Bruce L. Walcott

Combined observer-controller synthesis for uncertain dynamical systems with applications

Control of a class of nonlinear/uncertain systems is discussed using a variable-structure systems approach. Observations of the states of such systems is also considered. The natural extension to an observer-controller design is illustrated using a computer simulation example of a theta -r manipulator. Next, the problem of path planning is addressed using a combined observer-controller strategy. The aspects of hardware implementation of the proposed observer-controller are then analyzed. >

A study of cutting process stability of a boring bar with active dynamic absorber

Abstract In this paper, the use of an active dynamic absorber to suppress machine tool chatter in a boring bar is studied. The vibrations of the system are reduced by moving an absorber mass using an active device such as an piezoelectric actuator, to generate an inertial force that counteracts the disturbance acting on the main system. An equivalent lumped mass model of a boring bar with active dynamic absorber is considered. A cutting process model that considers the dynamic variation of shear and friction angle, that causes self-excited chatter during the cutting process, is applied to the lumped mass model. The theory of regenerative chatter is also applied to the model. Stability boundaries have been calculated for maximum permissible width of cut as a function of cutting speed. A comparison of the boundaries for chatter-free cutting operation of a plain boring bar, a boring bar with passive tuned dynamic absorber and a boring bar with active dynamic absorber is provided in this paper. The comparison shows that a substantial increase in the maximum permissible width of cut for stable cutting operation, over a range of cutting speeds, is obtained for a boring bar equipped with an active dynamic absorber.

Dynamic output feedback controller design for fuzzy systems

This paper presents dynamic output feedback controller design for fuzzy dynamic systems. Three kinds of controller design methods are proposed based on a smooth Lyapunov function or a piecewise smooth Lyapunov function. The controller design involves solving a set of linear matrix inequalities (LMIs) and the control laws are numerically tractable via LMI techniques. The global stability of the closed-loop fuzzy control system is also established.

Robust Control of Pulsed Gas Metal Arc Welding

A system is developed to control the pulsed gas metal arc welding process. To achieve controlled detachment of the droplet, the welding current is switched from a peak level to a background level to induce droplet oscillation. When the droplet moves downwards, the current is switched back to peak level. The combination of downward momentum of the oscillating droplet and increased electromagnetic force guarantees detachment of the droplet. Instead of adjusting duration of the background current, the waveform of the current is adjusted to control the melting rate of the electrode wire without having to change the transfer frequency. It is found that the dynamic model of the process depends on welding operational parameters, which vary with applications, and therefore it is unrealistic for operators to provide welding machines these parameters as inputs. Hence, welding operational parameters are considered as unfixed and their ranges are used to quantify the resultant uncertainty in the dynamic model. As a result, the process is controlled using a single algorithm at different operational parameters. Experiments verified the effectiveness of the system in overcoming two common variations in welding operational parameters, wire speed and contact tube-to-work distance.

Active optimal vibration control using dynamic absorber

A typical spring-lumped mass system undergoing forced vibrations is discussed. A secondary absorber mass connected to the main system through an active force generating element (such as a piezoelectric pusher) is considered as a viable means of suppressing vibrations of the system. State variable techniques are used to formulate the complete system, and optimal state feedback control is studied for such a system. Two approaches for optimal control are taken. First, an optimal control law for a system with known disturbance is considered, while in the second approach optimal control for a linear quadratic regulator problem is studied. The response of the system obtained with optimal control is compared with the response under no control. The results obtained from the two approaches of optimal control are then compared. The results are also compared with those obtained from a previous study of an active dynamic absorber.<<ETX>>

H/sup /spl infin// controller design of fuzzy dynamic systems with pole placement constraints

This paper presents a number of state feedback controller design methods for fuzzy dynamic systems with H/sup /spl infin// optimization and/or additional constraints on the closed-loop pole location. The controller design involves solving a set of linear matrix inequalities and the control laws are numerically tractable via LMI techniques. The global stability of the closed-loop fuzzy control system is also established.

Genetic control of a ball-beam system

This study presents a method of adaptive system control based on genetic algorithms. The method consists of a population of controllers evolving towards an optimum controller through the use of probabilistic genetic operators. A brief overview of genetic algorithms is first given. The remainder of the paper identifies the problems associated with genetic algorithms controllers, and addresses the key issue of stability. A theoretical analysis of the genetic algorithm controller shows the population converges to stable controllers. The controller is then employed to optimize the regulation of a ball-beam system. The dynamics of the ball-beam and the results of computer simulations of the control system are given in support of the developed theory. The genetic algorithm controller is shown to optimize the regulation of the ball-beam system in with respect to an LQR performance index.

H/sub /spl infin//-vibration control for machining using active dynamic absorber technology

A robust control design is developed to minimize a systems response to unknown disturbances. The method consists of on-line identification of the systems state space equations coupled with an H/sub /spl infin//-optimal controller design. The H/sub /spl infin// controller is designed such that the maximum of the systems closed-loop transfer function is less than /spl gamma/(/spl gamma/>0). This robust controller is used to eliminate vibrations in cutting operations of a boring bar with an active dynamic absorber. A boring bar is a metal cutting tool with a large overhang (length-to-diameter ratio). Due to this large overhang, a typical boring bar is characterized by a low dynamic stiffness and is therefore susceptible to excessive vibrations during the cutting process. These vibrations often lead to cutting instability, known as machine tool chatter. In this paper, the control of vibrations of a boring bar with an active dynamic absorber is studied. The robustness of the H/sub /spl infin//-optimal controller is demonstrated by varying the systems dynamic characteristics (i.e., changing the length-to-diameter ratio of the boring bar) without adjusting the calculated control parameters. The results obtained for the H/sub /spl infin// case are compared to similar results for a linear quadratic regulator control design.

Precision instrument for characterizing shape memory alloy wires in bias spring actuation

Some metallic alloys such as Nitinol (NiTi) exhibit the shape memory effect, which is suitable for generating force and displacement when the alloy changes phase during a heating and cooling cycle. These shape memory alloys are often formed into one-dimensional wires, tubes, and ribbons that are preloaded by bias springs to create inexpensive actuators for electromechanical devices. This article describes a new instrument for measuring the quasistatic characteristics of the alloy and the transient performance of bias-spring actuators when resistively heated and convectively cooled. The instrument achieves more accurate measurements by eliminating rolling friction and by sensing force and displacement in line with the bias spring and shape memory alloy wire. Data from the instrument enables calculation of stress and strain at constant temperatures and during actuation cycles.

Interval model based control of gas metal arc welding

A control system is developed to control pulsed gas metal arc welding process. To guarantee the desired metal transfer mode, i.e., one drop per pulse, the welding current is switched from the peak level to the background level so that an oscillation of the droplet is excited up. When the droplet moves downwards, the welding current is switched back to the peak level. The combination of the downward momentum of the oscillating droplet and the increased electromagnetic force guarantees that the droplet be detached. Instead of the duration of the background current, the waveform of the welding current is adjusted to control the melting rate of the electrode wire so that the metal transfer frequency can keep constant during welding. To simplify the control system, the ranges of the welding operational parameters are used to quantify the uncertainty in the dynamic model of the welding process. Based on the uncertainty range of the dynamic model, a single control algorithm has been developed to handle different operational parameters. Experiments confirmed effectiveness of the developed system.