Feiyue Li

Numerical approach for solving rigid spacecraft minimum time attitude maneuvers

The minimum time attitude slewing motion of a rigid spacecraft with its controls provided by bounded torques and forces is considered. Instead of the slewing time, an integral of a quadratic function of the controls is used as the cost function. This enables us to deal with the singular and nonsingular problems in a unified way. The minimum time is determined by sequentially shortening the slewing time. The two-point boundary-value problem is derived by applying Pontryagins maximum prinicple to the system and solved by using a quasilinearization algorithm. A set of methods based on the Eulers principal axis rotation is developed to estimate the unknown initial costates and the minimum slewing time as well as to generate the nominal solutions for starting this algorithm. It is shown that one of the four initial costates associated with the quaternions can be arbitrarily selected without affecting the optimal controls and thus simplifying the computation. Several numerical tests are presented to show the applications of these methods.

Analytic time-optimal control synthesis of fourth-order system and maneuvers of flexible structures

The analytic solution to the problem of minimum-time control of a fourth-order linear system near the origin is obtained by using Gulkos subsystem strategy. This system has two real eigenvalues (zeros) and two imaginary eigenvalues (vibrational frequency), which represents a flexible structure with one rigid-body mode and one flexible mode. The complete solution including the optimal switching times for the second-order subsystem is first obtained. Next, the geometry of the control switching surface near the origin for the third-order subsystem is analyzed through the phase-plane and phase-space technique. Then, the switching function for the full fourth-order system is constructed by using the roots of a quartic algebraic equation. This solution can be used to synthesize the feedback time-optimal control for the maneuvers of flexible structures. Numerical examples with one and more flexible modes are illustrated to show the applications of the solution.

Optimal large angle maneuvers of a flexible spacecraft

Abstract The optimal control of three-dimensional large-angle rapid maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagranges formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagins Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two-point boundary-value problem is then solved by using the quasilin-earization algorithm and the method of particular solutions. The numerical results for the flexible nonlinear system, the flexible linearized system, and the rigidized nonlinear system are presented to compare the differences in their time responses.

DESIGN OF A REDUCED ORDER H ROBUST CONTROLLER FOR AN EXPENDABLE LAUNCH VEHICLE IN THE PRESENCE OF STRUCTURED AND UNSTRUCTURED PARAMETER UNCERTAINTY

Abstract In order to improve the robust stability and robust performance of an expendable launch vehicle control system in which a PID controller was employed, an H∞ optimal robust controller has been successfully designed. The only weakpoint is the higher order of the H∞ controller as compared with that of the PID controller. When the system model will involve the flexibility of the first and second transverse bending modes and liquid fuel sloshing, the order of the full order H∞ optimal robust controller will reach 26. No doubt, this will create many difficulties for implementation. In this paper the design of the reduced order H∞ robust controller will be studied. The goal of the design not only requires the reduced order controller to be robust against the unstructured and structured parameter uncertainty, but also requires the controller to have a high accuracy and an optimal exogenous disturbance attenuation. After analysis, design and simulations, a 7th order (reduced order) H∞ robust controller has been synthesized. Two model reduction methods have been considered for finding the reduced plant design model: the State Space Truncation and Balanced Truncation. The design validity is certified by simulations of the control process for an expendable launch vehicle. The simulation results indicate that both the robust stability and the robust performance of the 7th order H∞ robust controller are all better than that of the classical PID controller.

Centralized, decentralized, and independent control of a flexible manipulator on a flexible base

Abstract The dynamics and control of a flexible manipulator arm with payload mass on a flexible base in space are considered. The controllers are provided by one torquer at the center of the base and one torquer at the connection joint of the robot and the base. The nonlinear dynamics of the system is modeled by applying the finite element method and Lagrangian formula. Three control strategies are considered and compared, i.e. centralized control, decentralized control, and independent control. All these control designs are based on the linear quadratic regulator theory. A mathematical decomposition is used in the decentralization process so that the coupling between the subsystems is weak, while a physical decomposition is used in the independent control design process. For both the decentralized and the independent controls, the stability of the overall linear system is checked before a numerical simulation is initiated. Two numerical examples show that the responses of the independent control system are close to those of the centralized control system, while the responses of the decentralized control system are not.

Minimum time attitude slewing maneuvers of a rigid spacecraft

The problems of large-angle attitude maneuvers of a spacecraft have gained much consideration in recent years. The configurations of the spacecraft considered are: completely rigid, a combination of rigid and flexible parts, or gyrostat-type systems. The performance indices usually include minimum torque integration, power criterion, and frequency-shaped cost functionals. The minimum time slewing problem of a rigid spacecraft was examined. Optimal control theory (Maximum Principal) was applied to the slewing motion of a general rigid spacecraft. Control torque about all three axes was computed. The equations for the system are composed of the Euler dynamical equations in the spacecraft body axes and the quaternion kinematical equation. By introducing the costates for the quaternion and the angular velocity, the Hamiltonian of the system can be formed and the optimal control obtained. Finally the methods are applied to the SCOLE slewing motion. The control variables include three control moments on the Shuttle and two control forces on the reflector. Numerical results are discussed.

Non-linear compensation control of a manipulator tip on a flexible body☆

Abstract The objective of this paper is to apply the compensation method to control the tip position of a rigid manipulator on a class of main flexible uniform beams. Here, it is proposed to add a compensator at the connection joint between the manipulator and the beam, so that the manipulator can be rotated and also programmed to change its length during the period of the two-dimensional system maneuvers. The non-linear open-loop compensation control law for the space manipulator presented here is extended from the concept of linear compensation control. The exact compensatory correction matches both the linear and non-linear range of system maneuvers. The control law of the system is synthesized based on linear quadratic regulator techniques, in which the inertial torque and force generated by the compensator are considered. The significant results of numerical simulations show that the tip co-ordinates of the manipulator can be made to very closely follow the rigid beam motion which is assumed a desired motion, and that the tip vibration can be successfully suppressed.