On-Off Decentralized Control of Flexible Structures

Abstract

A new near minimum fuel method for on-off decentralized control of flexible structures is introduced. Fuel minimization is achieved by turning on actuators when local velocities are in the neighborhood of a maximum and when local displacements are in the neighborhood of a minimum. Maximum velocity and minimum displacement neighborhoods at each actuator location are determined by recursively computing standard deviations of displacements and velocities over running intervals of time. The fuel consumed by on-off control is shown to be 20 percent lower than by linear optimal control for the same reductions in energy over the same periods of time. On-off control of a uniform beam illustrates the method.

Fuel consumption in optimal control

“…A partial answer to this question can be found in Ref. 6, where a simple impulsive control approximation posted a savings on the order of 20% over continuous control for vibration suppression of a cantilevered beam.…”

“…Note that interest in absolute fuel minimization has been rekindled due in part to the recent development of close approximations of the fuel optimal solution associated with controlling the motion of flexible structures. 6 Optimal control is reviewed in Sec. II along with two fundamental theorems associated with the properties of convex sets.…”

Light impulsive damping of spacecraft exhibiting normal mode behavior

“…(34) the impulsive damping control algorithm for the spacecraft where c rs are coupling coefficients. 8 The coupling coefficients can approximate the Kronecker delta function, that is, c rs d rs , where d rr = 1 and d rs = 0 for r ^ s. Note that the diagonalization of the coupling coefficients provides a fuel optimal basis for the optimal selection of the locations of the control forces and of the subdomain masses m r . 7 1) The impulsive damping control algorithm is independent of spacecraft stiffness.…”