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 fas

Nonlinear control of a class of underactuated systems

A theoretical framework is established for the dynamics and control of underactuated systems, defined as systems which have fewer inputs than degrees of freedom. Control system formulation of underactuated systems is addressed and the class of second-order nonholonomic systems is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the result

Synthetic Jet Actuator-Based Aircraft Tracking Using a Continuous Robust Nonlinear Control Strategy

A robust nonlinear control law that achieves trajectory tracking control for unmanned aerial vehicles (UAVs) equipped with synthetic jet actuators (SJAs) is presented in this paper. A key challenge in the control design is that the dynamic characteristics of SJAs are nonlinear and contain parametric uncertainty. The challenge resulting from the uncertain SJA actuator parameters is mitigated via innovative algebraic manipulation in the tracking error system derivation along with a robust nonlinear control law employing constant SJA parameter estimates. A key contribution of the paper is a rigorous analysis of the range of SJA actuator parameter uncertainty within which asymptotic UAV trajectory tracking can be achieved. A rigorous stability analysis is carried out to prove semiglobal asymptotic trajectory tracking. Detailed simulation results are included to illustrate the effectiveness of the proposed control law in the presence of wind gusts and varying levels of SJA actuator parameter uncertainty

A Sliding Mode LCO Regulation Strategy for Dual-Parallel Underactuated UAV Systems Using Synthetic Jet Actuators

A sliding mode control- (SMC-) based limit cycle oscillation (LCO) regulation method is presented, which achieves asymptotic LCO suppression for UAVs using synthetic jet actuators (SJAs). With a focus on applications involving small UAVs with limited onboard computational resources, the controller is designed with a simplistic structure, requiring no adaptive laws, function approximators, or complex calculations in the control loop. The control law is rigorously proven to achieve asymptotic regulation of both pitching and plunging displacements for a class of systems in a dual-parallel underactuated form, where a single scalar control signal simultaneously affects two states. Since dual-parallel underactuated systems cannot be expressed in a strict feedback or cascade form, standard backstepping-based control techniques cannot be applied. This difficulty is mitigated through careful algebraic manipulation in the regulation error system development, along with innovative design of the sliding surface. A detailed model of the UAV LCO dynamics is utilized, and a rigorous analysis is provided to prove asymptotic regulation of the pitching and plunging displacements. Numerical simulation results are provided to demonstrate the performance of the control law

A Sliding Mode LCO Regulation Strategy for Dual-Parallel Underactuated UAV Systems Using Synthetic Jet Actuators

A sliding mode control- (SMC-) based limit cycle oscillation (LCO) regulation method is presented, which achieves asymptotic LCO suppression for UAVs using synthetic jet actuators (SJAs). With a focus on applications involving small UAVs with limited onboard computational resources, the controller is designed with a simplistic structure, requiring no adaptive laws, function approximators, or complex calculations in the control loop. The control law is rigorously proven to achieve asymptotic regulation of both pitching and plunging displacements for a class of systems in a dual-parallel underactuated form, where a single scalar control signal simultaneously affects two states. Since dual-parallel underactuated systems cannot be expressed in a strict feedback or cascade form, standard backstepping-based control techniques cannot be applied. This difficulty is mitigated through careful algebraic manipulation in the regulation error system development, along with innovative design of the sliding surface. A detailed model of the UAV LCO dynamics is utilized, and a rigorous analysis is provided to prove asymptotic regulation of the pitching and plunging displacements. Numerical simulation results are provided to demonstrate the performance of the control law

Planar reorientation maneuvers of space multibody systems using internal controls

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77104/1/AIAA-11411-971.pd

Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero-momentum mode. Three-axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories.Two approaches are proposed and compared to achieve three-axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full-state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three-axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque

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 result