Adaptive and Supertwisting Adaptive Spacecraft Orbit Control Around Asteroids

This paper addresses the development of control systems for the orbit control of spacecraft around irregularly shaped rotating asteroids with uncertain parameters. The objective is to steer the spacecraft along prescribed orbits. First, a nonlinear adaptive law for orbit control was designed. This was followed by the design of a supertwisting adaptive (STWA) control system. In the closed-loop system, which includes the adaptive law or the STWA law, all the signals remain bounded, and the trajectory tracking error asymptotically converges to zero for any initial condition. Finally, under the assumption of boundedness of the derivative of the uncertain functions of the model in a region of the state space, a supertwisting control (STW) law for finite-time convergence of the trajectory was obtained. Based on the Lyapunov theory, stability properties of the closed-loop systems were analyzed. Simulation results for 433 Eros and Ida asteroids were presented for illustration. The results showed that control of spacecraft along closed orbits or to a fixed point is accomplished using each of these controllers, despite uncertainties in the parameters of the asteroid models

Non-Certainty-Equivalent Adaptive Control of a Nonlinear Aeroelastic System

The development of a non-certainty-equivalent adaptive control system for the control of a nonlinear aeroelastic system is the subject of this paper. The prototypical aeroelastic wing section considered here includes structural nonlinearity and a single control surface for the purpose of control. Its dynamical model has two-degree-of-freedom and describes the plunge and pitch motion. It is assumed that the model parameters (except the sign of one of the control input coefficients) are not known. The uncontrolled aeroelastic model exhibits limit cycle oscillation beyond a critical free-stream velocity. Based on the attractive manifold, and the immersion and invariance methodologies, a non-certainty-equivalent adaptive state variable feedback control law for the trajectory tracking of the pitch angle is derived. Using the Lyapunov analysis, asymptotic convergence of the state variables to the origin is established. It is shown that the trajectory of the system converges to a manifold. The special feature of the designed control system is that the closed-loop system asymptotically recovers the performance of a deterministic controller. This cannot happen if certainty-equivalent adaptive controllers are used. Simulation results are presented which show that the control system suppresses the oscillatory responses of the system in the presence of large parameter uncertainties

Experimental Dual-mode Control of a Flexible Robotic Arm

This paper focuses on the implementation of a dual-mode controller for the maneuver of a single link flexible robotic arm. The joint angle trajectory tracking is accomplished by a proportional and derivative PD and a feedforward controller. Based on the pole placement technique, a linear stabilizer is designed for elastic mode stabilization. The stabilizer is switched on when the trajectory reaches the vicinity of the terminal state, and the effect of . switching time on arm vibration is investigated. An optical deflection sensor is used for on-line measurements of elastic deflections, and also used for the prediction of the static deflection of the arm in the target position. The robustness of the linear stabilizer at varying payloads is presented

Variable Structure End Point Control of a Flexible Manipulator

We treat the question of control and stabilization of the elastic multibody system developed in the Phillips Laboratory, Edwards Air Force Base, California. The controlled output is judiciously chosen such that the zero dynamics are stable or almost stable. A variable structure control (VSC) law is derived for the end point trajectory control. Although, the VSC law accomplishes precise end point tracking, elastic modes are excited during the maneuver of the arm. A Linear stabilizer is designed for the final capture of the terminal state

Adaptive Control of Decouplable Systems and Nonlinear Flight Control Systems

This paper treats the question of output trajectory tracking in nonlinear systems in the presence of uncertainty. It is assumed that the nominal system is decouplable using state variable feedback. An adaptive control law is derived such that in the closed-loop system, output vector asymptotically converges to the given reference trajectory. The controller includes a dynamic system in the feedback path. This result is applied to design a flight control system to control roll angle, angle of attack and sideslip in rapid, nonlinear maneuvers of aircraft

Inverse Control and Stabilization of Free-flying Flexible Robots

The question of control and stabilization of flexible space robots is considered. Although, this approach is applicable to space robots of other configurations, for simplicity, a flexible planar two-link robot, mounted on a rigid floating platform, is considered. The robotic arm has two revolute joints and its links undergo elastic deformation in the plane of rotation. Based on nonlinear inversion technique, a control law is derived for controlling output variables describing the position and orientation of the platform and the joint angles of the robot. Although, the inverse controller accomplishes reference trajectory tracking, it excites the elastic modes of the arm. For the vibration suppression, three different stabilizer are designed. Using linear quadratic optimal control theory, a composite stabilizer for stabilization of the rigid and flexible modes and a decoupled flexible mode stabilizer are designed for regulating the end point of the robot to the target point and vibration suppression. Stabilization using only elastic mode velocity feedback is also considered. For large maneuvers, first the inverse controller is active, and the stabilizer is switched for regulation when the motion of the robot lies in the neighborhood of the terminal equilibrium state. Simulation results are presented to show that in the closed-loop system including the inverse controller and each of the stabilizers, trajectory tracking and stabilization of elastic modes are accomplished

Finite-time Sliding Mode and Super-twisting Control of Fighter Aircraft

The development of two nonlinear robust higher-order flight control systems for roll-coupled maneuvers of fighter aircraft with uncertain parameters is discussed in this article. The objective is to independently control the output variables (roll angle, pitch angle and sideslip angle) using aileron, elevator and rudder control surfaces. For a nominal model of aircraft, first a finite time stabilizing (FTS) control law, based on the notion of geometric homogeneity, is designed. Then for robust control in the presence of parameter uncertainties, (i) a discontinuous sliding mode (DSM) control law and (ii) a super-twisting (STW) continuous control law is designed. It is shown that in the composite closed-loop system consisting of either (a) the FTS and DSM control laws or (b) the FTS and STW control systems, the output trajectory tracking error and its first-order derivative converge to the origin in finite time. Digital simulation results for a swept-wing fighter aircraft, including the two composite control systems, are obtained. These results show that each of the designed flight controllers accomplishes precise simultaneous large longitudinal and lateral maneuvers, despite uncertainties in the aerodynamic and inertia parameters, turbulence, and partial loss of control surface effectiveness

Control and Stabilization of a nonlinear Uncertain Elastic Robotic Arm

An approach is presented to the control of an uncertain nonlinear flexible robot arm (PUMA-type) with three rotational joints. The third link is assumed to be elastic. A torquer control law, which is a function of the trajectory error, is derived for controlling the joint angles. The knowledge of the system dynamics is not required for the derivation of the controller. This controller includes a reference model to generate command joint angle trajectories, and a dynamic system in the feedback path which requires only joint angle and rate for feedback. The torquer controller asymptotically decouples the elastic dynamics into two subsystems, representing the transverse vibration of the elastic link in two orthogonal planes. For the damping of the elastic vibration, a force control law using modal velocity feedback is synthesized. Simulation results are presented to show that the combination of the torque and force control law accomplishes reference joint angle trajectory tracking and elastic mode stabilization despite the uncertainty in the system

Control of nearly Singular Decoupling Systems and nonlinear Aircraft Maneuver

The author treats the question of control of a class of nonlinear systems using state variable feedback whose input/output map is nearly singular. Although the existing decoupling theory is applicable to such systems, this requires a large amount of control, which may not be permissible. A decoupling approach using state variable feedback in an approximate sense, but requiring a small control magnitude is considered. A decoupling scheme is presented that gives rise to a singularly perturbed system describing the fast dynamics of the control vector. The quasi-steady-state solution of the system gives a control law that decouples the system in an approximate way. The controller includes a servo compensator and a reference trajectory generator. Based on this result, a control law for approximate decoupling of roll angle, angle of attack, and sideslip in rapid, nonlinear airplane maneuvers is derived. Simulated responses of the closed-loop system show that large, simultaneous lateral and longitudinal maneuvers can be accurately performed in spite of uncertainty in stability derivatives