Chuxiong Hu

An Orthogonal Global Task Coordinate Frame for Contouring Control of Biaxial Systems

Recent research on the coordinated control of biaxial machines for precise contour following has been using various locally defined task coordinate frames (LTCF) “attached” to the desired contour to approximately calculate the contour error for feedback controller designs. Contour error, by definition, is a geometrical quantity depending on the shape of the desired contour only and has nothing to do with the desired motion on the contour. As such, all those moving LTCF-based algorithms have to make the assumptions that the position tracking errors are much smaller than the radius of curvature of the desired contour and the calculated contour error is only an approximation of actual contour error. In contrast, this paper presents an orthogonal global task coordinate frame (GTCF) in which the calculation of contour error is exact to the first-order approximation of the actual contour error, no matter how large the position tracking errors would be. A systematic way to construct curvilinear coordinates of the proposed GTCF using any description of the geometry of the desired contour in a two-dimensional space is also given. Contouring control of a linear motor driven biaxial high-speed industrial gantry is then used as a case study. A simplistic direct adaptive robust controller (ARC) is constructed to deal with the effect of strong coupling of the system dynamics in the task space in addition to modeling uncertainties. The proposed GTCF-based ARC algorithm, along with the traditional LTCF-based ARC ones, are implemented and comparative experimental results are presented. The results validate the effectiveness of the proposed GTCF approach for free-form contouring control with large curvatures and arbitrary position tracking errors and confirm the excellent contouring performance of the proposed approach in general.

Coordinated Adaptive Robust Contouring Control of an Industrial Biaxial Precision Gantry With Cogging Force Compensations

Cogging force is an important source of disturbances for linear-motor-driven systems. To obtain a higher level of contouring motion control performance for multiaxis mechanical systems subject to significant nonlinear cogging forces, both the coordinated control of multiaxis motions and the effective compensation of cogging forces are necessary. In addition, the effect of unavoidable velocity measurement noises needs to be sufficiently attenuated. This paper presents a discontinuous-projection-based desired compensation adaptive robust contouring controller to address these control issues all at once. Specifically, the presented approach explicitly takes into account the specific characteristics of cogging forces in the controller designs and employs the task coordinate formulation for coordinated motion controls. Theoretically, the resulting controller achieves a guaranteed transient performance and a steady-state contouring accuracy even in the presence of both parametric uncertainties and uncertain nonlinearities. In addition, the controller also achieves asymptotic output tracking when there are parametric uncertainties only. Comparative experimental results obtained on a high-speed Anorad industrial biaxial precision gantry are presented to verify the excellent contouring performance of the proposed control scheme and the effectiveness of the cogging force compensations.

Adaptive Robust Precision Motion Control of Systems With Unknown Input Dead-Zones: A Case Study With Comparative Experiments

In this paper, the recently developed integrated direct/indirect adaptive robust control (DIARC) for a class of nonlinear systems with unknown input dead-zones is combined with the desired compensation strategy to synthesize practical high-performance motion controllers for precision electrical drive systems having unknown dead-zone effects. The effect of measurement noise is alleviated by replacing noisy state feedback signals with the desired state needed for perfect output tracking. Theoretically, certain guaranteed robust transient performance and steady-state tracking accuracy are achieved even when the overall system may be subjected to parametric uncertainties, time-varying disturbances, and other uncertain nonlinearities. Furthermore, zero steady-state output tracking error is achieved when the system is subjected to unknown parameters and unknown dead-zone nonlinearity only. The proposed algorithm is also experimentally tested on a linear motor drive system preceded by a simulated unknown nonsymmetric dead-zone. The comparative experimental results obtained validate the necessity of compensating for unknown dead-zone effects and the high-performance nature of the proposed approach.

Coordinated Adaptive Robust Contouring Controller Design for an Industrial Biaxial Precision Gantry

To achieve excellent contouring performance, it is no longer possible to neglect dynamic coupling phenomena that occur during contouring controls, especially for a linear-motor-driven industrial biaxial precision gantry, which often moves at high speeds. In addition, effects of significant parametric uncertainties and uncertain nonlinearities need to be addressed carefully. In this paper, a discontinuous-projection-based adaptive robust controller that explicitly takes into account the dynamic coupling effect is developed for the high-performance contouring controls of linear-motor-driven high-speed/acceleration systems under various parametric uncertainties and uncertain nonlinearities. Theoretically, the resulting controllers achieve certain guaranteed transient performance and steady-state tracking accuracy. In addition, asymptotic output tracking is achieved under parametric uncertainties only. Comparative experimental results are obtained for a linear-motor-driven biaxial high-speed industrial gantry. The results verify the excellent contouring performance of the proposed schemes, even in the presence of parametric uncertainties and uncertain nonlinearities.

Global Task Coordinate Frame-Based Contouring Control of Linear-Motor-Driven Biaxial Systems With Accurate Parameter Estimations

This paper presents a global task coordinate frame (TCF) (GTCF)-based integrated direct/indirect adaptive robust contouring controller for linear-motor-driven biaxial systems that achieves both stringent contouring performance and accurate parameter estimations. In contrast to the past research works those use various locally defined TCFs “attached” to the desired contour to approximately calculate the contouring error for feedback controller designs, this paper first formulates the contouring control problem using a recently developed GTCF, in which calculation of the contouring error is rather accurate and not affected by the curvature of the desired contour. A physical-model-based indirect-type parameter-estimation algorithm is then synthesized to obtain accurate online estimates of unknown physical model parameters. An integrated direct/indirect adaptive robust controller with dynamic-compensation-type fast adaptation is also constructed to preserve the excellent transient and steady-state performance of the direct adaptive robust control (ARC) designs. Comparative experimental results show that the proposed GTCF-based integrated direct/indirect ARC algorithm not only achieves the best contouring performance but also possesses rather accurate estimations of physical parameters.

Performance-Oriented Adaptive Robust Control of a Class of Nonlinear Systems Preceded by Unknown Dead Zone With Comparative Experimental Results

This paper presents an integrated direct/indirect adaptive robust control scheme for a class of nonlinear dynamic systems preceded by unknown nonsymmetric, nonequal slope dead-zone nonlinearity. Departing from existing approximate adaptive dead-zone compensations, this paper uses indirect parameter estimation algorithms along with on-line condition monitoring to obtain an accurate estimation of the unknown dead zone when certain relaxed persistent-excitation conditions are satisfied-a theoretical result that cannot be achieved with the existing methods. Such a result is obtained by making full use of the fact that though not being linearly parameterized globally, the unknown dead zone can still be linearly parameterized perfectly within certain known working ranges. With these accurate estimates of dead-zone parameters, perfect dead-zone compensation is then constructed and utilized in the development of a performance-oriented adaptive robust control algorithm for the overall system. Consequently, asymptotic output tracking is achieved even in the presence of unknown dead zone. In addition, the proposed algorithm achieves certain guaranteed robust transient performance and final tracking accuracy even when the entire system may be subjected to other uncertain nonlinearities and time-varying disturbances. The proposed algorithm is also experimentally tested on a linear motor drive system preceded by a simulated unknown nonsymmetric dead zone. Comparative experimental results obtained validate the effectiveness of dead-zone compensation and the high-performance nature of the proposed approach in practical implementation.

Brief paper: Integrated direct/indirect adaptive robust contouring control of a biaxial gantry with accurate parameter estimations

This paper presents an integrated direct/indirect adaptive robust contouring controller (DIARC) for an industrial biaxial high-speed gantry that achieves not only excellent contouring performance but also accurate parameter estimations for secondary purposes such as machine health monitoring and prognosis. Contouring control problem is first formulated in a task coordinate frame. A physical model-based indirect-type parameter estimation algorithm is then developed to obtain accurate on-line estimates of unknown model parameters. A DIARC controller possessing dynamic-compensation-like fast adaptation is subsequently constructed to preserve the excellent transient and steady-state contouring performance of the direct adaptive robust controller (DARC) designs. The proposed DIARC along with previously developed DARC contouring controllers are implemented on a high-speed industrial biaxial gantry to test their achievable performance in practice. Comparative experimental results verify the improved contouring performance and the accurate physical parameter estimates of the proposed DIARC algorithm.

Adaptive Robust Precision Motion Control of a High-Speed Industrial Gantry With Cogging Force Compensations

This paper studies the precision motion control of a high-speed/acceleration linear motor driven commercial gantry which is subject to significant nonlinear cogging forces. A discontinuous projection based desired compensation adaptive robust controller (DCARC) is constructed. In particular, based on the special structures of various nonlinear forces, design models consisting of known basis functions with unknown weights are used to approximate those unknown nonlinear forces with approximation errors being explicitly accounted for in the design process. Online parameter adaptation is then utilized to reduce the effect of various parametric uncertainties while certain robust control laws are used to handle effects of various modeling uncertainties. Theoretically, the resulting controller achieves a guaranteed transient performance and final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities. In addition, in the presence of parametric uncertainties, the controller achieves asymptotic output tracking. Comparative experimental results obtained on a high-speed Anorad commercial gantry with a linear encoder resolution of 0.5 μ m and a position measurement resolution of 20 nm by external laser interferometer are presented to verify the excellent tracking performance of the proposed control strategy.

Adaptive Robust Repetitive Control of an Industrial Biaxial Precision Gantry for Contouring Tasks

The periodicity of repetitive contouring tasks is utilized in this paper to synthesize an adaptive robust repetitive contouring controller (ARRC) for an industrial biaxial precision gantry to further improve the achievable contouring performance in practice. Specifically, repetitive-control-input-like terms are introduced to learn unknown but periodic nonlinearities when performing repetitive tasks. Physically, intuitive discontinuous projection modifications to the adaptation law are used to ensure all the on-line estimates within their known bounds. Robust control terms are also constructed to effectively attenuate the effect of model compensation errors due to various uncertainties including nonperiodic disturbances for a theoretically guaranteed transient performance and steady-state tracking accuracy in general. Comparative experiments are carried out on an industrial linear-motor-driven biaxial precision gantry. The experimental results show that the proposed ARRC controller not only achieves the best nominal contouring performance but also possesses strong performance robustness to large disturbances, which confirms the effectiveness of the proposed ARRC scheme in practical contouring applications.

Performance-Oriented Precision LARC Tracking Motion Control of a Magnetically Levitated Planar Motor With Comparative Experiments

Magnetically levitated planar motor is a new-generation motion device in modern precision industry, while its advanced motion controller design is still of main concern. In this paper, a learning adaptive robust control (LARC) motion controller is proposed for a magnetically levitated planar motor developed in our laboratory to achieve good tracking performance. The planar motor consists of a Halbach permanent magnetic array as the stator, and a levitated platen containing four groups of three-phase windings as the mover. Based on the Lorentz force law, the mover placed in the magnetic field is subjected to vertical force for levitation and horizonal force for planar motion through dynamics decoupling and current allocation. An LARC control scheme containing adaptive robust control (ARC) term and iterative learning control (ILC) term in a serial structure is then proposed for the magnetically levitated planar motor to achieve high-performance tracking even there exist parametric variations and uncertain disturbances. Comparative experiments between traditional lead, ARC, ILC, and the proposed LARC are carried out on the planar motor to track sinusoidal, point-to-point, and planar circular motions, respectively. The experimental results consistently validate that the proposed LARC control strategy outperforms other controllers much, and possesses not only good transient/steady-state tracking performance but also parametric adaptation ability and uncertain disturbance robustness. The proposed scheme actually provides a practically effective technique for motion control of magnetically levitated planar motors in industrial applications.