Haihua Mu

LFT Structured Uncertainty Modeling and Robust Loop-Shaping Controller Optimization for an Ultraprecision Positioning Stage

In this paper, a practical modeling and robust controller optimization strategy is presented for an ultraprecision positioning stage with position-dependent dynamics to achieve ultraprecision positioning accuracy. A linear-fractional-transformation structured uncertainty modeling procedure is proposed to describe the varying dynamics of the stage. The modeling process involves the global curve fitting of frequency response functions and dimensionality reduction for the uncertainty structure so that the uncertainty set could be minimized. Then, a robust loop-shaping controller optimization method is presented to improve the control performances. The optimization objective includes the control bandwidth and the disturbance rejection ability, and μ analysis is employed as a nonconservative robust condition with respect to the structured uncertainty. A genetic algorithm is then utilized to determine the optimal parameters of the controller. Comparative experiments on a developed ultraprecision positioning stage are finally conducted, and the results validate that significant improvements on rising time, settling time, and positioning accuracy have been achieved.

Augmentation of Propulsion Based on Coil Array Commutation for Magnetically Levitated Stage

This paper focuses on augmenting the propulsion via commutation of coil array for the long-stroke magnetically levitated stage with moving coils, whose mechatronics structure have been defined. The used commutation of coil array is based on the analytical force/torque-decomposing model of the stage and it is characterized by bounding the coil currents. Through this current-bounded commutation, the 1-norm of commutated coil current vector is increased so that the propulsion can be augmented, and simultaneously the infinite norm of commutated coil current vector is limited so that the amplitudes of commutated coil currents are not beyond the capacity of selected coil power amplifiers. By the investigation example of a long-stroke magnetically levitated stage with moving coils, it is theoretically verified that the propulsion (acceleration) can be augmented by 125% as well as the commutated coil currents can be kept within the capacity of selected coil power amplifiers, 3 A. The study results indicate that the propulsion of a magnetically levitated stage can be augmented via current-bounded commutation of coil array rather than via reconfiguring the mechatronics structure of stage or reselecting coil power amplifiers of larger capacity.

An Integrated Model-Data-Based Zero-Phase Error Tracking Feedforward Control Strategy With Application to an Ultraprecision Wafer Stage

In precision motion control, well-designed feedforward control can effectively compensate the reference-induced tracking error. To achieve excellent tracking performance such as nanometer accuracy regardless of reference variations, an integrated model-data-based zero-phase error tracking feedforward control (ZPETFC) strategy is synthesized for precision motion systems with complex and nonminimum phase (NMP) dynamics. The feedforward controller comprises a conventional ZPETFC controller and a gain compensation filter structured with symmetric finite impulse response (FIR) filter. Especially, the conventional ZPETFC is predesigned based on the plant model, and consequently, the feedforward controller is parameterized by the gain compensation filter coefficients, which results in excellent capacity for approximating the inverse behavior of the complex and NMP dynamics. In order to compensate the modeling error in the conventional ZPETFC design and improve the tracking performance, a data-based instrumental-variable method with impulse response experiment is developed to obtain the optimal parameter vector under the existence of noise and disturbances. Furthermore, the ridge estimate method using singular value decomposition is employed to guarantee a fast convergent iteration in the case of ill-conditioned Hessian matrix. The proposed ZPETFC strategy enables a convex optimization procedure with the inherent stability in the iterative tuning process, and is finally implemented on a developed ultraprecision wafer stage. Comparative experimental results demonstrate that the strategy is insensitive to reference variations in comparison with iterative learning control, and outperforms preexisting model-based ZPETFC and data-based FIR feedforward control.

Decoupling and levitation control of a six-degree-of-freedom magnetically levitated stage with moving coils based on commutation of coil array

The research in the present paper focuses on decoupling the six-degrees-of-freedom motions of a magnetically levitated stage with moving coils and controlling the levitation motion. The decoupling is based on commutation of coil array, which is obtained reversely from the electromagnetic force/torque model of the stage. The control of levitation motion is carried out by a phase lead-lag controller designed on the criterion of minimum integral of time-weighted absolute error after gravity compensation modeling of the plant dynamics. Comprehensive simulations of the control system in MATLAB/Simulink and real levitation experiments on a digital signal processor-centered test platform are made to verify the six-degrees-of-freedom decoupling effect and the closed-loop control performances of the levitation degree of freedom. The results indicate that the six-degrees-of-freedom motions of the stage can be decoupled through coil array commutation and the levitation motion can be controlled by the phase lead-lag controller based on the gravity compensation model and designed on the criterion of minimum integral of time-weighted absolute error.

Newton-ILC Contouring Error Estimation and Coordinated Motion Control for Precision Multiaxis Systems With Comparative Experiments

This paper proposes a Newton extremum seeking algorithm based iterative learning coordinated control (Newton-ILC) strategy for contouring motion accuracy of precision multiaxial systems. Specifically, as the contouring error estimation is critically important for coordinated contouring motion control, a cost function is constructed based on the reference contour, as well as the current position, and the minimal value of the function is searched to determine the contouring error point through an offline Newton algorithm. Consequently, high precision estimation of the contouring error can be achieved, even under extreme contouring tasks with high speed, large curvature, and sharp corners. The calculated contouring error is then projected to each axis, and the axial contouring errors are controlled by iterative learning method, while the learning results will be used to adjust the axial position reference commands for contouring accuracy improvement. Comparative experiments are conducted on a biaxial linear motor stage to validate the practical effectiveness of the proposed Newton-ILC strategy. The experimental results illustrate that the proposed Newton-ILC achieves not only nearly perfect contouring error estimation but obvious improvement of contouring accuracy as well after a few iterations. Particularly, in some extreme cases such as large initial tracking error, high speed, large curvature, and sharp corners, the proposed Newton-ILC strategy can achieve rather excellent contouring performance when compared with individual axis control, conditional cross-coupled control, and cross-coupled iterative learning coordinated control (CCILC) methods.

State/Model-Free Variable-Gain Discrete Sliding Mode Control for an Ultraprecision Wafer Stage

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. This paper presents a novel state/model-free variable-gain discrete sliding mode control (DSMC) to suppress the unmolded position-dependent dynamics and disturbances in the nanopositioning wafer stage. The proposed DSMC is essentially composed of feedforward control term, linear feedback control term, and nonlinear switching control term, which can be designed separately. The gain of the switching control term is meaningfully designed to be variable to balance the tradeoff between the robustness and the chattering. Data-driven parameter optimization approach is employed to achieve the optimal controller parameters of the typically nonlinear controller, where off-line parameter updating is iteratively carried out based on the input/output data to minimize a predefined objective function. This scheme facilitates a rapid implementation without either a parameter model or a state observer, and excellent tracking performance with the optimal controller parameters. Moreover, the closed-loop stability is analyzed, and the proposed DSMC is finally implemented on an ultraprecision wafer stage developed in our lab. Comparative experimental results demonstrate that it not only achieves nanoscale tracking accuracy but also possesses promising robustness to position-dependent dynamics and disturbances.

Real-time generation of trapezoidal velocity profile for minimum energy consumption and zero residual vibration in servomotor systems

In this paper, a real-time approach of generating trapezoidal velocity profile (known as T-curve) is newly proposed to simultaneously achieve minimum energy consumption and zero residual vibration for flexible servomotor systems. By establishing the cost function of minimum energy consumption and deriving the zero-residual-vibration conditions with respect to two tuning parameters, the T-curve generation is formulated into a nonlinear integer programming problem (NIPP). To solve this NIPP, a novel algorithm is presented using continuous relaxation method. This algorithm is computation-efficient and applicable in practice by utilizing the strictly quasi-convexity of the continuous relaxation problem. The proposed method is verified by comparative simulation examples.

Current-Bounded Commutation of a Long-Stroke Magnetically Levitated Stage with Moving Coils

Magnetically levitated stages(MLS) have potentials to obtain good motion performances in high vacuum environment. Yet the electromagnetic forces/torques corresponding to six degrees of freedom(DOF) motions have coupling relationship with each current of coil array, and this coupling is still associated with the relative positions between the mover and the stator of the stage. So it is quite difficult to control the 6-DOF motions of the stage. By reasonable commutation of coil array, this complicated coupling relationship can be decoupled. The analytical force/torque-decomposing model of the stage is established first. Then the initial currents of coil array are commutated based on the pseudo inverse of the analytical force/torque-decomposing model matrix. And then the coil array currents are commutated again with different current bounds given to the initial currents as well as in the sense of minimum 2-norm of currents vector. Using the long stroke magnetically levitated stage with moving coils under investigation as examples, the currents of coil array are commutated with different current bounds adopting the proposed commutation method, the determination of current bound and the current bounds’ influences on the heat-losses in coil array are analyzed, and the effectiveness of implementation algorithm of proposed commutation method is discussed. Simulation, analysis and discussion results indicate that the currents of coil array within the given current bound can be solved analytically by proposed commutation method, and the implementation algorithm does not need any searching or iteration. By the current-bounded commutation method proposed, the amplitude of coil array currents can be limited within an appropriate current bound(This is very beneficial to the improvement of the reliability and motion performance of the stage), as well as these currents can also generate the desired forces and torques.

A Variable-Gain Discrete Sliding Mode Control Strategy With PID-Type Sliding Surface for an Ultra-Precision Wafer Stage

The ultra-precision wafer stage is an important mechatronic unit in a wafer scanner for manufacturing integrated circuits while its motion control is still the main concern. To overcome the performance-limiting trade-offs of fixed-gain discrete sliding mode control (DSMC), a novel variable-gain DSMC strategy with PID-type sliding surface is proposed for an ultra-precision wafer stage. Specially, PID-type sliding surface is employed to avoid the steady-state error induced by external disturbances. Via the exponential reaching law approach, DSMC with PID-type sliding surface is synthesized. Variable-gain control methodology is newly introduced into DSMC, and the control gain varies with the trajectory phase that the wafer stage is in and the tracking error magnitude. Performance assessment on a developed wafer stage validates that with nano-scale tracking accuracy the proposed strategy not only improves the low-frequency tracking ability without the amplification of high-frequency noise, but also possesses the excellent robustness to external disturbances.Copyright

Closed-Loop Subspace Identification of MIMO Motion System With Flexible Structures for Motion Control

In this paper, we study the closed-loop subspace identification of MIMO motion system with flexible structures. The fundamental objective of identification experiment is to achieve the state space model for motion control. The model with flexible structures of the motion system is analyzed and deduced to the form of state space model, which is composed with rigid modes and flexible modes. As the stability and safety case, the closed-loop subspace identification method is employed. The proposed identification method is suitable for modern control algorithms to construct space state model. The rigid and flexible modes are obtained and updated by the modal approach. Identification experiment is carried on the industrial wafer stage, which is the typical MIMO motion system with flexible structures. The results of experiment verify the feasibility and validity of the proposed identification method.Copyright