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

Method and system to perform energy-extraction based active noise control

A method to provide active noise control to reduce noise and vibration in reverberant acoustic enclosures such as aircraft, vehicles, appliances, instruments, industrial equipment and the like is presented. A continuous-time multi-input multi-output (MIMO) state space mathematical model of the plant is obtained via analytical modeling and system identification. Compensation is designed to render the mathematical model passive in the sense of mathematical system theory. The compensated system is checked to ensure robustness of the passive property of the plant. The check ensures that the passivity is preserved if the mathematical model parameters are perturbed from nominal values. A passivity-based controller is designed and verified using numerical simulations and then tested. The controller is designed so that the resulting closed-loop response shows the desired noise reduction

Spacecraft Stabilization and Control for Capture of Non-Cooperative Space Objects

This paper addresses stabilization and control issues in autonomous capture and manipulation of non-cooperative space objects such as asteroids, space debris, and orbital spacecraft in need of servicing. Such objects are characterized by unknown mass-inertia properties, unknown rotational motion, and irregular shapes, which makes it a challenging control problem. The problem is further compounded by the presence of inherent nonlinearities, signi cant elastic modes with low damping, and parameter uncertainties in the spacecraft. Robust dissipativity-based control laws are presented and are shown to provide global asymptotic stability in spite of model uncertainties and nonlinearities. It is shown that robust stabilization can be accomplished via model-independent dissipativity-based controllers using thrusters alone, while stabilization with attitude and position control can be accomplished using thrusters and torque actuators

Robust control of nonlinear flexible multibody systems using quaternion feedback and dissipative compensation

Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages

Robust Stabilization of a Class of passive Nonlinear Systems

The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust

Three-axis stabilization of spacecraft using parameter-independent nonlinear quaternion feedback

This paper considers the problem of rigid spacecraft. A nonlinear control law which uses the feedback of the unit quaternion and the measured angular velocities is proposed and is shown to provide global asymptotic stability. The control law does not require the knowledge of the system parameters, and is therefore robust to modeling errors. The significance of the control law is that it can be used for large-angle maneuvers with guaranteed stability

Reciprocity of Algorithms Solving Distributed Consensus-Based Optimization and Distributed Resource Allocation

This paper aims at proposing a procedure to derive distributed algorithms for distributed consensus-based optimization by using distributed algorithms for network resource allocation and vice versa over switching networks with/without synchronous protocol. It is shown that first-order gradient distributed consensus-based optimization algorithms can be used for finding an optimal solution of distributed resource allocation with synchronous protocol under weaker assumptions than those given in the literature for non-switching (static) networks. It is shown that first-order gradient distributed resource allocation algorithms can be utilized for finding an optimal solution of distributed consensus-based optimization. The results presented here can be applied to time-varying and random directed networks with or without synchronous protocol with arbitrary initialization. As a result, several algorithms can now be used to derive distributed algorithms for both consensus-based optimization and resource allocation, that can overcome limitations of the existing results. While the focus of this paper is on the first-order gradient algorithms, it is to be noted that the results also work with second-order gradient algorithms.Comment: 8 page

A VOLTTRON based implementation of Supervisory Control using Generalized Gossip for Building Energy Systems

 Building energy systems comprising of many subsystems with local information and heterogenous preferences demand the need for coordination in order to perform optimally. The performance required by a typical airside HVAC system involving a large number of zones are multifaceted, involves attainment of various objectives (such as optimal supply air temperature) which requires coordination among zones. The use of traditional centralized optimization involving a large number of variables is very difficult to solve in near real time. This paper presents a novel distributed optimization framework to achieve energy efficiency in large-scale buildings. The primary goals are to achieve scalability, robustness, flexibility and low-cost commissioning. The results are presented using the proposed distributed optimization framework based on a physical testbed in the Iowa Energy Center and demonstrate the advantages of the proposed methodology compared to a typical baseline strategy. The paper outlines a real-life implementation of the proposed framework based on the VOLTTRONTM platform, recently developed by the Pacific Northwest National Laboratory (PNNL)

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