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.