Boundary Control for a General Class of String Models
ObjectiveThe chief objective behind this experiment is the control of an undamped, nonlinear string with actuator dynamics at the boundary.
BackgroundMany different types of flexible mechanical systems exhibit vibration in the presence of disturbances. One method for reducing string vibration is to increase the cable tension; however, this remedy induces high stresses which reduces the life of the cable. Another method for reducing cable vibration is the application of active boundary control via actuators. In this experiment we develop a boundary controller which asymptotically stabilizes the out-of-plane displacement. The control strategy developed removes the need for knowing the exact structure of the nonlinear tension function. The distributed mechanical model includes the dynamics which naturally occur due to the mass of the requisite boundary actuator. The controller requires the measurement of the slope (and its time derivative) of the string at the actuated boundary, the velocity of the string at the actuated boundary and the tension in the string.
Experimental SetupThe proposed controller was implemented on a cable control system designed and built in-house. An elastic nylon string, pinned at one end, and connected to a horizontally-translating gantry at the other end was used for the experiments. A brushed dc motor (Baldor model 3300) was coupled to the gantry using a timing belt. A 1000-count rotary encoder (Hohner) was used to measure the gantry position. A 4000-count rotary optical encoder mounted on the gantry was used to measure the string departure angle while the JR3 Inc. force-torque sensor mounted on at the pinned end measured the tension in the string. A 586 ISA-based Pentium PC hosting a Quanser Consulting MultiQ digital signal processing board served as the computational engine.
The MultiQ board also supported two channels of 16-bit ADCs and DACs. The angular velocity was obtained by applying a backwards difference algorithm to the angle signal. To eliminate quantization noise, the velocity signals were filtered using a second-order digital filter. The six vectors from the JR3 processor unit (forces along the 3 axes and moments along the 3 axes) were attained using DMA. The Processor board was initialized using serial port communication protocol. The control program (in C) was run in Fumotor environment, an in-house s/w control-package. A graphical user interface (GUI) aided the user to change control gains without recompiling the program. A pair of limit switches (using proximity sensors) were mounted at the two ends of the gantry path. These prevented the gantry from hitting the limits. To test the response of the proposed controller, the string was perturbed using a gravity-based drop hammer. The hammer was allowed to hit the string only once and always from the same height. This seemed to yield a consistent input and therefore allowed for comparison between the uncontrolled and controlled vibration of the string.
Plots: Comparing the
Angular Displacements of Open Loop, Damper Control and Full Order
Knowledge Based Controllers