Hariharan Krishnan

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.

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>>

Tracking in Control Systems Described by Nonlinear Differential-Algebraic Equations with Applications to Constrained Robot Systems

In this paper, we consider the problem of designing a feedback control law so that the outputs track desired reference inputs in control systems described by a class of nonlinear differential-algebraic equations. Assumptions are introduced a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.

Computation of state realizations for control systems described by a class of linear differential-algebraic equations

Control systems described in terms of a class of linear differential-algebraic equations are introduced. Under appropriate relative degree assumptions, a computational procedure for obtaining an equivalent state realization is developed using a singular value decomposition. Properties such as stability, controllability, observability, etc, for the differential-algebraic system may be studied directly from the state realization. For linear constrained hamiltonian systems, it is shown that the procedure provides a state realization in which the hamiltonian structure is preserved. Similar results are obtained for constrained gradient systems. Control of systems described by this class of differential-algebraic equations, using a transformation to obtain a state realization, completely avoids the need for any new control theoretic machinery.

Differential-algebraic equations and nonstandard singularly perturbed control systems

A class of control systems is studied that are represented by equations which are not in the standard singularly perturbed form. Assumptions are introduced which guarantee that an equivalent representation can be obtained which is in the standard singularly perturbed form, thereby justifying the two time scale property. It is then possible to show that the equations for the slow dynamics can be characterized by a set of differential-algebraic equations which are easily derived from the original equations by setting the parameter to zero; the original assumptions guarantee the existence of solutions of the obtained differential-algebraic equations. In addition, the equations for the fast dynamics can be expressed in terms of matrices that define the original control system. Control design for the system being considered is studied using the composite control approach. As an example, the problem of contact force and position regulation in a robot with its end effector in contact with a stiff surface is considered.<<ETX>>

Non-standard singularly perturbed control systems and differential-algebraic equations

We consider a class of linear control systems represented by equations depending on a small parameter but which are not in the standard singularly perturbed form. One of the challenging system theoretic problem is to obtain an equivalent representation for the control system which, if possible, is in the standard singularly perturbed form. Assumptions are introduced which guarantee that an equivalent representation can be obtained which is in the standard singularly perturbed form, thereby justifying the two time scale property. The equations for the slow dynamics are characterized by a set of differential-algebraic equations which are easily derived from the original equations by setting the parameter to zero; the original assumptions guarantee the existence of solutions of the obtained differential-algebraic equations. The fast dynamics are characterized by different equations in terms of matrices that define the original control system. Control design for the system being considered is studied using th...

Tracking reference inputs in control systems described by a class of nonlinear differential-algebraic equations

The authors consider the problem of designing a feedback control law in order to achieve tracking of reference inputs in control systems described by a class of nonlinear differential-algebraic equations. The approach is based on an extension of the extended linearization methodology to the class of nonlinear differential-algebraic equations studied. The procedure is reduced to the design of state feedback control laws which asymptotically stabilize a class of parametrized linear differential-algebraic equations. Using the stability theorem of M. Kelemen (1986) and the concept of state realizations for nonlinear differential-algebraic equations, it is shown that the control design guarantees, at least locally, that the tracking error is bounded by any given bound provided the reference inputs are sufficiently slowly varying.<<ETX>>