Adaptive Vibration Control of an AxiallyMoving String
Abstract
In this project, the displacement of an axially moving string isregulated using a control force and a control torque applied to thestring via a mechanical guide. Given the hybrid model of the stringsystem (i.e., distributed parameter field equation coupled todiscrete actuator equations), Lyapunov-type arguments are utilizedto design model-based and adaptive control laws that exponentiallyand asymptotically stabilize the string displacement, respectively.The proposed control laws are based on measurements of the stringdisplacement, velocity, slope, and slope rate at the mechanicalguide. While the model-based controller requires exact knowledge ofthe actuator/string parameters (e.g., actuator mass and stringtension), the adaptive controller estimates the parameters online.
Theory
High speed manufacturing and transport of axially moving materials(e.g., webs, filaments, belts, and bands) require control of thelarge vibration that can result from material non-uniformity,support roller motion/eccentricity, or aerodynamic excitation.Material failure due to excessive vibration wastes product andtime, limiting the process productivity. Active vibration controlhas the potential to greatly increase process productivity byeliminating vibration-induced process failures.A number of researchers have developed boundary controllers(i.e., control force applied at the system boundary) based ondistributed parameter models of strings. The use of boundarycontrol to damp out vibration in axially moving systems, however,may be difficult to implement in practice. The size and weight ofthe entry/exit rollers, for example, and their inherent dynamiccoupling with adjacent spans may limit the applicability ofboundary control in axially moving systems.
We developed a novel vibration control system that uses twocontrol inputs to regulate the displacement of a distributed axialmoving string model. The variation of the position and orientationof a mechanical guide located within the material span (see thefigure below) is used to actively damp the string vibration. Basedon a hybrid model of the mechanical system (i.e., a distributedparameter field equation coupled to discrete actuator equations),Lyapunov-type arguments are used to first design a model-basedcontrol law that exponentially stabilizes the string displacementand requires exact knowledge of the actuator/string parameters(e.g., actuator mass and string tension). The control law is thenredesigned as an adaptive controller that asymptotically stabilizesthe string displacement while compensating for parametricuncertainty.
Schematic diagram of the axially moving string and actuatorsystem
Photograph of the axially moving string and actuatorsystem
Experimental Results
See a movie telling you about the experiment [1.1MB in RM format]Displacement of string when an impulse is introduced.
