Modal Control of Flexible Systems Using Distributed Sensing

Abstract:

Vibration and noise reduce the perceived quality, productivity, and efficiency of many mechanical systems. We have designed a modal controller for conservative flexible systems that uses distributed sensing. Spatial filtering of the distributed displacement and velocity measurements based on the system eigenfunctions prevents spillover instabilities in the closed-loop system. The proposed control is proven to stabilize a discrete set of controlled modes without destabilizing the remaining, residual modes. We then apply the theory to a single flexible link robot arm and experimentally demonstrate the feasibility of the proposed control strategy. The experiments use high speed video feedback with image processing to determine the spatial beam curve. The controller quickly damps the first modal response without causing instability in the remaining modes.

Experimental Setup:

The experimental testbed consists of thin flexible beam actuated at one end by a switched reluctance motor (SRM) and carrying a payload mass of 0.1 [kg].

The following control hardware is used :

  • A Dalsa CAD-6 camera that captures 955 frames per second with 8-bit gray scale at a 256X256 pixel resolution
  • Road Runner Model 24 video capture board
  • Two Pentium II-based personal computers (PCs) operating under QNX (micro kernel-based, real-time operating system).
A 102,400-count resolver is mounted on the SRM to measure hub angular displacement. Data acquisition and control implementation are performed at 1 [kHz] via the Quanser MultiQ I/O Board and interfacing circuitry. The Dalsa camera, with lens of 0.08[m] focal length, is mounted 1.2[m] above the robot workspace. One PC hosts the video capture board and acquires and processes the visual data from the high-speed camera. This raw data is processed to obtain distributed displacement measurements.

The time derivative calculations are implemented using a standard, backwards difference/filtering algorithm. The control algorithms are written in C++ and implemented using the QMotor real-time control environment.

Figure (a) shows a photograph of the experimental setup as seen by the camera. The camera viewing area is square and does not include the entire link. This simplifies the image processing. A snapshot, the beam centerline pixel data, and a best fit cubic polynomial are shown in Figures (b)-(d). The four time-varying polynomial coefficients are then transmitted via a fast, dedicated TCP/IP connection to the other PC, where the control algorithm and other I/O operations associated with the flexible link robot are implemented.

Experimental Results:

The objective of the experiment is to regulate the angular displacement of the flexible link robot arm to a setpoint of 20[deg] starting from an initial angle of 0[deg].

A PD control Law is initially implemented with the control gains tuned to achieve the best performance. The proposed Modal controller is then implemented and its performance is compared with that of the PD Controller.

  • Hub Angular Displacement: These figures illustrate that both the controllers achieve the same angular displacement of the arm (as measured at the hub).
  • Camera Measured Displacements: These figures show the camera measured displacements at x=0.45L and x=0.85L, respectively, measured in pixels to quantify and compare the vibration regulation performance of both controllers.
  • Controller Torques : These figures illustrate that the Modal Controller achieves the same Hub Angular Displacement as the PD Controller with nearly 60% lower torque.
  • Modal coordinates : These figures show the Modal coordinate and its time derivative for the Controlled Mode of the Flexible Link Robot Arm.

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