Atul G. Kelkar

Dissipative Controllers for Nonlinear Multibody Flexible Space Systems

The problem of controlling a class of nonlinear multibody flexible space systems is considered. The system configuration consists of a flexible central body to which a number of flexible articulated appendages are attached, resulting in highly nonlinear dynamics. Assuming collocated actuators and sensors, global asymptotic stability of such systems is established using a nonlinear passivity-based control law. In addition, a special case where the central-body motion is small while the appendages can undergo unlimited motion, it is shown that the system, although highly nonlinear, can be stabilized by linear static and dynamic dissipative control laws. Furthermore, the static dissipative control law preserves stability despite actuator and sensor nonlinearities of certain types. In all cases, the stability does not depend on the knowledge of the model and hence is robust to modeling errors and uncertainties. The results are applicable to a broad class of systems, such as flexible multilink manipulators and multipayload space platforms. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Inner loop control of supersonic aircraft in the presence of aeroelastic modes

Longitudinal control system design is considered for a linearized dynamic model of a supersonic transport aircraft concept characterized by relaxed static stability and significant aeroelastic interactions. Two LQG-type controllers are designed using the frequency-domain additive uncertainty formulation to ensure robustness to unmodeled flexible modes. The first controller is based on a 4th-order model containing only the rigid-body modes, while the second controller is based on an 8th-order model that additionally includes the two most prominent flexible modes. The performance obtainable from the 4th-order controller is not adequate, while the 8th-order controller is found to provide better performance. Frequency-domain and time-domain (Lyapunov) methods are subsequently used to assess the robustness of the 8th-order controller to parametric uncertainties in the design model.

Dynamic dissipative compensators for multibody flexible space structures

The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Lyapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as satellites with multiple payloads and space-based manipulators.<<ETX>>

CSI design of articulated space structures

Integrated control and structural design of flexible spacecraft with articulated appendages is considered. A procedure is proposed by which the resulting design is optimal with respect to a measure of performance for all possible system articulation conditions. The controller design is of the dynamic dissipative type which provides guaranteed closed-loop stability. The procedure is demonstrated for a simple multibody flexible spacecraft model with an articulated appendage.

Computing maximum tracking error due to payload dynamics

The determination of maximum endpoint tracking error due to uncompensated inertial payload dynamics is investigated. The problem is formulated on the basis of well-known kinetic and kinematic relationships with constraints on maximum joint positions and velocities as well as the generalized force/speed constraint relationship for each actuator. An endpoint tracking error objective function is formed, and numerical optimization is used to determine the maximum. An example computation is presented to show the tracking error under progressively increasing payload using a PUMA 560 manipulator with its first three joints in motion.<<ETX>>

Global Asymptotic Stability of Dynamic Dissipative Compensators for Multibody Flexible Space Structures

The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Lyapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as flexible space structures with articulated flexible appendages.