Narendra S. Khot

Predictions of Store-Induced Limit-Cylce Oscillations Using Euler and Navier-Stokes Fluid Dynamics

Store-induced limit cycle oscillation of a rectangular wing with a tip store in transonic flow is simulated. Stability boundaries for this wing are computed for both clean and tip store configurations and behavior beyond the critical freestream velocity is examined at a Mach number of 0.92. The Euler equations are used to model the fluid dynamics and a modal approach is used to model the structural response. Solutions obtained with the Euler equations are compared with results obtained using linear and transonic small disturbance theories. All methods are shown to give similar predictions of the stability boundary in the lower transonic regime but differences develop as the Mach number approaches unity. The linear method fails to capture the rise in flutter speed beyond the flutter dip and is, of course, unable to capture limit cycle behavior. The Euler and transonic small disturbance theories show reasonable qualitative agreement in predicting both unbounded and bounded behavior across a wide range of Mach numbers. There are, however, notable quantitative differences between the Euler and transonic small disturbance theories in the limit cycle onset velocities and response amplitudes and frequencies. The results suggest that the transonic small disturbance theory is a practical alternative to the Euler and Navier-Stokes theories for predicting store-induced limit cycle behavior so long as the small disturbance assumption is valid.

Optimization for efficient structure-control systems

The efficiency of a structure-control system is a nondimensional parameter which indicates the fraction of the total control power expended usefully in controlling a finite-dimensional system. The balance of control power is wasted on the truncated dynamics serving no useful purpose towards the control objectives. Recently, it has been demonstrated that the concept of efficiency can be used to address a number of control issues encountered in the control of dynamic systems such as the spillover effects, selection of a good input configuration and obtaining reduced order control models. Reference (1) introduced the concept and presented analyses of several Linear Quadratic Regulator designs on the basis of their efficiencies. Encouraged by the results of Ref. (1), Ref. (2) introduces an efficiency modal analysis of a structure-control system which gives an internal characterization of the controller design and establishes the link between the control design and the initial disturbances to affect efficient structure-control system designs. The efficiency modal analysis leads to identification of principal controller directions (or controller modes) distinct from the structural natural modes. Thus ultimately, many issues of the structure-control system revolve around the idea of insuring compatibility of the structural modes and the controller modes with each other, the better the match the higher the efficiency. A key feature in controlling a reduced order model of a high dimensional (or infinity-dimensional distributed parameter system) structural dynamic system must be to achieve high efficiency of the control system while satisfying the control objectives and/or constraints. Formally, this can be achieved by designing the control system and structural parameters simultaneously within an optimization framework. The subject of this paper is to present such a design procedure.

Design of smart structures with bounded controls

This paper describes an approach for designing a structure-control system based on the linear quadratic regulator which suppresses vibrations in structures. Bounds are placed on the control forces to simulate real actuators. The structure and control system are optimized with an objective function of the total weight of the structure and the control devices. The design variables are the bounds (which are proportional to the weight of the control devices) on each control force and the cross-sectional areas of the structural elements. A constraints are placed on the time required to reduce the energy of the vibration to 5% of its initial value, structural frequencies and upper and lower bounds on the design variables. As an example to illustrate the application of an approach, a wing box idealized by rod elements is used. The actuators and sensors are collocated and assumed to be embedded in structural elements.

Design and optimal control in smart structures

This paper describes an approach for designing a structure-control system based on the linear quadratic regulator (LQR) which suppresses vibrations in structures. Bounds are placed on the control forces to simulate real actuators. The control system is optimized with an objective function of the time to reduce the energy of the vibrations to 5% of its initial value. The design variables are the bounds on each control force with a constraint on the sum of the bounds. As an example to illustrate the application of an approach, a wing box idealized by rod elements is used. Control systems are designed for this structure using four and eight actuators for several locations.

Acceleration based smart structure (MEMS) control design for aerospace applications

In this paper, a design approach for controlling a composite plate structure subject to aeroelastic loading using piezoelectric actuators and sensors is presented. The nature of the sensing variables is exploited and accommodated in the control design algorithm. The controller is a state estimate based feedback using various measurements related to motion variables such as accelerations, velocities and displacements. Controller designs are based on equivalent first-order state-space baseline design gains that use existing algorithms. The proposed method provides different norms for estimator and controller gains, thereby allowing more flexibility in gain magnitudes and selection of sensors.

Aeroelastic control using smart structures and acceleration feedback

In this paper, a design approach for controlling a composite plate structure subject to aeroelastic loading using piezoelectric actuators and sensors is presented. The nature of the sensing variables is exploited and accommodated in the control design algorithm. The controller is a feedback controller that uses various measurements related to motion variables such as accelerations, velocities and displacements. Proposed controller designs in this paper are based on equivalent first order state-space baseline design gains that use existing control system design software. The proposed method provides different norms for controller gains, thereby allowing more flexibility in gain magnitudes and selection of sensors and still meet the time response specifications.

Static aeroelastic control for pull-up maneuver of a flexible wing with internal actuation

A technique of deforming a flexible wing to hold the airplane in a steady pull-up maneuver with required load factor at high dynamic pressures is examined. Rather than using an elevator system for pull-up, symmetric elastic twist and camber is determined to achieve the required pitching moment for increase in the angle of attack and change in the pitch rate to generate the required lift forces for pull-up maneuver. The elastic twist and camber is achieved by providing a system of actuating elements distributed within the internal substructure of the wing to provide control forces. The modal approach is used to develop equilibrium equations for the steady pull-up maneuver of a wing subjected to aerodynamic loads and the actuating forces. The distribution of actuating forces required to achieve specified load factor was determined by using an iterative procedure in conjunction with an optimal control design approach. Here, a full-scale flexible realistic wing is considered for the assessment of strain energy as a measure of the necessary power required to produce the symmetric twist and camber deformation to achieve the required lift forces. Subsonic and supersonic design conditions are investigated.

DESIGN OF STRUCTURE CONTROL SYSTEM USING BOUNDED LQG

An approach for designing a structure and its control system for vibration suppression is presented. The control system is based on the Linear Quadratic Gaussian (LQG) and is modified to allow bounds on the actuators forces to simulate real actuators. The simultaneous design of the structure and control problem is formulated as a nonlinear optimization problem. The system is designed for minimum weight where the weight includes both the weight of the structure and the weight of the actuators. The weight of an actuator is assumed to be proportional to the bound on the maximum force that it can supply. The design variables include the cross-sectional areas of the structural members and the bounds on the actuator forces. The constraints are imposed on the closed loop frequency distribution and the time to reduce the energy of vibration to a small portion of the initial vibrational energy of the system. The structure is analyzed using a finite element approach. For illustration of the design approach, a truss...

Ply orientation as a design variable in aeroelastic optimization

A wing design optimization study is conducted on a composite wing. The objective is to evaluate the effect of the composite layup orientation on the optimized weight while satisfying constraints on strength, roll reversal velocity and flutter velocity. The wing optimization studies are presented with the composite layups oriented at 5° increments up to ± 20° from the mid spar of the wing, the multidisciplinary optimization system, ASTROS, was used in the design study. This study, although not conclusive, indicates that optimal designs when subjected to multiple structural constraints are relatively insensitive to the orientation of the laminate layup.

Wing shaping for optimum roll performance using independent modal-space control technique

A technique for deforming a flexible wing to achieve a specified roll rate within a specified time at different Mach Numbers is examined. Rather than using an aileron system for roll, antisymmetric elastic twist and camber is determined to achieve the required rolling moment for a specified roll rate. The elastic twist and camber is achieved by providing a system of actuating elements distributed within the internal substructure of the wing to provide control forces. The modal approach is used to develop the dynamic equilibrium equations which culminates in the steady roll maneuver of a wing subjected to aerodynamic loads and the actuating forces. The distribution of actuating forces to achieve the specified steady flexible roll rate within a specified time was determined by using Independent Modal-Space Control (IMSC) design approach. Here, a full-scale realistic wing is considered for the assessment of the strain energy required to produce the antisymmetric twist and camber deformation to achieve the specified roll performance.