Control of Vibration in Mechanical Systems Using Shaped Reference Inputs

Dynamic systems which undergo rapid motion can excite natural frequencies that lead to residual vibration at the end of motion. This work presents a method to shape force profiles that reduce excitation energy at the natural frequencies in order to reduce residual vibration for fast moves. Such profiles are developed using a ramped sinusoid function and its harmonics, choosing coefficients to reduce spectral energy at the natural frequencies of the system. To improve robustness with respect to parameter uncertainty, spectral energy is reduced for a range of frequencies surrounding the nominal natural frequency. An additional set of versine profiles are also constructed to permit motion at constant speed for velocity-limited systems. These shaped force profiles are incorporated into a simple closed-loop system with position and velocity feedback. The force input is doubly integrated to generate a shaped position reference for the controller to follow. This control scheme is evaluated on the MIT Cartesian Robot. The shaped inputs generate motions with minimum residual vibration when actuator saturation is avoided. Feedback control compensates for the effect of friction Using only a knowledge of the natural frequencies of the system to shape the force inputs, vibration can also be attenuated in modes which vibrate in directions other than the motion direction. When moving several axes, the use of shaped inputs allows minimum residual vibration even when the natural frequencies are dynamically changing by a limited amount.

A Systems Approach to the Torque Control of a Permanent Magnet Brushless Motor

Many approaches to force control have assumed the ability to command torques accurately. Concurrently, much research has been devoted to developing accurate torque actuation schemes. Often, torque sensors have been utilized to close a feedback loop around output torque. In this paper, the torque control of a brushless motor is investigated through: the design, construction, and utilization of a joint torque sensor for feedback control; and the development and implementation of techniques for phase current based feedforeward torque control. It is concluded that simply closing a torque loop is no longer necessarily the best alternative since reasonably accurate current based torque control is achievable.

Modeling Robot Dynamic Performance for Endpoint Force Control

This research aims to understand the fundamental dynamic behavior of servo-controlled machinery in response to various types of sensory feedback. As an example of such a system, we study robot force control, a scheme which promises to greatly expand the capabilities of industrial robots by allowing manipulators to interact with uncertain and dynamic tasks. Dynamic models are developed which allow the effects of actuator dynamics, structural flexibility, and workpiece interaction to be explored in the frequency and time domains. The models are used first to explain the causes of robot force control instability, and then to find methods of improving this performance.

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.