Mi-Ching Tsai

Real-time NURBS command generators for CNC servo controllers

This study proposes a real-time Non-Uniform Rational B-Spline (NURBS) motion command generator for computer numerical control (CNC) machines to achieve the goal of high-speed and highly accurate machining. Different numerical algorithms for implementing the NURBS motion command generator are compared on the basis of both the computation time and the precision of geometric representation. In addition, to reduce the computation time such that the corresponding servo control laws can be executed in real time, both the NURBS motion command generator and the servo control laws are realized using a digital signal processor. Experimental results indicate that the proposed real-time NURBS command generator is able to provide a satisfactory performance.

Development of a Magnetic Planetary Gearbox

In this paper, we describe a new design for a magnetic planetary gearbox. We discuss the theory of operation and a simulated design. We constructed and verified the simulation by measuring the transmitted torque and cogging torque. A magnetic planetary gearbox operates like a mechanical planetary gearbox, except that it is contact-free and needs no gear lubrication. Hence, it has the same characteristics of three transmission modes, a high-speed-reduction ratio, and high durability. The starting point for the design procedure is to avoid possible sliding (i.e., pole-slipping), and we propose three steps to obtain the maximum number of magnetic planet gears. We show that using more planetary gears is a way to increase the transmission torque. Cogging torque can be high in this design. We assessed this potential by using finite-element analysis and then measuring performance of the fabricated gearbox. While the simulation overestimates the cogging torque (for various reasons), we propose a method to reduce the cogging torque to a very low value. We present a literature review to illustrate the development of magnetic gearing and highlight the innovation of this design.

State-space formulae for discrete-time H∞ optimization

Abstract State-space formulae and proofs are given for ail the important steps in discrete-time H 8 optimization. The steps closely follow the algorithms for continuous-time systems, but there are some technically involved differences in the detail that make their derivation non-trivial.

A real-time NURBS surface interpolator for precision three-axis CNC machining

Abstract Due to the fact that the cutting occurs around the cutter contact (CC) point, the efficiency and quality of CNC machining can be improved significantly if the CC velocity along the surface is kept costant. Conventional approaches to machining mainly maintain a constant cutter location (CL) velocity, so that the CC velocity along the surface is often not constant and usually results in non-uniform machining and unsatisfactory quality. To overcome this difficulty, this paper presents a novel NURBS surface interpolator that is capable of real-time generation of CL motion command for ball-end milling of NURBS surfaces and maintaining a constant CC velocity along the CC path and its intervals. For performance evaluation, a three-axis servomechanism driven by three servomotors is controlled to track segments represented by NURBS surfaces. Experimental results verify the effectiveness of the proposed method.

Design of a plug-in type repetitive controller for periodic inputs

This paper presents some practical design criteria for a plug-in type repetitive controller to achieve good tracking performance within a specified frequency range. Upper and lower bounds of the repetitive controller parameters that ensure the stability and the desired performance are derived. It has been found that the decay rate of the tracking error due to periodic inputs is related to the peak value of a defined regeneration spectrum function. The control performance of the present method is evaluated in an experimental software cam system, which needs periodic linear motions, where the real-time control algorithms are implemented using a floating-point digital signal processor (DSP). Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.

Pole-zero cancellations and closed-loop properties of an H ∞ mixed sensitivity design problem

Abstract We examine an H ∞ mixed sensitivity design problem in order to gain an understanding of the pole-zero cancellation phenomenon that is known to occur with such designs. It is shown how the pole-zero cancellation phenomenon is dependent upon the choice of weighting functions used in the problem formulation, and a particular construction of weighting function is given that gives the designer freedom to exploit or prevent the phenomenon. Furthermore, this weighting function is then a mechanism for (partial) pole placement. As a consequence of the construction of this weighting function, it is shown that for a certain class of plant, the Normalized Coprime Factor design procedure of Glover and McFarlane (1989, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions . Springer-Verlag, Berlin) gives rise to (possibly undesirable) pole-zero cancellations. The results are presented for multivariable systems, and are illustrated with a simple design example.

A real-time predictor-corrector interpolator for CNC machining

This paper presents a predictor-corrector interpolator (PCI) for the CNC machining of parts with parametric curves or surfaces. In contrast to existing parametric interpolators, the proposed method uses a simple algorithm as a predictor and the current feedrate command feedback compensation scheme as the corrector. The predictor adjusts itself according to the current feedrate command feedback, it also has the capability of predicting the next reference point of the parametric curves from the current reference point. As a result, the deviations between the current and desired feedrate commands will always fall within the specified feedrate command tolerances. This study aims at developing the mathematical analysis of the PCI, where the convergence condition is derived for the corrector. In this present approach, the user can specify either constant or variable federate and also its feedrate command accuracy. Both the simulation and experiment results are presented to demonstrate the feasibility of the proposed PCI for machining the parametric curves represented in the Non-Uniform Rational B-Spline (NURBS) form.

A novel switched reluctance motor with C-core stators

This paper presents a novel switched reluctance motor (SRM) design in which the stator is simply formed from C-cores. Unlike conventional SRMs, the windings of the new motor can be individually wound into the stator cores without complex winding equipment. Because of the inherent axial field distribution, this type of SRM requires a three-dimensional (3-D) finite-element analysis (FEA) model for detailed flux analysis. This paper proposes an approximated two-dimensional FEA model to speed up computational time. In addition, since the proper current that ensures operation in the saturated region (to maximize torque and efficiency) is often hard to determine systemically, the paper proposes a simple method to determine the optimum operating current so that one can easily decide the rated current and also obtain the maximum motor efficiency. Finally, the paper compares some characteristics of a traditional SRM with those of the proposed SRM. The comparison shows that the proposed SRM performs well in terms of torque and efficiency, and provides a higher degree of flexibility in winding design.

A Variable-Speed Method for Improving Motion Characteristics of Cam-Follower Systems

A cam is often assumed to be operated at a constant speed in designing a cam-follower system. The motion characteristics of the follower are determined once the cam displacement curve is designed. The traditional design method for improving the motion characteristics is to find a new displacement curve which has better motion characteristics. This paper, however, presents an alternative approach by varying the speed of the cam to reduce the peak values of the follower output motion characteristics. Constraints and design criteria for selecting suitable cam speed trajectories are then developed. Finally, examples are given to illustrate the design procedure and also to show its feasibility.

Design and Operation of Interior Permanent-Magnet Motors With Two Axial Segments and High Rotor Saliency

Skewing the magnets in a brushless interior permanent-magnet motor can be difficult. One method to overcome this problem is to use axial segments that are rotated (“twisted”) with respect to each other. Compared to other methods of rotor skewing, this method may reduce manufacturing cost and the complexity of the rotor. This paper addresses the use of two axial segments and the associated effects on the back-electromotive force (EMF) waveform and motor performance. The back-EMF waveforms of an interior permanent-magnet motor are deeply influenced by the tooth-slot and winding harmonics. They should be sinusoidal to reduce torque ripple for ac motor servo drives and other applications where smooth operation is required. In the paper, we present the two-segment rotor structure together with a simple technique for reducing high-order back-EMF harmonics, and we derive the optimal twisted angle of the proposed two-segment rotor. This minimizes the total harmonic distortion of the back-EMF waveform due to tooth-slot effects. We examine cogging torque and the reduction in cogging torque. We apply the twisted angle rotor to two different compressor motors. In addition to the back-EMF, we address the torque ripple under load and the effect of twist on back-EMF constant. We examine the results using finite-element analysis and validate them by experimental measurement.