital Vehicle and tested in the Kistler Integrated Vehicle Simulation at Draper Laboratory. Resultsindicatethattheapproachto entry/returncontrolisbothfuelefe cientandeffectivefroma landingaccuracy perspective.

Neural-fuzzy scheduling of H robust controllers for a high performance fighter aircraft under a Herbst-like manoeuvre

This paper presents a flight control system design method witha neural-fuzzy gain-scheduling algorithm with learning capability for a high performance fighter aircraft undergoing a high angle of attack velocity vector roll manoeuvre. This manoeuvre is similar to the Herbst manoeuvre, hence also called a Herbst-like manoeuvre. Two linear H robust controllers are designed by using the mu -synthesis method at two trim conditions that cover the whole dynamic range of this manoeuvre. Then a scheduling technique is proposed, using the neural-fuzzy concept, together witha dynamic back propagation algorithm for its training. Simulation results, using a recently developed non-linear six-degree-of-freedom aircraft simulation package, demonstrate that the neural-fuzzy scheduler can be trained by using the dynamic back propagation algorithm to achieve better closed-loop tracking performance, and the proposed neural-fuzzy scheduled flight control system gives satisfactory performance inexecuting this Herbst-like manoeuvre.