Gradient-Based Aeroservoelastic Optimization with Static Output Feedback

Loads analysis and structural design are core steps of the aircraft design process. To reduce wing loads and with it the wing structural mass, methods of passive and active loads alleviation have been researched in recent years. However, those methods are currently implemented without the consideration of dynamic simulations or unsteady aerodynamics in the optimization process in aircraft predesign. The purpose of this research is to investigate the influence of passive and active loads alleviation methods on the structural mass in aircraft preliminary design. The methods have been applied on the wing of a Generic Mid-Range (GMR) aircraft configuration. The models have been created with ModGen, an in-house program at DLR Institute of Aeroelasticity. The models comprise FE-models for the structure and masses, as well as DLM (Doublet-Lattice-Method) model for the aerodynamics. For the investigation of the influence of the loads alleviation systems, a loop of loads analysis and subsequent structure optimization has been conducted. The loads analysis consists of gust and maneuver simulations. For the passive loads alleviation, an aeroelastic tailoring of the wing structure has been implemented, whereas for the active loads alleviation the ailerons are deflected to redistribute lift during maneuvers and to partially compensate lift increment during gust encounters. With the implemented methods, a first quantification of the influence of loads alleviation methods on the structural mass in aircraft predesign is possible.

This thesis develops and demonstrates an aircraft pre-design process for loads analysis, load alleviation, structural optimization and fatigue analysis. It is shown that the consideration of maneuver and gust load alleviation in early design stages is a promising concept to reduce wing bending moments, structural mass and extend the fatigue life. The reference aircraft considered are two mid-range configurations: one with a backward and another one with a forward swept wing, respectively.
\nIn the loads analysis, quasi-steady maneuvers and dynamic 1-cos gusts are considered. For the load alleviation during maneuvers, the ailerons are deflected symmetrically with precalculated amplitudes. For the gust load alleviation, a feed-forward, proportional control algorithm is set up and the main input for the controller is the gust angle of attack. Analogous to maneuver load alleviation, the ailerons are deflected symmetrically.
\nWith the post-processed loads from the simulations, the structure of the wing and horizontal tailplane (HTP) is optimized toward mass minimization. The constraints considered are material strength, buckling stability and static aeroelastic requirements. The steps loads analysis and structure optimization of the developed design process are conducted iteratively until the wing box mass converges. For the reference aircraft, the load alleviation yields a reduction of wing box mass by 2.8% and 6.1%, respectively.
\nBeyond that, a qualitative fatigue analysis is carried out to compare the fatigue behaviors of the active and passive aircraft (with and without load alleviation). In this step, loads due to continuous turbulence and ground-air-ground cycles are considered. For the reference missions, the fatigue life of the active aircraft is improved by 28% and 12% respectively, on top of the mass benefit. However, these numbers of fatigue life improvement are only valid for the considered loads and selected positions. If more loading conditions or structure elements are taken into account, the fatigue benefit may vary.
\nAs a conclusion, the proposed process can serve to gain an insight into the benefits of load alleviation for a given aircraft in the pre-design phase, before it advances to the next design stage.

Maneuver load alleviation, gust load alleviation, and natural laminar flow are integrated into aircraft conceptual design. The concurrent design of the aircraft and its active load alleviation systems can yield significant gains. The simultaneous application of maneuver load alleviation and gust load alleviation to a short-haul aircraft leads to an 11% reduction in fuel burn and 7% reduction in direct operating cost. These savings are diminished if maneuver load alleviation and gust load alleviation are applied independently. The synergy between active load control and natural laminar flow is also explored. It is possible to invest some of the weight savings from load alleviation to achieve extensive laminar flow. The combination of load alleviation and natural laminar flow increases the fuel and cost savings to upwards of 18 and 11%, respectively. It is concluded that load alleviation can shift the transonic transport optimum toward low-sweep, natural laminar flow wings. Sensitivity studies finally demonstrate that contemporary commercial aircraft should be able to meet the control requirements for effective gust load alleviation.

As aircraft wings become much more flexible due to the use of light-weight composites material, adverse aerodynamics at off-design performance can result from changes in wing shapes due to aeroelastic deflections. Increased drag, hence increased fuel burn, is a potential consequence. Without means for aeroelastic compensation, the benefit of weight reduction from the use of light-weight material could be offset by less optimal aerodynamic performance at off-design flight conditions. Performance Adaptive Aeroelastic Wing (PAAW) technology can potentially address these technical challenges for future flexible wing transports. PAAW technology leverages multi-disciplinary solutions to maximize the aerodynamic performance payoff of future adaptive wing design, while addressing simultaneously operational constraints that can prevent the optimal aerodynamic performance from being realized. These operational constraints include reduced flutter margins, increased airframe responses to gust and maneuver loads, pilot handling qualities, and ride qualities. All of these constraints while seeking the optimal aerodynamic performance present themselves as a multi-objective flight control problem. The paper presents a multi-objective flight control approach based on a drag-cognizant optimal control method. A concept of virtual control, which was previously introduced, is implemented to address the pair-wise flap motion constraints imposed by the elastomer material. This method is shown to be able to satisfy the constraints. Real-time drag minimization control is considered to be an important consideration for PAAW technology. Drag minimization control has many technical challenges such as sensing and control. An initial outline of a real-time drag minimization control has already been developed and will be further investigated in the future. A simulation study of a multi-objective flight control for a flight path angle command with aeroelastic mode suppression and drag minimization demonstrates the effectiveness of the proposed solution. In-flight structural loads are also an important consideration. As wing flexibility increases, maneuver load and gust load responses can be significant and therefore can pose safety and flight control concerns. In this paper, we will extend the multi-objective flight control framework to include load alleviation control. The study will focus initially on maneuver load minimization control, and then subsequently will address gust load alleviation control in future work.

This paper presents a method to design a static output feedback active suspension controller for ride comfort improvement and motion sickness reduction in a real vehicle system. Full-state feedback controller has shown good performance for active suspension control. However, it requires a lot of states to be measured, which is very difficult in real vehicles. To avoid this problem, a static output feedback (SOF) controller is adopted in this paper. This controller requires only three sensor outputs, vertical velocity, roll and pitch rates, which are relatively easy to measure in real vehicles. Three types of SOF controller are proposed and optimized with linear quadratic optimal control and the simulation optimization method. Two of these controllers have only three gains to be tuned, which are much smaller than those of full-state feedback. To validate the performance of the proposed SOF controllers, a simulation is carried out on a vehicle simulation package. From the results, the proposed SOF controllers are quite good at improving ride comfort and reducing motion sickness.

We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations (ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ;ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> ;LQR) and previous works have focussed on characterizing classes of structural constraints that allow efficient solution through convex optimization or dynamic programming techniques. In this paper, we propose a new control objective based on eigenvalues of the covariance matrix of trajectories of the system and show that this formulation makes the problem of computing optimal linear feedback matrices convex under arbitrary convex constraints on the feedback matrix. This allows us to solve problems in distributed control (sparsity in the feedback matrices), control with delays and variable impedance control. Although the control objective is nonstandard, we present theoretical and empirical evidence that it agrees well with standard notions of control. We numerically validate the our approach on problems arising in power systems and simple mechanical systems.

Any linear control system, including those with complex structure and dynamic compensation can systematically be formulated as a static output feedback problem where the control system parameters are contained in the output feedback matrix. For this reason, many numerical techniques have been developed specifically to solve the 7/2 optimal ouput feedback problem posed in static output feedback form. Current numerical techniques for computing the output feedback gain matrix recast the problem as a coupled set of Lyapunov equations. Various numerical techniques effectively solve the Lyapunov equations differently. Here, we propose a new numerical method for solving the output feedback gain matrix by direct solution of the cost function using Fade approximation. Using this technique, analytic expressions for cost function derivatives can be written compactly, allowing for efficient solution using second order optimiztion methods. Using a flight control system example, the new method is compared to existing optimal output feedback algorithms.

Circulation control has the potential to improve current gust and maneuver load alleviation schemes, with the ultimate goal of reducing wing structure weight and saving fuel. A Coandă-type flow actuator is integrated on the pressure side of a two-dimensional airfoil model, and its load alleviation performance and dynamic behavior are determined experimentally. Quasi-steady force and wake measurements are conducted in a wind tunnel to quantify the effect of the actuator on lift and drag. Lift decrements of are reached for steady blowing, exceeding typical gust-induced wing loads in magnitude. For pulsed blowing, only moderate mass flow reductions of up to 25% are achieved, caused by discontinuous flow turning around the Coandă surface. Unsteady force and pressure measurements characterize the dynamic lift response to the actuation. The total onset time of the lift response, normalized by the ratio of chord length to freestream velocity, is for actuator activation and for actuator deactivation. These values are below typical onset times for gust loads (). The present results show a high-lift reduction potential and fast dynamic behavior of the Coandă-type flow actuator, making it a viable candidate for fast and effective load alleviation.

This work eonsiden the H, norm control of structural systems with collocated sensors and actuators using an analytical upper bound approach. A parametrization of the output feedback control gains that achieve a desired H, norm bound is obtained using an analytical solution of the Bounded Real Lemma. This approach is verified experimentally on a cantilevered aluminum beam with two collocated pairs of piezoceramic patches that serve as sensors and actuators. The finite element model of this beam is developed and the simulations show a drop of -6 dB in the H, norm of the closed loop system. Experimental results verify the simulated results and demonstrate the effectiveness of this method. The proposed control methodology has obvious computational advantages compared to traditional H, control design methods, especially for lnrge scale systems. The control of structural systems with collocated sensors and actuators has been shown to provide great advantages from a stability, passivity, robustness and an implementation viewpoint. For example, collocated control can easily be achieved in a space structure when an attitude rate sensor is placed at the same point as a torque actuator.(l)(2) The actuator placement and sizing optimization for vibration sup pression of a collocated beam structure is discussed in Ref. (3).Collocation of sensors and actuators leads to symmetric transfer functions. Several other classes of engineering sys- tems, such as circuit systems, chemical reactors and power networks, can be modelled as systems with symmetric trans- fer functions. Stabilization, robustness, model reduction and control of such systems has been examined recently.(4)(5) The H, norm control of structural systems has attracted a lot of attention recently due to the interpretation of the H, norm in the frequency domain. In early work, D-K iteration method was used to design H, controllers for a non-collocated flexible shucture. Now state space H, control based on the standard Riccati equation approach or the linear matrix inequality (LMI) formulation is a well developed control synthesis tool. The optimal static state feedback and full-order dynamic output feedback H, con- trol synthesis problems can be solved using iterations on the corresponding Riccati solutions or via the computational solution of a convex LMI optimization problem.(7)(8) On the other hand, the static output feedback and the fixed-order dynamic output feedback H, control synthesis problems are difficult computational problems since they require the

SummaryA real-time optimal excitation controller (RTOEC) is proposed in this paper. The identifier in the RTOEC can properly identify the system parameters by the nonlinear least squares method. Thus a new optimal feedback matrix can be calculated in real-time from the identification results and the disturbances in the system. So the RTOEC can track quickly the operating status of the generator and always provide optimal control. Simulation studies carried out on the Three Gorges 700MW hydropower generator show that the RTOEC can provide good performance over a wide range of operating conditions and improve the static and transient stability of power system effectively.

An integrated modelling approach, suitable for flight loads analysis and flight dynamics investigations is presented. These scenarios need fast loop capable simulation models. Typically, they are evaluated many times in the entire flight envelope, for varying mass cases and for changing parameters during the aircraft design process. Further, the simulations models have very different requirements depending on their application. Flight dynamics models must account for large nonlinear rigid Body motions and aerodynamic nonlinearities, manoeuvre loads analysis, additionally need to take flexible deformations into account, and hence require distributed aerodynamics, and for gust loads Analysis unsteady aerodynamic effects are essential. The proposed integrated model is based on nonlinear equations of motion using mean axes constraints. Potential flow based aerodynamics with low computational cost are the method of choice for most aeroelastic applications. Presented in this paper are some important aspects regarding the aerodynamic modelling, which are handled differently compared to other implementations. Instead of the Doublet Lattice Method (DLM), the 3D panel method NEWPAN is used, which is able to capture previously neglected flight mechanical effects such as roll-yaw coupling and induced drag. Since, the Aerodynamic Influence Coefficient (AIC) matrices obtained from NEWPAN are nonlinearly dependent on the flight state, a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD) is setup and subsequently interpolated. The proposed ROM interpolates directly AIC matrices (AIC-ROM) instead of pressures. The advantages of a ROM based on AIC matrices over similar approaches based on pressure coefficients are explained. Similarly to the Doublet Lattice Method, the 3D panel code is able to compute frequency based unsteady Aerodynamic Influence Coefficient (AIC) matrices, which are approximated by a Rational Functions (RFA) to make them amenable for time domain simulations. Unlike other approaches, the physical RFA allows a clear separation of quasi-steady, added mass and unsteady lag terms. Several application examples are presented and their particular needs are addressed. The proposed modelling approach supports flight dynamics by including previously neglected aerodynamic roll yaw coupling and nonlinear angle of attack dependencies, manoeuvre loads, including aeroelastic deformations, and gust loads analyses, including unsteady aerodynamics in one integrated model and is suitable for for investigations regarding active gust and manoeuvre load alleviation, primary flight control design, or performance improvement through lift redistribution.

The paper presents the design of a symmetric, active, gust load alleviation system for a regional transport aircraft, based on a static output feedback with a constrained structure. The design is carried out on a comprehensive finite state aeroservoelastic model, including sensor units and actuator transfer functions, and verified by taking into account saturated control positions, rates, and hinge moments. The controller is designed within a quadratic optimal framework, through a second-order Hessian-based optimization algorithm, exploiting block diagonal Schur transformations of the closed-loop state equations and performance weightings. An accurately chosen worst discrete gust and a reference flight condition provide a baseline design, which is significantly effective in alleviating continuous turbulence loads. Such a reference design proves itself robust enough to alleviate atmospheric loads over the complete flight envelope and is eventually further improved and robustified through a simple bilinear algebraic scheduling.

This paper presents a method for designing a static output feedback integrated path tracking controller for autonomous vehicles. For path tracking, state–space model-based control methods, such as linear quadratic regulator, H∞ control, sliding mode control, and model predictive control, have been selected as controller design methodologies. However, these methods adopt full-state feedback. Among the state variables, the lateral velocity, or the side-slip angle, is hard to measure in real vehicles. To cope with this problem, it is desirable to use a state estimator or static output feedback (SOF) control. In this paper, an SOF control is selected as the controller structure. To design the SOF controller, a linear quadratic optimal control and sliding mode control are adopted as controller design methodologies. Front wheel steering (FWS), rear wheel steering (RWS), four-wheel steering (4WS), four-wheel independent braking (4WIB), and driving (4WID) are adopted as actuators for path tracking and integrated as several actuator configurations. For better performance, a lookahead or preview function is introduced into the state–space model built for path tracking. To verify the performance of the SOF path tracking controller, simulations are conducted on vehicle simulation software. From the simulation results, it is shown that the SOF path tracking controller presented in this paper is effective for path tracking with limited sensor outputs.

We develop a general class of stochastic optimal control problems for which the problem of designing optimal linear feedback gains is convex. The class of problems includes arbitrary time varying linear systems and costs that are mixtures of exponentiated quadratics. This allows us to model problems with quadratic state costs and linear constraints on states and state transitions. Further, convexity in the feedback gains lets us impose arbitrary convex constraints or penalties on the feedback matrix: Thus we can model problems like distributed control (by imposing a sparsity structure on the feedback matrix) and variable-stiffness control (by applying time-varying penalties to feedback gain matrices). We show that the convex optimization problem can be solved efficiently by using the structure of the matrices involved. Finally, we present an application of these ideas to a practical problem arising in distributed control of power systems.

Review for "Passive Load Alleviation on Wind Turbine Blades from Aeroelastically Driven Selectively Compliant Morphing"