Han Ding

Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design, and Experimental Evaluation

In this paper, a general skeleton on modeling, controller design, and applications of the piezoelectric positioning stages is presented. Toward this framework, a general model is first proposed to characterize dynamic behaviors of the stage, including frequency response of the stage, voltage-charge hysteresis and nonlinear electric behavior. To illustrate the validity of the proposed general model, a dynamic backlash-like model is adopted as one of hysteresis models to describe the hysteresis effect, which is confirmed by experimental tests. Thus, the developed model provides a general frame for controller design. As an illustration to this aspect, a robust adaptive controller is developed based on a reduced dynamic model under both unknown hysteresis nonlinearities and parameter uncertainties. The proposed control law ensures the boundedness of the closed-loop signals and desired tracking precision. Finally, experimental tests with different motion trajectories are conducted to verify the proposed general model and the robust control law. Experimental results demonstrate the excellent tracking performance, which validates the feasibility and effectiveness of the proposed approach.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

A connector-based hierarchical approach to assembly sequence planning for mechanical assemblies

This paper presents an approach to find feasible and practical plans for mechanical assemblies based on a connector-based structure (CBS) hierarchy. The basic idea of the approach is to construct plans for an assembly (i.e. the root node of the CBS hierarchy) by systematically merging plans for primitive structures in the CBS hierarchy, while the plans for primitive structures are built using one of three methods: by reusing the existing plans, by retrieving the stored plans, and by geometric reasoning. The input to the approach consists of the assembly solid model, the connector-based relational model (CBRM) graph, the spatial constraint graphs, and the selected base part for the assembly, all of which are assumed to be generated previously in an interactive and/or automated way. Then, a CBS hierarchy for the assembly is automatically derived from the input CBRM by firstly establishing its functional model, which is constructed from the CBRM by decomposing the assembly or resulted part sets with respect to their connectors. Based on the CBS hierarchy, a set of assembly precedence diagrams representing good plans for the assembly are generated by merging plans for primitive structures systematically in a bottom-up manner. It can be proved that the proposed approach is both correct and complete. To verify the validness and efficiency of the approach, a variety of assemblies including some complicated products from industry are tested in the experimental CBHAP planner.

Point-to-Point Motion Control for a High-Acceleration Positioning Table via Cascaded Learning Schemes

In this paper, effort is devoted to point-to-point motion control for the high-acceleration positioning table driven by linear motors. New performance indices for point-to-point motion are first introduced. Then, a cascaded controller is designed. It consists of an inner loop velocity PI controller and an outer loop position P plus A-type iterative learning controller. In the subsequence, the convergence analysis in both time and frequency domains is given. The control strategy has the property that only the position signal is required in the outer loop. With the common motion profiles, i.e., T-curve and S-curve, and partial knowledge of the system, point-to-point motion experiments are carried out. The maximum acceleration of the motion profile is 0.04 (about 4.07 g), and the maximum velocity is 0.4 mm/ms. Experimental results illustrate that the proposed controller can greatly improve the performance, and the S-curve motion profile has advantages over the T-curve one.

Virtual prototyping of mold design: geometric mouldability analysis for near-net-shape manufactured parts by feature recognition and geometric reasoning

This paper presents a virtual prototyping (VP) approach for geometric mouldability analysis of near-net-shape manufactured parts. The geometric mouldability of a part depends on the geometry of the part and is affected by the number and types of undercut features. A virtual prototype (VP) of a mold, which is a realistic digital product model, is generated by combining automated and interactive approaches to evaluate the mouldability of a part in the early stages of the product development cycle. The automated approaches for generating a VP are proposed to construct the parting surface, cores and cavity of the mold based on the recognized undercut features. Interaction with the VP in the virtual reality environment allows the designers to evaluate the mouldability of a part in an intuitive way. A new volume-based feature recognition method and data structure using non-directional blocking graph (NDBG) have been developed to recognize both isolated and interacting undercut features in a uniform way. Firstly, a set of potential undercuts are generated by performing the regularized difference between the part and its convex hull. The optimal parting direction is then determined by minimizing the number of undercuts. Finally, undercut features are identified from a set of potential features with respect to the optimal parting direction. The potential features of an interacting feature are generated by two stages: volume decomposition, in which the volume to be recognized is decomposed into convex cells by intersecting it with half spaces of its faces having concave edges; and reconstruction of features, in which potential features are reconstructed through systematically connecting the small cells using NDBG of the cells and the part. Moreover, multiple interpretations of an interacting feature can be easily generated by simply subtracting potential external undercut features from each other in different orders. A system configuration for the proposed VP has been developed and implemented using available virtual reality technologies.

A Distance Function Based Approach for Localization and Profile Error Evaluation of Complex Surface

This paper presents a unified framework for best-fitting of complex rigid surface to measured 3-D coordinate data by adjusting its location (position/orientation). For a point expressed in the machine reference frame and a nominal surface represented in its own model frame, a signed point-to-surface distance function is defined, and its properties are investigated, especially, its increment with respect to the differential motion of the surface, up to the second order, is derived. On this basis, localization and profile error evaluation of complex surface are formulated as a nonlinear least-squares problem and nonlinear constrained optimization problem respectively, and sequential approximation algorithms are developed to solve them. The two algorithms have the advantages of implementational simplicity, computational efficiency and robustness. Also strategies for estimating initial solution and compensating probe radius are presented. Examples confirm the validity of the proposed approach.

High-Acceleration Precision Point-to-Point Motion Control With Look-Ahead Properties

This paper investigates the effects of two control algorithms on high-performance point-to-point motions. The emphasis here is to overcome challenges in precision positioning of high-acceleration tables in the presence of significant external disturbances and exited vibration: an A-type of iterative learning control (ILC) (A-ILC) algorithm for repetitive motions and a look-ahead finite impulse response (FIR) filter plus sliding-mode control (SMC) for nonrepetitive motions. The model-free convergence condition and the fastest converging parameter equation for A-ILC are given in the frequency domain. Then, the FIR coefficients are decided through the ILC results and modified to eliminate the friction effect. Experimental studies demonstrate that both the algorithms perform well and the FIR-SMC algorithm is robust in various experimental scenarios which include high acceleration (of 73.7 m/s2 or about 7.5 g), model parameters, and disturbance deviations from the position, velocity, and acceleration at which the ILC (and, hence, FIR) is trained.

Global optimization of tool path for five-axis flank milling with a conical cutter

In this paper, optimum positioning of the conical cutter for five-axis flank milling of slender surfaces is addressed from the perspective of approximating the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. Based on the observation that a conical surface can be treated as a canal surface, i.e. envelope surface of one-parameter family of spheres, the swept envelope of a conical cutter is represented as a sphere-swept surface. Then, an approach is presented to efficiently compute the signed distance between a point in space and the swept surface without constructing the swept surface itself. The first order differential increment of the signed point-to-surface distance with respect to the differential deformation of the tool axis trajectory surface is derived. By using the distance function, tool path optimizations for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework, and a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are given to confirm the validity and efficiency of the proposed approach. Comparing with the existing approaches, the present one improves the machining accuracy greatly. The rationale developed applies to general rotary cutters.

An alternative time-domain index for condition monitoring of rolling element bearings—A comparison study

Abstract Statistical moments have been widely used for detection and diagnosis of rolling element bearing damage. Among them, Kurtosis and Honarvar third moment S r are the major parameters. In this paper a new statistical moment, from the viewpoint of Renyi entropy, is derived, which is shown to be as effective as kurtosis and S r . Comprehensive comparisons of kurtosis, S r and this moment are performed, and the results from simulations and experiments show the new moment has a better overall performance than kurtosis and S r . On the one hand, this moment behaves much like kurtosis but is less susceptible to spurious vibrations, which is considered to be one of the main shortcomings of higher statistical moments including kurtosis. On the other hand, from the viewpoint of sensitivity to incipient faults, which is the major drawback of lower statistical moments including S r , the new moment is superior to S r . Moreover, the sensitivity of this new moment to changes of bearing speed and load is also less than kurtosis and is close to that of S r .

A steepest descent algorithm for circularity evaluation

This paper presents a novel algorithm for evaluating the circularity of a mechanical part by using measurement points obtained with a coordinate measuring machine (CMM). Following the minimum zone criterion set forth in the current ANSI and ISO standards, evaluation of circularity is formulated as a non-differentiable unconstrained optimization problem, and based on the geometric representation of the necessary and sufficient condition for the optimal solution, an efficient steepest descent optimization procedure is proposed to find the circularity value. The steepest descent direction is determined by the method of calculating the minimum translational distance between two convex polygons, which is initially introduced in the field of robot path planning, and the length of the moving step is exactly determined by a presented geometrical method. A computational geometry-based method for pre-processing the measured data is also proposed. In comparison with existing methods, this algorithm has the advantages of computational efficiency and high precision. Simulations and practical example confirm the validity of the presented algorithm.