Article

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

Nat. Dong Hwa Univ., Hualien
(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: )( ) ( ) ( ) ( = + +   ) ) ( ) ( ) ( ) ( ) (         +                 − − =           ) ( ) ( ) ( ) ( − − − = − − − ) ( − − − + + = , ( − − + . . ∞ < + + ∑ ∞ ) ( ) ( ) ( ) ( + + ∞ ( ) ( ) ( = − − ∞ → , ( ) , ( ) , ( = − − ∫ ∞ → ( ) ( ) − − = ) ( ) ( ) ( ( ) ( ) ∑ ∫ = − − + ) ( ) , ( ) ( ) , ( ) ( ∞ . =   = ) ( ) ( ) ( ) ( ) ( − [ ] ∫ − − ) ( ) , ( ) ( ) ( ) ⋅ + + + −   = , = ( ) ( ) ]( [ ) , ( * ) ( = ∫ ] , , ] , , ∫ = , ) ( , ) ]( [ ) , ( ) ( ∫ = , ) ( , ) ]( [ ) , ( ) ( ) ( ) ]( [ ) , ( ) ( , ) ( , ≤ ≤ ∫ , , ) ≤ . ( = ( + ≤ . + ≤ ) [ ) , , , ∈ ) + − = ) ( * , ) = ) ( ) ]( [ ) , ( ( ) ( , > ( * , = ; ( ) ( , < ( * , = ; ) ( ) ( ) ( , , ≤ ≤ ( * ) ( ) ) ( ) * = . ( , ( * ) ( ) ( * ) ( ) ( * ≤ ≤ ) ( ) ( , ) ( ) ( ) ( ∫ + ) ]( [ ) , ( ∫ − + ) ]( [ ) , ( ) ( ) ( ) + + = − . ) + ) ]( [ ) ( ∫ − + ) ]( [ ) ( ) ( ) ( ) ( ) + + + + = − . ) ) ( + ) ( ) ( + + =                 − − − − − − − − − − − − ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( −         +         = ≤ ≤ ) ( ) ( , ) ( ) ( ) ( + + ≤ ≤ ≤ ≤ ) ( ) ( , ) ( , = ) ( ∞ ( ) ( ) ( = − ∞ → . ) ( ∞ . ) ( ∞ , )) ( − × )) ( − × = , , . , − = . , = = − = − ) ) . ( − + + . . = . . . , , = = . = = . . .