Sahjendra N. Singh

Decoupling in a Class of Nonlinear Systems by State Variable Feedback

For a class of nonlinear systems we derive a necessary and sufficient condition for the existence of a state variable feedback control law which accomplishes decoupling, as well as some conditions which characterize the class of decoupling control laws. Several examples are presented to illustrate the application of these results. For a special subclass which includes the so-called bilinear systems, we give two equivalent forms of the necessary and sufficient condition.

Adaptive control of chaos in Lorenz system

This paper treats the control of chaos in Lorenz systemsin the presence of system parameter uncertainty. An adaptivecontrol law is derived such that in the closed-loop system thestate of the system can be regulated to a specified point inthe state space. Simulation results are presented which showthe suppression of chaotic behavior and the regulation of statevector to the desired terminal point in spite of the uncertaintyin system parameters.

Direct Adaptive and Neural Control of Wing-Rock Motion of Slender Delta Wings

The question of wing-rock suppression of slender delta wings is considered. Based on a nonlinear model, an adaptive control law for wing-rock control is derived. In this derivation, it is assumed that the aerodynamic parameters in the nonlinear model are not known. The derivation of a control law for wing-rock suppression using neural networks when the dynamics of wing rock are completely unknown is also treated. A radial basis function network is used for synthesizing the controller. An adaptation law is derived for adjusting the parameters of the network. Digital simulation results show that in the closed-loop system wing-rock motion is suppressed using the adaptive and neural controllers.

Adaptive Output Feedback Control of a Nonlinear Aeroelastic Structure

Based on a backstepping design technique, a new adaptive controller for the control of an aeroelastic system using output feedback is derived. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. Theparameters of thesystem areassumed to becompletely unknown, and only the plunge displacement and the pitch angle measurements are used for thesynthesis of thecontroller. A canonical state variable representation of the system is derived, and e lters are designed to obtain the estimates of the derivatives of the pitch angle and the plunge displacement. Then adaptive control laws for the trajectory control of the pitch angle and the plunge displacement are derived. In the closed-loop system the state vector asymptotically converges to the origin. Simulation results are presented, which show that regulation of the state vector to the equilibrium state and trajectory following are accomplished using a single control surface in spite of the uncertainty in the aerodynamic and structural parameters. Nomenclature a = nondimensionalized distance from the midchord to the elastic axis bs = semichord of the wing ch = structural damping coefe cient in plunge caused by viscous damping ci, L, Li, = design parameters di, C ca = structural damping coefe cient in pitch caused by

Adaptive model following control of nonlinear robotic systems

An adaptive model following control law for nonlinear robotic systems with rotational joints is presented. The derivation of the controller does not require any knowledge of nonlinear system matrics and the uncertainty in the system. In the closed-loop system the joint angles asymptotically converge to the reference trajectories.

Invertibility and trajectory control for nonlinear maneuvers of aircraft

This paper presents an application of the inversion theory to the design of nonlinear control systems for simultaneous lateral and longitudinal maneuvers of aircraft. First, a control law for the inner loop is derived for the independent control of the angular velocity components of the aircraft along roll, pitch, and yaw axes using aileron, elevator, and rudder. Then by a judicious choice of angular velocity command signals, independent trajectory control of the sets of output variables (angle of attack, roll, and sideslip angles), (roll rate, angle of attack, and yaw angle), or (pitch, roll, and yaw angles) is accomplished. These angular velocity command signals are generated in the outer loops using state feedback and the reference angle of attack, pitch, yaw, and roll angle trajectories. Simulation results are presented to show that in the closed-loop system, various lateral and longitudinal maneuvers can be performed in spite of the presence of uncertainty in the stability derivatives.

Output Feedback Variable Structure Adaptive Control of a Flexible Spacecraft

Abstract Based on the variable structure model reference adaptive control theory, a new control system for the control of an orbiting flexible spacecraft, using output feedback, is designed. The spacecraft consists of a main rigid body to which elastic appendages are attached. For the purpose of control, a moment generating device is located on the rigid hub. For the derivation of control law, it is assumed that the parameters and the structure of the nonlinear functions in the model are unknown. It is shown that in the closed-loop system including the variable structure model reference adaptive control system designed using bounds on uncertain functions, the pitch angle tracks given reference trajectory and the vibration is suppressed. Digital simulation results show that the closed-loop system has good transient behavior and robustness to the uncertainties, unmodeled dynamics, and disturbance inputs.

Control of Elastic Robotic Systems by Nonlinear Inversion and Modal Damping

Energy efficient, lightweight robot arms for space applications have considerable structural flexibility. For large and fast motions, both the nonlinear coupled dynamics and the elastic behavior of the robots must be considered in control system designs. This paper presents an approach to the control of a class of flexible robotic systems. A control law is derived which decouples the joint-angle motion from the flexible motion and asymptotically decomposes the elastic dynamics into two subsystems, representing the transverse vibrations of the elastic link in two orthogonal planes. This decomposition allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertainty in system parameters. Simulation results are presented to show that large, fast control of joint angles can be performed in spite of space vehicle motion and uncertainty in the payload.

Adaptive output feedback control of spacecraft with flexible appendages by modeling error compensation

Abstract A new adaptive control system for the rotational maneuver and vibration suppression of an orbiting spacecraft with flexible appendages is designed. The model of the spacecraft includes unstructured modeling uncertainties. For the purpose of control, a moment generating device is located on the rigid hub. For the synthesis of the control law, only the output variable (pitch angle) is used for feedback. An adaptive feedback linearizing control law is derived for the trajectory control of the pitch angle. Interestingly, the structure of the controller is independent of the elastic mode dynamics of the spacecraft, since unmodeled functions appearing in the inverse (feedback linearizing) control law are estimated using a high-gain observer for feedback. It is shown that the closed-loop system is exponentially stable. An additional attractive feature of the control system is that it accomplishes compensation of unstructured uncertainties in the model. Simulation results for the spacecraft model show precise trajectory control and vibration suppression.

Adaptive Control of Feedback Linearizable Nonlinear Systems With Application to Flight Control

The question of output trajectory control of a class of input-output feedback linearizable nonlinear dynamical systems using state variable feedback in the presence of parameter uncertainty is considered. For the derivation of a control law, a hypersurface is chosen which is a linear function of the tracking error, its derivatives, and the integral of the tracking error. An adaptive control law is derived such that in the closed-loop system, the trajectory asymptotically converges to this hypersurface. For any trajectory evolving on this surface, the tracking error tends to zero. Based on these results, a new approach to the design of an adaptive flight control system is presented. In the closed-loop system, trajectory control of the sets of output variables roll angle, angle of attack, and sideslip angle ( ,#,/?) using aileron, rudder, and elevator control is presented. Simulation results are obtained to show that precise simultaneous longitudinal and lateral maneuvers can be performed in spite of large uncertainty in the aerodynamic parameters.