Soichi Ibaraki

Rank minimization approach for solving BMI problems with random search

Presents the rank minimization approach to solve general bilinear matrix inequality (BMI) problems. Due to the NP-hardness of BMI problems, no proposed algorithm that globally solves general BMI problems is a polynomial-time algorithm. We present a local search algorithm based on the semidefinite programming relaxation approach to indefinite quadratic programming, which is analogous to the well-known relaxation method for a certain-class of combinatorial problems. Instead of applying the branch and bound method for global search, a linearization-based local search algorithm is employed to reduce the relaxation gap. Furthermore, a random search approach is introduced along with the deterministic approach. Four numerical experiments are presented to show the search performance of the proposed approach.

Monitoring and Control of Cutting Forces in Machining Processes: A Review

Much research has gone into machining process monitoring and control. This paper reviews monitoring and control schemes of cutting force and torque. Sensors to measure cutting force and torque, as well as their indirect estimation, are reviewed. Feedback control schemes and model-based feedforward scheduling schemes of cutting forces, as well as tool path optimization schemes for cutting force regulation, are reviewed. The authors’ works are also briefly presented.

Design of Luenberger state observers using fixed-structure H/sub /spl infin// optimization and its application to fault detection in lane-keeping control of automated vehicles

Lane-keeping control forms an integral part of fully automated intelligent vehicle highway systems (IVHS) and its reliable operation is critical to the operation of an automated highway. We present the design of a fault detection filter for the lane-keeping control systems onboard vehicles used by California-PATH, USA in its automated highways program. We use a Luenberger structure for the fault detection filters and tune the observer gains based on an H/sub /spl infin//-based cost. Such a choice of cost was motivated by the need to explicitly incorporate frequency-domain-based performance objectives. The linear matrix inequality (LMI)-based formulation of an H/sub /spl infin// optimization problem of Luenberger state observers does not allow for the augmentation with dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We present an algorithm to locally solve the problem of the design of Luenberger state observers using H/sub /spl infin// optimization by transforming the problem into an H/sub /spl infin// static output feedback controller problem. Experimental results demonstrate the efficacy of the tuning methodology by comparing the fault detection performance of filters that use H/sub /spl infin// Luenberger observers versus those that use Kalman filters. Implementation issues of the observers are also discussed.

A new formulation of laser step-diagonal measurement-two-dimensional case

The laser step-diagonal measurement modifies the diagonal displacement measurement by executing a diagonal as a sequence of single-axis motions. It has been claimed that the step-diagonal test enables the identification of all the volumetric error components, including linear errors, straightness and squareness errors, in three-dimensional space. In this paper, we show that the conventional formulation of the step-diagonal measurement is valid only when implicit assumptions related to the configuration of laser and mirror setups are met, and that its inherent problem is that it is generally not possible to guarantee these conditions when volumetric errors of the machine is unknown. To address these issues, we propose a new formulation of the step-diagonal measurement, in order to accurately identify volumetric errors even under the existence of setup errors. To simplify the discussion, this paper only considers the two-dimensional version of laser step-diagonal measurement to estimate volumetric errors on the XY plane. The effectiveness of the proposed modified identification scheme is experimentally investigated by an application example of two-dimensional laser step diagonal measurement to a high-precision machine tool.

Tuning of a Hard Disk Drive Servo Controller Using Fixed-Structure H∞ Controller Optimization

To address the problem of improving the positioning accuracy of the read write head of hard disk drives (HDDs), we present a tuning methodology for the HDD servo controller based on the fixed-structure H∞ controller optimization. Since optimization is carried out under the fixed controller structure without any additional sensor, no extra cost is introduced. The effectiveness of the proposed method is demonstrated by simulation and experimentation.

A Tool Path Modification Approach to Cutting Engagement Regulation for the Improvement of Machining Accuracy in 2D Milling With a Straight End Mill

In two-dimensional (2D) free-form contour machining by using a straight (flat) end mill, conventional contour parallel paths offer varying cutting engagement with workpiece, which inevitably causes the variation in cutting loads on the tool, resulting in geometric inaccuracy of the machined workpiece surface. This paper presents an algorithm to generate a new offset tool path, such that the cutting engagement is regulated at a desired level over the finishing path. The key idea of the proposed algorithm is that the semi-finish path, the path prior to the finishing path, is modified such that the workpiece surface generated by the semi-finish path gives the desired engagement angle over the finishing path. The expectation with the proposed algorithm is that by regulating the cutting engagement angle along the tool path trajectory, the cutting force can be controlled at any desirable value, which will potentially reduce variation of tool deflection, thus improving geometric accuracy of machined workpiece. In this study, two case studies for 2D contiguous end milling operations with a straight end mill are shown to demonstrate the capability of the proposed algorithm for tool path modification to regulate the cutting engagement. Machining results obtained in both case studies reveal far reduced variation of cutting force, and thus, the improved geometric accuracy of the machined workpiece contour.

H/sub /spl infin// optimization of Luenberger state observers and its application to fault detection filter design

This paper considers H/sub /spl infin// optimization of Luenberger state observers. The conventional formulation of H/sub /spl infin//-optimal state observers does not allow the augmentation of dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We propose an algorithm to locally solve an H/sub /spl infin// optimization problem of Luenberger state observers by transforming the problem into an H/sub /spl infin// optimization problem of a static output feedback controller. The proposed approach offers an intuitive and efficient way to explicitly design the estimation error dynamics of the observer in the frequency domain. As an application example, the proposed approach is applied to the tuning of fault detection filters for lateral control of automated passenger vehicles. Numerical simulations are conducted to show the effectiveness of the proposed tuning method.

A Five-Axis Machining Error Simulator for Rotary-Axis Geometric Errors Using Commercial Machining Simulation Software

This paper presents a simulator that graphically presents the influence of rotary-axis geometric errors on the geometry of a finished workpiece. Commercial machining simulation software is employed for application to arbitrary five-axis tool paths. A five-axis kinematic model is implemented with the simulator to calculate the influence of rotary-axis geometric errors. The machining error simulation is demonstrated for 1) the cone frustum machining test described in ISO 10791-7:2015 [1], and 2) the pyramid-shaped machining test proposed by some of the authors in [2]. The influences of the possible geometric errors are simulated in advance. By comparing the measured geometry of the finished workpiece to the simulated profiles, major error causes are identified without numerical fitting to the machine’s kinematic model.

Thermal Test for Error Maps of Rotary Axes by R-Test

Thermal distortions are regarded as one of major error factors in a machine tool. ISO 230-3 [1] describes tests to evaluate the influence of thermal distortions caused by linear motion and spindle rotation on the tool center position (TCP). No test is described in these standards on the thermal influence of a rotary axis. Furthermore, conventional thermal tests only measure thermal influence on the positioning error at a single point, not error motions of an axis. This paper proposes a method to calibrate thermal influence on error motions of rotary axes in five-axis kinematics by the static R-test. The R-test measurement clarifies how error motions of a rotary table changes with the rotation of a swiveling axis, and how error motions are influenced by thermal changes. Experimental demonstration will be presented.

Non-Contact R-Test for Error Calibration of Five-Axis Machine Tools

The R-test is a new instrument to measure three-dimensional displacement of a precision sphere attached to a spindle relative to a work table by using three displacement sensors. Its application to error calibration for five-axis machine tools has been studied in both academia and industry. For the simplicity in calculating the sphere center displacement, all conventional R-test devices use contact-type displacement sensors with a flat-ended probe. Conventional contact-type R-test may be potentially subject to the influence of the friction or the dynamics of supporting spring in displacement sensors particularly in dynamic measurement. This paper proposes a non-contact R-test with laser displacement sensors. A new algorithm was proposed to estimate the three-dimensional displacement of sphere center by using laser displacement sensors, It compensates the measurement uncertainty caused by the inclination of the target surface. Experimental case studies are presented to evaluate its measurement performance by comparing with the conventional contact-type R-test device.Copyright