Gerald Cook

Microsaccades and the Velocity-Amplitude Relationship for Saccadic Eye Movements

The maximum velocities of microsaccades (flicks) are an increasing function of amplitude of movement. Measured velocities fall on the extrapolation of the curve of maximum velocity versus amplitude for voluntary saccades and involuntary corrective saccades. Hence all these movements are produced by a common physiological system, or the characteristics of the movements are determined by a single dynamically limiting element.

Suboptimal control for the nonlinear quadratic regulator problem

In this paper a suboptimal solution to the nonlinear quadratic regulator and tracking problem with infinite final time is investigated. The plant may well be time-varying and nonlinear in state and control. The plant is represented by an apparent linearization and the suboptimal control at any given instant is determined by the optimal control law for the linear model valid at the particular instant. It is shown that with certain restrictions the suboptimal control law exists and is a continuous function of state and time. It is further shown that this suboptimal control law results in a closed-loop system which is asymptotically stable in a sufficiently small region. A computational method for obtaining the suboptimal control law is presented which reduces the amount of computations significantly. This suboptimal control law, based on the solution to the linear regulator problem, involves the steady-state solution to the Riccati differential equation. This matrix is expanded in a Taylor series. The terms of this series can be calculated recursively off-line and thus the problem of repeatedly solving the Riccati equation circumvented. It is shown that the control law obtained by using any finite number of terms in this series preserves the stability of the system.

Weld modeling and control using artificial neural networks

Artificial neural networks were evaluated for monitoring and control of the variable polarity plasma arc welding (VPPAW) process. Three areas of welding application were investigated: weld process modeling, weld process control, and weld bead profile analysis for quality control. Experiments and analysis confirm that artificial neural networks are powerful tools for analysis, modeling, and control applications. They are particularly attractive in view of their capabilities to process nonlinear and noisy data, learn from actual welding data, and execute at relatively high speed. It is shown that neural networks are capable of modeling parameters of the VPPAW process to on the order of 10% accuracy or better. The same was observed when neural networks were used to select welding equipment parameters and the resulting bead geometries were estimated. These performance figures suggest that a VPPA welding control system can be implemented based on neural network models and control mechanisms. >

Derivation of a model for the human eye-positioning mechanism

A model for the human eye-movement mechanism is derived. The derivation is based on a literature search directed toward identifying and mathematically describing each component through physiological and anatomical considerations. It is felt that although certain parameter values may not be exactly correct (for the data were taken from a wide variety of animals), we can place a great deal of confidence in the configuration.

An application of half-cycle Posicast

The problem of compensating a fourth-order, lightly-damped linear feedback system by means of half-cycle Posicast [1] is examined and the results of analog computer simulations are shown. Transient and frequency responses are presented. Although half-cycle Posicast is ideally suited for driving a second-order system, the resulting behavior of the fourth-order system is seen to be quite good with half-cycle Posicast bringing about a fast step response with almost no ripple and eliminating completely any resonant peaking in the frequency response. The sensitivity of behavior to variations in system parameters is examined. Also the system is tested with a quasi-random input signal. In both cases, results are favorable.

Piecewise Linear Control of Nonlinear Systems

Using a Taylor series expansion, nonlinear control systems are approximated about desired equilibrium points in state space as linear control systems. The techniques of the linear regulator problem are then used to calculate the linear state variable feedback gains needed to keep the system at the desired equilibrium point. Liapunovs second method is the basis for determining stable regions of operation about the equilibrium points. When driving the system from one equilibrium point to another, the piecewise linearization method is also used but with intermediate equilibrium points successively utilized. Enough equilibrium points are used so that the system is stable throughout the region of interest. Thus, a nonlinear system is controlled using linear state variable feedback. A small digital computer is required to implement this strategy.

Design and Application of a Microprocessor PID Predictor Controller

A digital PID predictor controller is designed and implemented in a microprocessor. The general purpose system controller described permits the use of integer arithmetic for efficient operation with minimum throughput delay time. The stability of the system is investigated and a normalized chart for the selection of the control coefficients for a class of applications is developed. The controller has been applied to the control of a manipulator as a design example.

General Scheme for Automatic Control of Continuous Bending of Beams

The paper addresses the problem of automating the process of continuous bending of metal beams. The history of previous efforts along these lines is presented and a comparison of this problem with that of numerical control in metal cutting is made. A mathematical model of the bending process suitable for a control system is presented. The uncertainties due to springback and the stochastic nature of bending properties of the beam material are discussed. The needs for parameter identification and output prediction are described. A block diagram for a closed-loop system to control this process is introduced. Results are presented which demonstrate that it is possible to bend to desired curvature if the springback characteristics are known. It is concluded that automatic control of this process is feasible making possible continuous bending of beams into arbitrary desired shapes.

Automated visual inspection and interpretation system for weld quality evaluation

The visual inspection of weld beads and subsequent evaluation of the weld quality is an integral part of the commercial welding environment. However, this inspection process tends to be both time and labor intensive. An automated system for the performance of this task has been developed. The sequence of events in the operation of the vision-based system are: (1) image capture; (2) image enhancement; (3) image processing; and (4) image evaluation. To minimize cost and complexity, the system uses conventional video camera and related hardware and software for the image-capture and image enhancement portion of the evaluation process. Various weld processes were observed to have certain characteristic features which were most relevant for the inspection and evaluation of the particular process. Image processing codes were written to extract those features of the weld beads and store this information in data files for subsequent assessment. Numerical algorithms were written, tailored to each of the weld processes, to perform the image evaluation portion of the quality evaluation process. This result is expressed as a relative quality rating which was found to correlate well with a quality rating derived by direct observation by a human inspector of various quality welds. The vision-based weld quality evaluation system has potential for use as a post-weld quality evaluation system, or, due to the high update rate of the overall vision system (>10 Hz), as part of a real-time control system.

Optimal control of a single link flexible manipulator

This paper deals with an exact state space dynamic model for manipulators with flexible links. We use the Bernoulli-Euler beam equations to derive a frequency domain matrix transfer function. This transfer function is then used to compute the Laplace transform of the state vector as a function of the lateral position along a single link manipulator. The problem of optimal end point control of the beam is then addressed. A sixth-order state space model is derived for the manipulator and the controller is based on this model. Several control laws are studied for this model. Next, the manipulator is modeled as eighth order but the control law based on the sixth-order model is retained. We then estimate the six states from the output of the eighth-order model and feed these states back to the controller to derive the control torque used to drive the manipulator. A filter is introduced to compensate for spillover. The results are very satisfactory, and are illustrated by simulated case studies.