Positioning and Active Damping of Spring-Mass Systems

Abstract

In this paper, we investigate an alternate approach to the design of controllers for positioning and damping of a system which can be reduced to an equivalent system of springs and masses. The approach taken is to design a controller which uses open-loop positioning followed by closed-loop control for damping. By so doing, we can avoid a conflicting requirements problem associated with traditional state variable feedback design. The open-loop portion of the control is based on optimal control theory, which allows for control saturation. In particular, during this phase of the control, the time to position is minimized. This results in a bang-bang type of control. Once the system has been “positioned,” the controller switches to a closed-loop phase. The particular closed-loop control used here is based on energy methods and is not a full state variable feedback design. The method is illustrated using a low-order spring-mass example, and the results are compared with an LQ design.

Controlling a large flexible structure to mimic a rigid one

“…Because the control forces are bounded, the system may become unstable [2,3]. One way to avoid the saturating control obtained here would be to put a greater penalty on the use of control in the performance index (2.5).…”

“…For example, we could use two actuators to maneuver the system and, when the system reached the desired position, we could use the dosed-loop control to damp out the rest energy in the system. Consider To get a correspondence as close as possible between the LQ method used above, we take as the performance the sum of the total system energy and the total control action as follows [2][3][4] This yields a controlled system with closed-loop eigenvalues…”

“…According to the maximum principle, one can show that the quickest way to perform a rigid body slew maneuver is with bang-bang control [2][3][4][5][20][21][22]. With large control forces, the slew is quick, but large forces may impart an excessive amount of energy into the flexible modes.…”

“…Recently, many control systems have been developed for flexible structures to handle the attitude and shape control problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Most control system designs are based on state variable feedback methods or modern control techniques which are generated without regard to the locations of the actuators.…”

“…Also it has been shown that traditional state variable feedback methods may not be satisfactory when applied to the positioning of flexible structures [3,4]. The objective of this dissertation is to investigate a control design philosophy which, for a given number of actuators, will allow for the positioning of a flexible structure with minimum excitation of internal flexible energy [5].…”