T. A. Posbergh

Solution of Large-Scale Optimal Unit Commitment Problems

This paper is concerned with the solution of large-scale unit commitment problems. An optimization model has been developed for these problems that incorporates minimum up and down time constraints, demand and reserve constraints, cooling-time dependent startup-costs, and time varying shutdown costs, as well as other practical considerations. A solution methodology has been developed for the optimization model that has two unique features. First, computational requirements grow only linearly with the number of units. Second, performance of the algorithm can be shown (rigorously) to actually improve as the number of units increases. With a preliminary computer implementation of the algorithm, we have been able to reliably solve problems with 250 units over 12 (2-hour) time periods, and we expect to be able to easily double these numbers.

Stabilization of a rotating rigid body by the energy momentum method

The authors discuss the stabilization by feedback control of a rigid body uniformly rotating about an arbitrary axis. They consider a class of feedback laws that depend on a parameter matrix W, which is nonsingular and symmetric. It is shown that under this class of feedback laws, the closed loop system is Hamiltonian and represents the motion of a generalized rigid body. For such systems the energy-momentum method enables determination of feedback gains which ensure the stability for the closed loop system. Several examples are used to demonstrate the methodology.<<ETX>>

Feedback stabilization of uniform rigid body rotation

Abstract This abstract discusses the stabilization of uniform rigid body rotation about an arbitrary axis by feedback control. The class of feedback control laws considered is linear and is shown to robustly stabilize rotation with respect to inertia uncertainty. The methodology developed in this paper is based on the energy-momentum method of stability analysis and fully exploits the underlying geometry. The methodology is illustrated with several examples.

Robust stabilization of a heavy top

This paper investigates the robust stabilization of relative equilibria. The motivating example is that of a heavy top. For the heavy top conditions which ensure the robust stabilization of the system are derived and discussed. These conditions generalize previous results for the rigid body. These conditions are then examined in the case of structured uncertainty in the mass and inertia properties of the top. Bounds are obtained for the family of stabilizing feedback gains and the corresponding error in the rotation axis is investigated. These results are then applied to the specific example of a heavy top with a mass imbalance spinning below critical velocity.

Robust Stabilization of A Uniformly Rotating Rigid Body

This paper presents a method of control design for the stabilization of uniform rotation about an arbitrary axis in a rigid body. The control law introduced in this paper is linear and robust. In contrast to existing methods, the methodology developed here fully exploits the geometric structure of rigid body motion by using the energy-momentum method of stability analysis. The methodology is illustrated with several examples.

Application of Time Optimal Control to the Scole Configuration

The large-angle, nonlinear slew of the Spacecraft Control Laboratory Experiment (SCOLE) is treated with the assumption that the body is rigid. The optimal axis of rotation is first determined and then a time-optimal, bang-bang controller is designed. The controller is implemented in both open-loop and closed-loop form in a numerical simulation using DISCOS. Results are presented which demonstrate controller performance with respect to dynamic coupling compensation, size of the integration time step, and time delay in the response of sensors. This work establishes the theoretical limit of expected performance and provides a foundation upon which a complete, flexible-body control methodology will be developed.

Formulation and simulations of the conserving algorithm for feedback stabilization on rigid body rotations

The problem of stabilization of rigid bodies has received a great deal of attention for many years. People have developed a variety of feedback control laws to meet their design requirements and have formulated various but mostly open loop numerical algorithms for the dynamics of the corresponding closed loop systems. Since the conserved quantities such as energy, momentum, and symmetry play an important role in the dynamics, we investigate the conserved quantities for the closed loop control systems which formally or asymptotically stabilize rigid body rotation and modify the open loop numerical algorithms so that they preserve these important properties. Using several examples, the authors first use the open loop algorithm to simulate the tumbling rigid body actions and then use the resulting closed loop one to stabilize them.

Stabilization of a rotating geometrically exact rod

The problem of stabilization of the uniform rotation of a geometrically exact rod is investigated. A three dimensional, geometrically exact rod model including shear, extension, torsion and flexure is stabilized by means of a feedback torque applied to the boundary. The energy-momentum method of stability analysis is used as the basis of the feedback control design. The result shows that there exist critical rotation rates associated with the internal vibrations which cannot be removed by torque feedback. An example is presented for the case of uniform axial rotation.

Attitude drift for systems with partial internal damping

The use of feedback for the asymptotic stabilization of uniform motion introduces partial internal damping in the system dynamics. For such systems the dynamics converge to relative equilibria of the undamped system. In converging to these relative equilibria the dissipation introduced by the control law does work on the system and moves the spatially referenced angular momentum vector. In this paper we compare attitude drift for the closed loop dynamics with the undamped case and estimate the displacement of the spatially referenced angular momentum vector. The results are illustrated by several numerical examples.<<ETX>>