Article

An Integrator-Backstepping-Based Dynamic Surface Control Method for a Two-Axis Piezoelectric Micropositioning Stage

Nat. Dong Hwa Univ., Hualien
IEEE Transactions on Control Systems Technology (Impact Factor: 2.47). 10/2007; 15(5):916 - 926. DOI: 10.1109/TCST.2006.890290
Source: IEEE Xplore

ABSTRACT

In this paper, an integrator-backstepping-based dynamic surface control method for a two-axis piezoelectric micropositioning stage is proposed. First, according to the dynamics of motion of a mechanical mass-spring system, mathematical equations that contain a linear viscous friction, a varied elasticity with cross-coupling effect due to mechanical bending, and dynamics of a hysteresis variable is proposed to describe the motion dynamics of the two-axis piezopositioning stage. Next, from the equations, a state-space model in which the applied voltage to the stage is defined as an output of an integrator is derived. On the basis of this state-space model, the integrator-backstepping-based dynamic surface control is proposed. By using the proposed control method to trajectory tracking of the two-axis piezopositioning stage, the dynamic performance, robustness to parameter variations, and trajectory tracking error can be improved. Experimental results of the time responses from the computer-controlled two-axis piezopositioning stage illustrate the validity of the proposed control method for practical applications in trajectory tracking.

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    • "Recently, piezo-actuated stage has many effective applications in ultra-high precision positioning systems (Chen and Hisayama, 2008; Fleming and Moheimani, 2007; Krejci and Kuhnen, 2001; Kuhnen and Krejci, 2009; Moheimani and Goodwin, 2001; Shieh and Hsu, 2007). The piezo electric actuator (PEA) is used to meet the requirement of nanometer resolution in displacement, high stiffness and rapid response. "
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    ABSTRACT: The XY table is composed of two piezo electric actuators (PEA) and a positioning mechanism (PM). Due to existence of hysteretic nonlinearity in the PEA and the friction in the PM, the high precision control for the XY table is a challenging task. This paper discusses the high precision adaptive control for the XY talbe, where the hysteresis is described by Prandtl-Ishlinskii model. The proposed control law ensures the global stability of the controlled stage, and the position error can be controlled to approach to zero asymptotically. Experimental results show the effectiveness of the proposed method.
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    No preview · Article · Jan 2011
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    ABSTRACT: )( ) ( ) ( ) ( = + +   ) ) ( ) ( ) ( ) ( ) (         +                 − − =           ) ( ) ( ) ( ) ( − − − = − − − ) ( − − − + + = , ( − − + . . ∞ < + + ∑ ∞ ) ( ) ( ) ( ) ( + + ∞ ( ) ( ) ( = − − ∞ → , ( ) , ( ) , ( = − − ∫ ∞ → ( ) ( ) − − = ) ( ) ( ) ( ( ) ( ) ∑ ∫ = − − + ) ( ) , ( ) ( ) , ( ) ( ∞ . =   = ) ( ) ( ) ( ) ( ) ( − [ ] ∫ − − ) ( ) , ( ) ( ) ( ) ⋅ + + + −   = , = ( ) ( ) ]( [ ) , ( * ) ( = ∫ ] , , ] , , ∫ = , ) ( , ) ]( [ ) , ( ) ( ∫ = , ) ( , ) ]( [ ) , ( ) ( ) ( ) ]( [ ) , ( ) ( , ) ( , ≤ ≤ ∫ , , ) ≤ . ( = ( + ≤ . + ≤ ) [ ) , , , ∈ ) + − = ) ( * , ) = ) ( ) ]( [ ) , ( ( ) ( , > ( * , = ; ( ) ( , < ( * , = ; ) ( ) ( ) ( , , ≤ ≤ ( * ) ( ) ) ( ) * = . ( , ( * ) ( ) ( * ) ( ) ( * ≤ ≤ ) ( ) ( , ) ( ) ( ) ( ∫ + ) ]( [ ) , ( ∫ − + ) ]( [ ) , ( ) ( ) ( ) + + = − . ) + ) ]( [ ) ( ∫ − + ) ]( [ ) ( ) ( ) ( ) ( ) + + + + = − . ) ) ( + ) ( ) ( + + =                 − − − − − − − − − − − − ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( −         +         = ≤ ≤ ) ( ) ( , ) ( ) ( ) ( + + ≤ ≤ ≤ ≤ ) ( ) ( , ) ( , = ) ( ∞ ( ) ( ) ( = − ∞ → . ) ( ∞ . ) ( ∞ , )) ( − × )) ( − × = , , . , − = . , = = − = − ) ) . ( − + + . . = . . . , , = = . = = . . .
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