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The effects of input shaping on trajectory following were investigated by simulating the response of a fourth-order system with orthogonal modes and conducting experiments on an XY positioning stage. For nearly all values of damping and frequency ratio, the shaped inputs result in significantly better trajectory following than unshaped inputs. When the(More)
Input shaping reduces residual vibrations by convolving a sequence of impulses, an input shaper, with the desired system command. Using negative impulses in the shaper leads to faster maneuvers. Unfortunately, when negative input shapers are used, there is no guarantee that the shaped command will satisfy actuator limitations. A new type of negative input(More)
Input shaping is a method for reducing residual vibrations in computer controlled machines. Vibration is eliminated by convolving an input shaper, which is a sequence of impulses, with a desired system command to produce a shaped input. The shaped input then becomes the command to the system. Requiring the vibration reduction to be insensitive to modeling(More)
Precise manipulation of payloads is difficult with cranes. Oscillation can be induced into the lightly damped system by motion of the bridge or trolley, or from environmental disturbances. To address both sources of oscillation, a combined feedback and input shaping controller is developed. The controller is comprised of three distinct modules. A feedback(More)
Precise position control and rapid rest-to-rest motion is the desired objective in a variety of applications. The desire for reducing the maneuver time requires reducing the inertia of the structure which subsequently results in low frequency dynamics. The requirement of precise position control implies that the residual vibration of the structure should be(More)
In this paper, we consider the air-traffic conflict-resolution problem and develop an optimization model to identify the required heading and speed changes of aircraft to avoid conflict such that fuel costs are minimized. Nonconvex fuel functions in the optimization problem are modeled through tight linear approximations, which enable the formulation of the(More)