Keum W. Lee

Multi-Input Noncertainty-Equivalent Adaptive Control of an Aeroelastic System

This paper treats the question of noncertainty-equivalent adaptive control of a nonlinear aeroelastic system with leading- and trailing-edge control surfaces. The model describes the plunge and pitch dynamics of a prototypical wing section. It is assumed that all the system parameters, except the signs of principal minors of the input matrix, are unknown. The objective is to asymptotically regulate the pitch angle and plunge displacement to the origin using two control surfaces. The derivation of the control system is based on the attractive manifold design procedure, which retains interesting features of the immersion and invariance approach, and on the matrix decomposition. The control system has a modular structure consisting of a control module and an identifier and is well defined for arbitrary perturbations in the parameters. Based on the Lyapunov analysis, it is shown that in the closed-loop system, the pitch angle and plunge displacement converge to zero, and the trajectories are ultimately confined to a manifold on which the controller recovers the performance of a deterministic control system. Simulation results are presented that show suppression of oscillatory responses for large parameter uncertainties.

Noncertainty-Equivalent Adaptive Missile Control via Immersion and Invariance

[Abstract] This paper presents a noncertainty-equivalent new adaptive control (NCEA) system for the control of missile based on immersion and invariance approach. The mathematical model of the missile represents the nonlinear longitudinal dynamics, and it is assumed that all the aerodynamic parameters (except the sign of a single control input gain) are not known. Although, other choices of controlled output variables, which are nonlinear functions of state variables are possible, in this paper control of angle of attack is considered. A nonlinear adaptive autopilot for the trajectory control of the angle of attack is derived. The autopilot has a modular structure, which consists of a stabilizer and a parameter estimator. In the closed-loop system, it is seen that the trajectory is conflned to a manifold in the space of missile states and estimated parameters. A special feature of the designed autopilot (unlike the traditional certainty-equivalent (CEA) adaptive systems) is that, whenever the estimated parameters attain their true values, they remain frozen thereafter, and the autopilot recovers performance of deterministic control system. Simulation results are presented which show that the designed autopilot accomplishes trajectory control of the angle of attack despite uncertainties in the system parameters.

Global Robust Control of an Aeroelastic System Using Output Feedback

A EROELASTIC systems exhibit a variety of phenomena including instability, limit cycle, and even chaotic vibration. Researchers in aerodynamics, structures, materials, and control have made interesting contributions to the analysis and control of aeroelastic systems [1]. Readers may refer to an excellent article by Mukhopadhyay [2] for the analysis and control of aeroelastic systems. A benchmark active control technology (BACT) windtunnel model has been designed at the NASA Langley Research Center and control algorithms for flutter suppression have been developed [3–5]. At Texas A&Ma 2-degrees-of-freedom aeroelastic model has been developed and tests have been performed in a wind tunnel to examine the effect of nonlinear structural stiffness, and control systems have been designed using linear control theory, feedback linearizing technique, and adaptive control strategies [6– 10]. Based on the Euler–Lagrange theory, control of an aeroelastic model has been considered [11]. The state variable and output feedback designs of [8–10] are based on adaptive control techniques. The synthesis of adaptive controllers is not simple because a large number of parameters must be updated in the dynamic feedback loop. It is also well known that unmodeled dynamics of the system can cause parameter divergence and instability in the closed-loop system. Therefore, it is interesting to design nonadaptive control systems for uncertain aeroelastic models which can be synthesized relatively easily. The contribution of this paper lies in the design of a robust control system for the global regulation of an aeroelastic system which describes the plunge and pitch motion of a wing. The model has polynomial type structural nonlinearity and only the pitch angle is measured for feedback. It is assumed that all the system parameters are unknown to the designer, but the bounds on uncertainties are known. For the purpose of design, afirst-order dynamic compensator is introduced and a “chained” structure of the aeroelastic model including the dynamic compensator is obtained by an appropriate coordinate transformation. Then using the Lyapunov stability theory, a control law for robust output regulation of the transformed system including the compensator is derived. In the closed-loop system, the controller accomplishes global robust stabilization of the aeroelastic system and system trajectories converge to the origin. Simulation results for various flow velocities and elastic axis locations are obtainedwhich show that the control system is effective in flutter suppression in spite of the large parameter uncertainties. An attractive feature of this control system lies in its simplicity from the point of view of implementation.

Immersion and Invariance Based Adaptive Control of a Nonlinear Aeroelastic System

This paper treats the question of adaptive control of prototypical aeroelastic wing sections with structural nonlinearity based on the immersion and invariance approach. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. A single control surface is used for the purpose of control. It is assumed that the model parameters except the sign of coefficient of control input are unknown. A noncertaintyequivalent adaptive control law for the trajectory tracking of the pitch angle is derived. Using Lyapunov analysis, asymptotic convergence of the state variables to the origin is established. Unlike the certainty-equivalent control laws developed in literature for aeroelastic systems, this new control system can accomplish superior tracking performance. A special feature of the designed control system is that, whenever the estimated parameters coincide with their true values, the adaptation stops and the closed-loop system recovers the performance of deterministic closed-loop system. This cannot happen if certainty-equivalent adaptive controllers are used. Furthermore, the trajectory of the closed-loop system, including the noncertainty-equivalent adaptive law, is eventually confined to a manifold in the space of state variables and parameter estimates. Simulation results using the new controller and the conventional certainty-equivalent controller are presented. These results show that the new controller performs better in suppressing oscillatory responses of the wing in the presence of large parameter uncertainties.

ℒ1 adaptive control of a nonlinear aeroelastic system despite gust load

The development of a control system for the suppression of aeroelastic vibration of a two-dimensional nonlinear wing-flap system based on the ℒ1 adaptive control theory is the subject of this paper. The prototypical aeroelastic wing section model considered here includes structural nonlinearity, parameter uncertainties and gust loads. For the purpose of control, a single trailing-edge control surface is used. The uncontrolled aeroelastic model exhibits limit cycle oscillations beyond a critical free-stream velocity. An ℒ1 adaptive law is developed for the suppression of aeroelastic oscillations using the pitch angle and pitch rate feedback. The control system includes a state predictor. The adaptation gain and the parameter of a filter are properly chosen to satisfy desirable performance bounds on the system trajectories. Simulation results are presented which show that the control system suppresses the oscillatory responses of the system in the presence of large parameter uncertainties and triangular, sinusoidal, and exponential gust loads.

Adaptive Variable Structure Control of Aircraft with an Unknown High-Frequency Gain Matrix

This paper presents nonlinear adaptive and sliding-mode flight control systems for the roll-coupled maneuvers of aircraft. It is assumed that the parameters of the aircraft, as well as its high-frequency gain matrix, are unknown. Based on a backstepping design approach, nonlinear control laws (an adaptive variable structure control law and an adaptive control law) for the trajectory control of the roll angle, angle of attack, and sideslip angle using the aileron, elevator, and rudder are derived. The decomposition of the high-frequency gain matrix is used for the derivation of singularity-free flight control laws. An additional advantage of the control laws lies in the choice of design parameters of matrix decomposition for shaping the response characteristics. In the closed-loop system, the roll angle, angle of attack, and sideslip angle trajectories asymptotically follow the reference output trajectories. Simulation results are presented that show that in the closed-loop system, simultaneous longitudinal and lateral maneuvers are precisely performed in spite of the uncertainties in the aircraft parameters using each control system.

Adaptive Control of Multi-Input Aeroelastic System with Constrained Inputs

The development of an adaptive control system for the control of an uncertain aeroelastic system, in the presence of constraints on the leading- and trailing-edge control surface deflections, is the subject of this paper. The model describes the nonlinear plunge and pitch dynamics of a prototypical wing section. The open-loop system exhibits limit-cycle oscillations beyond a critical freestream velocity. It is assumed that all the system parameters, except the signs of principal minors of the high-frequency gain matrix, are unknown, and external disturbance inputs are present. The objective is to design a saturating control system for suppressing the limit-cycle oscillations. An adaptive control system is designed for tracking reference pitch angle and plunge displacement trajectories. For avoiding singularity in the adaptive law, a decomposition of the input matrix is used for the design. For the analysis of the effect of input saturation, an auxiliary dynamic system is introduced. By the Lyapunov stabil...

Robust Higher-Order Sliding-Mode Finite-Time Control of Aeroelastic Systems

I N THE past, considerable effort has been made for the analysis of aeroelastic instabilities and development of control systems for the stabilization of aeroelastic systems [1]. The analysis of divergence, flutter, and limit-cycle oscillations (LCOs) of a transonic airfoil configuration [2] and supersonic wing section has been performed [3]. A review of the wide range of physical phenomena associated with unsteady transonic flow is provided byMabey [4]. A boundary-element method for the predicton of performance of flapping foils with unsteady leading-edge separation has been developed by Pan et al. [5]. Authors have presented robust aeroservoelastic stability analysis using the μ method [6]. Several authors have designed control systems for the flutter suppression of the benchmark active control technology wind-tunnel model constructed at the NASALangleyResearchCenter [7–9]. Also, at the Texas A&M University, a two-degree-of-freedom experimental apparatus has been constructed for the study of the aeroelastic phenomena [10–13]. For this laboratory model, a variety of control systemshave beendesignedusing a single trailing-edge control surface as well as leadingand trailing-edge control surfaces [10,12–14]. A control lawbased on the state-dependentRiccati equationmethod has been proposed [15]. A robust global control law using output feedback [16] and a variable structure controller using partial state feedback have been designed [17]. Authors have developed several adaptive control systems for this aeroelastic system with uncertainties [13,18–27]. Control of aeroelastic systems using a neural network has also been considered [20,24]. A model reference output feedback adaptive variable structure control law including relays for this system has been also developed [25]. Recently, a noncertainty-equivalent control law and L1 adaptive control systems have been designed for the suppression of LCOs [23,26,27]. The design of robust continuous control systems using parameter adaptation and robustifying signals has been considered [28,29]. An adaptive controller for a minimum-phase airfoil model under unsteady flow has been designed [30]. Researchers have investigated finite-time control of a class of nonlinear systems [31–33]. Also, for a class of uncertain nonlinear multivariable systems, a higher-order sliding-mode control law for the finite-time control has been developed [34], which has a simple structure compared to adaptive systems. In view of its simple structure, it is of interest to design a higher-order sliding-mode finite-time control system for the stabilization of aeroelastic systems. (A comparison of this controller with adaptive controllers designed for aeroelastic systems is provided in Sec. III.) The contribution of this technical Note lies in the design of a second-order sliding-mode control system for the finite-time stabilization of an aeroelastic system, using a leadingand a trailingedge control surface. The model includes parametric uncertainties as well as external disturbance force and moment. A robust control system is designed for the tracking of reference plunge and pitch angle trajectory. The control law includes a nominal finite-time stabilizing continuous control signal designed for the model without uncertainties and a discontinuous control signal for nullifying the effect of uncertain functions in the model. In the closed-loop system, finite-time control of the complete state vector of the aeroelastic model to the origin is accomplished. Simulation results are presented that show that the controller suppresses the oscillatory motion of the system, despite parameter uncertainties and gust loads.

Tuning functions-based output feedback adaptive spacecraft formation flying despite disturbances

This article presents a non-linear adaptive satellite formation control system based on the tuning functions design method using output feedback. A leader spacecraft is orbiting in an elliptic orbit, and a follower satellite is in motion around it. It is assumed that unknown periodic disturbance forces as well as random disturbances are acting on the follower spacecraft, and its mass is not known. Furthermore, only the relative position of the follower satellite, with respect to the leader satellite, is measured for feedback. The objective is to design an adaptive controller so that the follower spacecraft remains in a specific formation with respect to the leader spacecraft. For the purpose of design, first a simplified model including only periodic disturbance inputs is considered, and a canonical representation of the non-linear relative dynamics is obtained. Based on this canonical form, filters are designed to obtain the estimate of the relative velocity of the follower spacecraft and an output feedback adaptive law is derived for the relative position trajectory control. Based on the Lyapunov approach, it is shown that the closed-loop system is globally uniformly stable, and that the adaptive law accomplishes global asymptotic tracking of the reference trajectory in the presence of periodic disturbances. For robustness with respect to random forces in the model, a modified form of the adaptation law using σ-modification is synthesized. Simulation results are presented, which show that the designed output feedback control system achieves precise formation control, despite the periodic and random disturbance forces and parameter uncertainty in the model.

Multi-input submarine control via ℒ1 adaptive feedback despite uncertainties

The development of a novel adaptive autopilot for the dive-plane control of multi-input multi-output submarines with unmodeled dynamics, based on the ℒ1 adaptive control theory, is the subject of this article. An ℒ1 adaptive autopilot is designed for the trajectory control of the depth and pitch angle using bow and stern hydroplanes. Interestingly, the structure of the adaptive controller remains fixed, regardless of the nonlinearities and external disturbance inputs, retained in the model of the submarine. Unlike the traditional adaptive control laws, the ℒ1 adaptive control input is generated by filtering the estimated control signal. A nice feature of the control law is that it is possible to achieve fast adaptation and desirable performance bounds in the closed-loop system by the choice of large adaptation gains. Simulation results are presented, which show that the autopilot accomplishes precise trajectory control in the dive plane, despite parametric uncertainties, unmodeled nonlinearities, and random disturbance inputs.