Mahmut Reyhanoglu

Control and stabilization of nonholonomic dynamic systems

A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested. >

Exponential stabilization of an underactuated autonomous surface vessel

This paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters. It is first shown that although the system is not asymptotically stabilizable to a given configuration using a time-invariant continuous feedback, it is strongly accessible and small-time locally controllable at any equilibrium. Time-invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates. A simulation example is included to demonstrate the results.

Attitude stabilization of a rigid spacecraft using two control torques: a nonlinear control approach based on the spacecraft attitude dynamics

The attitude stabilization problem of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. If the uncontrolled principal axis of the spacecraft is not an axis of symmetry, then the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback. A discontinuous stabi- lizing feedback control strategy is constructed which stabilizes the spacecraft to any equilibrium attitude. If the uncontrolled principal axis of the spacecraft is an axis of symmetry, the complete spacecraft dynamics are not even assessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback, but again a discon- tinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between several feedback functions which are selected to accomplish a sequence of spacecraft maneuvers. The results of the paper show that although standard nonlinear control techniques are not applicable, it is possible to construct a nonlinear discontinuous control law based on the dynamics of the particular physical system.

Attitude stabilization of a rigid spacecraft using two momentum wheel actuators

It is well known that three momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished using smooth feedback. If failure of one of the momentum wheel actuators occurs, we demonstrate that two momentum wheel actuators can be used to control the attitude of a rigid spacecraft and that arbitrary reorientation maneuvers of the spacecraft can be accomplished. Although the complete spacecraft equations are not controllable, the spacecraft equations are controllable under the restriction that the total angular momentum vector of the system is zero. The spacecraft dynamics under such a restriction cannot be asymptotically stabilized to any equilibrium attitude using a timeinvariant continuous feedback control law, but discontinuous feedback control strategies are constructed that stabilize any equilibrium attitude of the spacecraft in finite time. Consequently, reorientation of the spacecraft can be accomplished using discontinuous feedback control.

Control and stabilization of an underactuated surface vessel

This paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters. It is first shown that although the system is not asymptotically stabilizable to a given equilibrium configuration using a time-invariant continuous feedback, it is strongly accessible and small-time locally controllable at any equilibrium. Time-invariant discontinuous feedback control laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates. A simulation example is included to demonstrate the results.

Switched mode feedback control laws for nonholonomic systems in extended power form

Abstract A class of nonholonomic control systems in extended power form is studied. It is demonstrated that under appropriate assumptions Lagranges equations, including classical nonholonomic constraints, can be transformed into the extended power form. A switched mode feedback controller is used to obtain global convergence of the states of the extended power form to the origin. This feedback controller can be interpreted as a hybrid system consisting of a high level discrete event supervisor and a family of low level feedback controllers. The closed loop system exhibits finite-time responses.

Regulation and tracking of the nonholonomic double integrator: a field-oriented control approach

Abstract In this paper we show how a slight modification to the well-known field-oriented control of induction motors allows us to provide simple solutions to the problems of global regulation and tracking for the nonholonomic double integrator. Two controllers are proposed, one motivated by the well-known direct field-oriented motor control, which is a simple continuous static-state feedback that guarantees exponential convergence for all initial conditions in R 3 — {x 2 = x 2 = 0}. To overcome the latter restriction we add a dynamic extension to transfer this (initial conditions) singularity to the controller state, hence making the stability global. This controller is a direct outgrowth of indirect field oriented motor control. In view of the well-known Brocketts condition we obviously do not ensure Lyapunov stability.

Attitude stabilization of a rigid spacecraft using gas jet actuators operating in a failure mode

The authors consider the attitude stabilization of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes. First, the case where the uncontrolled principal axis of the spacecraft is not an axis of symmetry is considered. In this case, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to an equilibrium attitude. Next, the case where the uncontrolled principal axis of the spacecraft is an axis of symmetry is considered. In this case, the complete spacecraft dynamics are not even accessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to an equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is considered. In both cases, the discontinuous feedback controllers are constructed by switching between one of several feedback functions.<<ETX>>

Feedback control of a space vehicle with unactuated fuel slosh dynamics

We develop a mathematical model that describes the accelerating flight of a spacecraft in a fixed plane. The spacecraft is represented as a rigid body and fuel slosh dynamics are included using a common pendulum model. The control inputs are defined by a transverse body fixed force and a pitching moment about the center of mass of the spacecraft; the slosh dynamics are assumed to be unactuated. The model is placed in the form of a nonlinear control system that allows for the study of planar vehicle maneuvers. We develop a nonlinear feedback controller that stabilizes a relative equilibrium corresponding to suppression of the transverse, pitch, and slosh dynamics. This controller is a significant extension of what has been done previously, since it simultaneousl y controls both the rigid vehicle motion and the fuel slosh dynamics.

On the stabilization of a class of nonholonomic systems using invariant manifold technique

This paper presents an asymptotically stabilizing discontinuous feedback controller for a class of nonholonomic systems. The controller consists of two parts: the first part yields an invariant manifold on which all trajectories of the closed-loop system tend to the origin, and the latter part renders the invariant manifold attractive, while avoiding a discontinuity surface. The controller yields exponential stability so that the convergence can be chosen arbitrarily fast.