Vibration Isolation Using a Multi-axis Robotic Platform

Stewart platform is a good candidate for high speed and six degree of freedom motion control, finding its application in the area of multi-axis vibration control. The critical problems associated with Stewart platform are the high non-linearity and uncertainty in its dynamics. To model the system dynamics of the Stewart platform a simple linear model is developed, for the motion of the Stewart platform in stationary position using Newton-Euler equations of motion for rigid body. The damping and stiffness matrix are found to be proportional to each other and so simplifying the dynamics. For the developed dynamic model various control strategies are applied and the performance of the system is studied to identify the best suited control strategy for vibration isolation applications. Modeling and testing of the control strategies are done using MATLAB and is to be verified experimentally. INTRODUCTION Control of vibration has received a great deal of interest in all precision pointing and positing systems. Control of vibration is achieved by both passive and active means. While passive means are effective in unpowered configurations introducing no risk of instability. Active means are found to be well suited for dynamic systems, promising increased isolation performance. In general, the requirements for vibration control in precision applications maybe classified into two levels, vibration isolation[1] at a component level and structural vibration suppression at a system level. Vibration isolation at component level would be referred to as active vibration control in this paper. In component level isolation, a vibration isolation device provides articulation while reducing the vibration transmission between vibration source and parts, which needs to be vibration-free. Among others, the Stewart platform manipulator is a good candidate for high speed and six degree of freedom(DOF) motion control[2] finding its applications in the area of multi-axis vibration control of a structure even under a relatively large payload[1,2,4,5]. The vibration control application of a Stewart platform is quite different from using a Stewart platform as a flight simulator or as a multiple DOF parallel link manipulator. The stroke of actuators required for damping structural vibration is of the order of magnitude of microns, and frequency response performance should achieve the range of kHz. Force capability required by vibration control devices varies in different applications as per the requirement. On the other hand, the Stewart platform manipulator has a critical drawback, against the conventional vibration control devices, that the high nonlinearity and uncertainty in its dynamics. So, one of the open problems as mentioned by Dasgupta et. al.[3], study of dynamic behavior of the manipulator through extensive simulation and analytical/numerical tools for ODE system, is combined along with the application of a simple control strategy, for the vibration isolation application. This paper is organized as the following: In section II we would present why we use cubic configuration of Stewart platform for vibration isolation applications stating the advantages over conventional configurations. The section III carries the Newton-Euler’s closed-form dynamic formulation for the general Stewart platform and its application to vibration isolation problem. The results obtained by applying a simple PD control algorithm to the system is shown and discussed in section VI.