Abstract
Piezoelectric materials naturally possess high potential to deliver nano-scale positioning resolution; hence, they are adopted in a variety of engineering applications widely. Unfortunately, unacceptable positioning errors always appear because of the natural hysteresis effect of the piezoelectric materials. This natural property must be mitigated in practical applications. For solving this drawback, a nonlinear positioning design is proposed in this article. This nonlinear positioning design of piezoelectric materials is realized by the following four steps: 1. The famous Bouc–Wen model is utilized to present the input and output behaviors of piezoelectric materials; 2. System parameters of the Bouc–Wen model that describe the characteristics of piezoelectric materials are simultaneously identified with the particle swam optimization method; 3. Stability verification for the identified Bouc–Wen model; 4. A nonlinear feedback linearization control design is derived for the nano-scale positioning design of the piezoelectric material, mathematically. One important contribution of this investigation is that the positioning error between the output displacement of the controlled piezoelectric materials and the desired trajectory in nano-scale level can be proven to converge to zero asymptotically, under the effect of the hysteresis.
Highlights
The ultrahigh precision motion of a nano-scale workspace is required for the development of precision industries
For the purpose of effectively modeling the behavior of the piezoelectric materials with a simple form, the Bouc–Wen model [6,7], with a set of first order differential equations, was proposed because this model has the advantages of computational simplicity and practical similarity
A realizable nonlinear feedback linearization controller is proposed for treating the positioning problem of piezoelectric materials with hysteresis effects
Summary
The ultrahigh precision motion of a nano-scale workspace is required for the development of precision industries. For the purpose of effectively modeling the behavior of the piezoelectric materials with a simple form, the Bouc–Wen model [6,7], with a set of first order differential equations, was proposed because this model has the advantages of computational simplicity and practical similarity. A realizable nonlinear feedback linearization controller is proposed for treating the positioning problem of piezoelectric materials with hysteresis effects. In this investigation, the overall nano-scale positioning design of piezoelectric materials in the presence of the hysteresis nonlinearity is divided into four parts: 1. A nonlinear control law based on the feedback linearization method is derived to guarantee the convergence of the positioning error between the piezoelectric material’s output trajectory and the desired trajectory.
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