Dynamics and Control of Smart Structures for Space Applications

Smart materials are one of the key emerging technologies for a variety of space systems ranging in their applications from instrumentation to structural design. The underlying principle of smart materials is that they are materials that can change their properties based on an input, typically a voltage or current. When these materials are incorporated into structures, they create smart structures. This work is concerned with the dynamics and control of three smart structures: a membrane structure with shape memory alloys for control of the membrane surface flatness, a flexible manipulator with a collocated piezoelectric sensor/actuator pair for active vibration control, and a piezoelectric nanopositioner for control of instrumentation. Shape memory alloys are used to control the surface flatness of a prototype membrane structure. As these actuators exhibit a hysteretic nonlinearity, they need their own controller to operate as required. The membrane structures surface flatness is then controlled by the shape memory alloys, and two techniques are developed: genetic algorithm and proportional-integral controllers. This would represent the removal of one of the main obstacles preventing the use of membrane structures in space for high precision applications, such as a C-band synthetic aperture radar antenna. Next, an adaptive positive position feedback law is developed for control of a structure with a collocated piezoelectric sensor/actuator pair, with unknown natural frequencies. This control law is then combined with the input shaping technique for slew maneuvers of a single-link flexible manipulator. As an alternative to the adaptive positive position feedback law, genetic algorithms are investigated as both system identification techniques and as a tool for optimal controller design in vibration suppression. These controllers are all verified through both simulation and experiments. The third area of investigation is on the nonlinear dynamics and control of piezoelectric actuators for nanopositioning applications. A state feedback integral plus double integral synchronization controller is designed to allow the piezoelectrics to form the basis of an ultra-precise 2-D Fabry-Perot interferometer as the gap spacing of the device could be controlled at the nanometer level. Next, an output feedback linear integral control law is examined explicitly for the piezoelectric actuators with its nonlinear behaviour modeled as an input nonlinearity to a linear system. Conditions for asymptotic stability are established and then the analysis is extended to the derivation of an output feedback integral synchronization controller that guarantees global asymptotic stability under input nonlinearities. Experiments are then performed to validate the analysis. In this work, the dynamics and control of these smart structures are addressed in the context of their three applications. The main objective of this work is to develop effective and reliable control strategies for smart structures that broaden their applicability to space systems

Integrated Optimal and Robust Control of Spacecraft in Proximity Operations

With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances

Robust Control of Nonlinear Multibody Flexible Space Structures

A generic nonlinear math model of a multibody flexible system is developed. Asymptotic stability of such systems using dissipative compensators is established. It is proved that, under certain conditions, this class of systems exhibit global asymptotic stability under dissipative compensation. The dissipative compensators considered are static as well as dynamic dissipative compensators. The stability proofs are based on passivity approaches, Lyapunov methods, as well as a key property of such systems, i.e., skew-symmetricity of certain matrix. The importance of the stability results obtained is that the stability is robust to parametric uncertainties and modeling errors. For static dissipative compensators, it is shown that stability is not only robust to parametric uncertainties and modeling errors but also to certain actuator and sensor nonlinearities. Actuator nonlinearities considered are (0, ∞) sector monotonically non-decreasing type, which include realistic nonlinearities such as the saturation nonlinearity. In the presence of dead-zone and hysteresis type nonlinearities, system trajectories do not approach equilibrium point asymptotically, however, it is shown that there is a compact region of ultimate boundedness and system trajectories do not go unbounded. The sensor nonlinearities considered are (0,$\infty$) sector nonlinearities. A more versatile class of dissipative compensators, called dynamic dissipative compensators, is next considered. A control designer has more design freedom with dynamic dissipative compensators than with the static dissipative type. The increased design degrees of freedom can be used to enhance the performance of the control system. The synthesis techniques for static as well as dynamic dissipative compensators for multibody, nonlinear, flexible systems are currently unknown and it is a topic of future research. The asymptotic stability property of a static dissipative controller for multibody, nonlinear, flexible space structures is demonstrated through a simulation example. The example system used consists of a flexible 10-bay truss structure with a flexible, 2-link manipulator arm attached at one end of the truss. This example system is representative of the class of spacecraft envisioned for the future missions. For dynamic dissipative compensators an application example is shown for a multibody planar system with an articulated member. The controller design is based on locally linearized models in the configuration space of the articulated member. This example also demonstrates the use of dissipative compensators in the integrated design framework

Modeling, Analysis, and Optimization Issues for Large Space Structures

Topics concerning the modeling, analysis, and optimization of large space structures are discussed including structure-control interaction, structural and structural dynamics modeling, thermal analysis, testing, and design

Modeling and Slew-Maneuver Control of a Flexible Spacecraft

Slew-maneuver control problem is studied for a flexible spacecraft consisting of a rigid main body to which a long flexible appendage is attached. Nonlinear dynamical system models are developed using both distributed parameter modeling and discrete parameter modeling; these models are shown to be equivalent for appropriately chosen system parameters. Lyapunov-based nonlinear feedback controllers are designed for the control of rigid-body motion while suppressing the lowest frequency vibrational mode. In case of large-angle maneuvers, these nonlinear controllers are shown to outperform the linearization-based controllers including the filtered proportional-derivative (PD) controllers as well as the linear quadratic regulator (LQR) controllers. Finally, the theoretical development is applied to a benchmark flexible system and a number of computer simulations are included to illustrate the results

A class of stabilizing controllers for flexible multibody systems

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems

Control and structural optimization for maneuvering large spacecraft

Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment

Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 1

The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems

Variable structure and singular perturbation control of elastic dynamical systems

This thesis treats the question of control of flexible dynamical systems for space applications. Two elastic dynamical systems are considered; The multibody system developed in Phillips Laboratory, Edwards Air Force Base, CA consists of two elastic links actuated by electric motors at the joints and rotate on a smooth horizontal granite table. An air bearing is used, which allows the whole system to float on the air so that the frictional forces do not exist between the support plate and the granite table. The controlled output is judiciously chosen such that the zero dynamics are stable or almost stable. For the control of the end point, two kinds of parameterizations of end effector position are considered. A variable structure control (VSC) law is derived for the end point trajectory control of each chosen output. Stability of zero dynamics associated with end point control is examined. 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; The second flexible system considered in this thesis is the elastic space vehicle. For the attitude control and vibration stabilization of the elastic space craft (spacecraft-beam-tip body configuration), singular perturbation technique is used. Based on nonlinear inversion, a control law is derived to decouple the attitude angle and the dominant flexible modes from the remaining elastic modes. The inverse control law decomposes the spacecraft dynamics into a slow and a fast subsystem. Based on singular perturbation theory, controllers are designed for each lower-order subsystem. Then a composite state feedback control is obtained by combining the slow and the fast control laws. (Abstract shortened by UMI.)