Karthik Palaniappan

Optimal Control of LCOs in Aero-Structural Systems

Aero-elastic systems, by their very nonlinear nature, frequently encounter Limit Cycle Oscillations (LCOs). An LCO occurs when the system being described reaches a periodic steady state where there is a constant exchange of energy between the various degrees of freedom, in this case: the Aero and Structural components. These LCOs might be benevolent at times, but are not so in most cases. In this paper we study Active and Passive Control Strategies for LCOs and explore the possibility of harnessing the nonlinearities to our benefit. After defining a control approach based on Optimal Control Theory, we study the specific case of a nonlinear panel interacting with a supersonic flow and undergoing LCOs, and tailor the system parameters to achieve the desired control objectives.

Design of Adjoint-Based Laws for Wing Flutter Control

An airplane, by its nature of being, is constructed so that it is as light as possible. The structural design is guided by static and dynamic factors. The more stringent constraints on the structural design are due to dynamic loads, caused by aero-elastic interactions. One of the most commonly encountered problems in aeroelasticity is flutter, a term that is used to recognize the transfer of energy from unsteady aerodynamics associated with the surrounding fluid to the wing structure, resulting in rapidly divergent behaviour. If flutter can be controlled at cruise speeds, we can design lighter wings and consequently more efficient airplanes. It is therefore, in the aircraft designer’s best interest to design innovative ways in which flutter can be controlled without making the resulting structure too heavy. There are three important choices to make while designing active control strategies for suppressing flutter. The first is the choice of actuator. In this paper, the actuators we use are jets in the walls through which there is a small mass flow, either by way of blowing or suction. The second is to define a clear control objective. Finally, we need to design a control law that will make suitable state measurements and drive the actuators so that the desired control objective is achieved. The concept of Active Flow Control is fast gaining popularity in Fluid Mechanics circles. Indeed, it is important to realize that adding or removing fluid at the wing surface is equivalent to effecting a shape modification. Flow control using surface jets should, in principle, have an effect very similar to that of morphing surfaces. The capability to directly alter the flow field offers a huge realm of possibilities. Seifert, Theofilis and Joslin categorize the problems that are amenable to using Active Flow Control:

Rapid Estimation of Impaired Aircraft Aerodynamic Parameters

An estimation of aerodynamic models of impaired aircraft using an innovative differential vortex-lattice method tightly coupled with extended Kalman filters is discussed. The proposed approach significantly reduces the order of the estimation problem by exploiting the prior knowledge about the undamaged aircraft and the detected information on the approximate location and extent of damage. Three different extended Kalman filter formulations are developed and their comparative analyses are performed through numerical simulations. Algorithms given in this paper can be used as the basis for online derivation of an aircraft performance model, which can then form the basis for designing safe landing guidance laws for damaged aircraft.

Active Flutter Control using an Adjoint Method

Flutter is one of the most frequently encountered problems in aeroelasticity. Flutter control is therefore of great importance. It has been shown that flutter can be adequately modeled using a simple two degree of freedom, spring mass system with forcing from the aerodynamics. In the following paper, control by means of blowing and suction is used to control flutter. This is based on deriving a feedback control law from a linearized model of the aero-structural system. The feedback matrix thus derived is tested on the nonlinear model and is found to control flutter effectively.

Bodies Having Minimum Pressure Drag in Supersonic Flow: Investigating Nonlinear Effects

T HE life cycle of engineering design involves innovating to introduce a product, and when that is done, looking for ways to make itwork better. Supersonic aerodynamics can be looked atwith a similar perspective. Man has always wanted to fly faster. While the basicmechanics of supersonic flightwas laid out in the 1950s, people are yet to find ways in which to make Supersonic flight more efficient. One of the classic research problems in supersonic flight has been that of finding two-dimensional and axisymmetric profiles that have minimum pressure drag in supersonic flow. The two-dimensional sections are used as wing-profile sections, and the axisymmetric profiles are useful in that the distribution of the cross-sectional area is made to follow the optimumdistribution (the area rule). This problem becomes redundant without suitable constraints. The minimum drag shape is a flat plate in two-dimensional flow and a needle-like profile in axisymmetric flow. This, however, is not a meaningful result. To make the problem more meaningful, the enclosed area/volume should be kept constant. The ends should also be kept pointed. This is to anchor the shocks firmly to the leading and trailing edges. This problem has been solved in the fifties using a linear flow model. However, recent advances in computational fluid dynamics and aerodynamic shape optimization have made it possible for this problem to be analyzed using a nonlinear flow model. The results of this exercise are discussed in this paper.

An Analysis of Bodies Having Minimum Pressure Drag in Supersonic Flow: Exploring the Nonlinear Domain

One of the most interesting problems in supersonic aerodynamics has been to find profile shapes that have minimum pressure drag, subject to a set of geometric constraints. Considerable work was done in this area in the fifties, all of which relied on a linearized flow model. We revisit this problem using a more sophisticated flow model. It is logical to expect the optimum profile shape to look different. We confirm this, but also note that the differences are very small. We then examine the equations of fluid flow and try to see why the linearized flow model works well for this problem and where the differences come from.

Feedback Control of Aerodynamic Flows

Every airplane has an associated external flow field that is extraordinarily rich in terms of its flow physics. It is intuitively obvious that the shape and configuration of the airplane influences the external flow physics, and the nature of the flow field influences the aerodynamic performance. An airplane is designed to perform optimally under certain operating conditions. Its aerodynamic performance is, consequently, sub-optimal at neighbouring operating points. In order to acheive close to optimum performance under such conditions, we need to be able to control the behaviour of the external flow field as required. The objective of this paper is to explore means for flow control, and derive the necessary control laws. It should be noted that the external flow is nonlinear, and hence finding a feedback control law is a mathematically hard problem.

Nonlinear Filter Formulation for Rapid Estimation of Damaged Aircraft Performance

Estimation of aerodynamic models of damaged aircraft using an innovative differential vortex lattice method tightly coupled with extended Kalman filters is discussed. The approach exploits prior knowledge about the undamaged aircraft to reduce the order of the estimation problem. Three different extended Kalman filter formulations are given, together with a comparative analysis. An approach for designing test maneuvers to improve the observability of the system dynamics is also discussed. Algorithms given in this paper can be used as the basis for online derivation of aircraft performance model, which can then form the basis for designing safe landing guidance laws for damaged aircraft. I. Introduction daptive control of damaged aircraft is being investigated at NASA and other aerospace research laboratories in the U.S. 1,2 The focus of these research efforts has been in maintaining control over the attitude dynamics of the damaged aircraft. Assuming that the aircraft remains controllable at its current flight conditions, it is important to be able to predict its performance at other flight conditions in order to derive maneuver constraints that should be enforced to ensure safe transition of the aircraft to landing configuration. The objective of the research discussed in this paper is to develop estimation schemes for rapidly extracting the aerodynamic parameters of damaged aircraft to enable the assessment of aircraft performance. The performance data of interest include flight envelope boundaries and maneuver limits. This data can form the basis for the design of safe landing guidance laws. Several innovative concepts have been advanced in this paper. Firstly, a rapid approach for deriving aerodynamic models of damaged aircraft termed as the Differential Vortex Lattice Method (DVLM) was developed. This approach recasts the well known Vortex Lattice Method (VLM) 3 to reduce the dimension of the aerodynamic problem. The DVLM formulation exploits prior knowledge about the airframe to create a low-order computational methodology for relating the changes in the vehicle geometry due to damage to its aerodynamic parameters. This low-order method can be implemented in real-time onboard for the aircraft to provide estimates of the aerodynamic parameters for use in the computation of flight envelope and maneuver limits, and for adaptive guidance law synthesis. Approaches for estimating the maneuver limits and structural dynamic characteristics are also outlined. Secondly, the Extended Kalman filtering (EKF) approach 4-6 is employed for online estimation of damaged aircraft parameters based on the DVLM. Design of maneuvers for enhancing the observability of the damaged aircraft model parameters is also discussed. The model parameters derived from the estimator can be used for computing the flight envelope and the maneuver limits. These can then be used in the synthesis of safe guidance laws for landing the aircraft. Unlike the airframe stabilization problem, the guidance task is almost entirely based on predictive information about the aircraft dynamics. For instance, landing guidance requires the aircraft to slow down to the approach speeds while descending to the correct altitude at a specified heading. Since damaged aircraft may have a high drag and lower stall angle of attack, the aircraft energy has to be carefully managed to ensure that adequate lift is maintained until flare altitude and touchdown. This will require energy conservative maneuvers and descent strategies. Since damaged aircraft may not be able to employ all its high-lift devices, its speed must be carefully managed to avoid premature loss of lift. These factors make it important to derive a reasonably accurate performance model of the aircraft for the design of a viable guidance system. It may be noted that although most inner-loop flight control systems operate well within the limits of controllability most of the time, the guidance task often involves operating near the edges of the operational envelope.