Neil C. Singer

Time-Optimal Negative Input Shapers

Input shaping reduces residual vibration in computer controlled machines by convolving a sequence of impulses with a desired system command. The resulting shaped input is then used to drive the system. The impulse sequence has traditionally contained only positively valued impulses. However, when the impulses are allowed to have negative amplitudes, the rise time can be improved. Unfortunately, excitation of unmodeled high modes and overcurrenting of the actuators may accompany the improved rise time. Solutions to the problem of high-mode excitation and overcurrenting are presented. Furthermore, a simple look-up method is presented that facilitates the design of negative input shapers. The performance of negative shapers is evaluated experimentally on two systems; one driven by a piezo actuator and the other equipped with DC motors.

Extra-insensitive input shapers for controlling flexible spacecraft

A procedure for designing command profiles for flexible spacecraft is presented. The command profiles are required to move a spacecraft from rest to rest or to accelerate a spacecraft to a constant velocity with very little residual vibration. To model the case where the spacecraft is equipped with on-off reaction jets, the command signals are restricted to positive or negative constant-amplitude pulses. The technique results in command profiles that are significantly more robust to modeling errors than profiles developed with similar procedures that have been previously reported. Commands are generated that are much more fuel efficient than profiles obtained with related methods. A technique for eliminating multiple modes of vibration is presented. The control technique is evaluated with both hardware experiments and a highly realistic computer simulation that is used to plan Space Shuttle flights.

An input shaping controller enabling cranes to move without sway

A gantry crane at the Savannah River Technology Center was retrofitted with an Input Shaping controller. The controller intercepts the operator`s pendant commands and modifies them in real time so that the crane is moved without residual sway in the suspended load. Mechanical components on the crane were modified to make the crane suitable for the anti-sway algorithm. This paper will describe the required mechanical modifications to the crane, as well as, a new form of Input Shaping that was developed for use on the crane. Experimental results are presented which demonstrate the effectiveness of the new process. Several practical considerations will be discussed including a novel (patent pending) approach for making small, accurate moves without residual oscillations.

Vibration reduction using multi-hump input shapers

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 robust to modeling errors and system nonlinearities is critical to the success of the shaping process on any real system. Input shapers can be made very insensitive to parameter uncertainty; however, increasing robustness usually increases system delays. A design process is presented that generates input shapers with insensitivity-to-time-delay ratios that are much larger than traditionally designed input shapers. The advantages of the new shapers are demonstrated with computer simulations and their performance is verified with experimental results from the MIT Middeck Active Control Experiment, which was performed on board the Space Shuttle Endeavor.

Improving repeatability of coordinate measuring machines with shaped command signals

Performance of coordinate measuring machines (CMMs) is adversely effected by structural vibrations. The effect of input shaping, a method of reducing residual vibration, on the quality of CMM measurements has been investigated. Measurements of a CMM show a reduction of structural deflection when input shaping is used. Additional tests indicate that input shaping improves measurement repeatability over a large range of operating parameters.

Shaping inputs to reduce vibration: a vector diagram approach

A method is described for limiting vibration in flexible systems by shaping the system inputs. Unlike most previous attempts at input shaping, this method does not require an extensive system model or lengthy numerical computation; only knowledge of the systems natural frequency and damping ratio is required. The effectiveness of this method when there are errors in the system model is explored and quantified. An algorithm is presented which, given an upper bound on acceptable residual vibration amplitude, determines a shaping strategy that is insensitive to errors in the estimated natural frequency.<<ETX>>

Effects of input shaping on two-dimensional trajectory following

Input shaping is a method of reducing residual vibrations in computer-controlled machines. Input shaping is implemented by convolving the desired command signal with a sequence of impulses. The result of the convolution is then used to drive the system. Because input shaping alters the commanded trajectory, it has had questionable utility for trajectory following applications such as painting, cutting, and scanning. 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 experimental parameters, input shaping improved trajectory following.

An extension of command shaping methods for controlling residual vibration using frequency sampling

The authors present an extension to the impulse shaping technique for commanding machines to move with reduced residual vibration. The extension, called frequency sampling, is a method for generating constraints that are used to obtain shaping sequences which minimize residual vibration in systems such as robots whose resonant frequencies change during motion. The authors present a review of impulse shaping methods, a development of the proposed extension, and a comparison of results of tests conducted on a simple model of the Space Shuttle robot arm. Frequency shaping provides a method for minimizing the impulse sequence duration required to give the desired insensitivity.<<ETX>>

Comparison of Filtering Methods for Reducing Residual Vibration

This paper compares command filtering techniques for reducing the residual vibration of computer-controlled machines. Input shaping is a relatively new technique that generates vibration-reducing commands by convolving a sequence of impulses with any desired command. The convolution product is then used as the command signal. The simple version of input shaping considered in this paper is a form of finite impulse response (FIR) notch filtering designed to suppress vibration in mechanical systems. Given the great variety of FIR and infinite impulse response (IIR) filters, it is of interest to compare input shaping to conventional filtering. Several types of input shapers are presented and shown to be more effective at reducing residual vibration than any of the conventional filters considered in this paper.

Design and comparison of command shaping methods for controlling residual vibration

The authors evaluate a signal generation technique for commanding high-performance machines to move without exciting residual vibration. This time-domain input-shaping technique works like a filter that is designed to eliminate decaying sinusoidal resonance responses. It is compared to a variety of filtering techniques and is shown to perform more effectively than any of them. In particular, frequency-domain filter design techniques are less effective for shaping vibration-reducing inputs to systems. The three-impulse shaping sequence offers significant performance advantages in that moves require less time and result in little or no residual vibration. In addition, the response is not sensitive to variations in the system parameters.<<ETX>>