Piezoelectric and other smart material-based actuators are widely used in micro- and nano positioning applications. However, the intrinsic hysteretic behavior of these actuators deteriorates their tracking performance. This dissertation, composed of three parts, is focused on nonlinear control methods for compensating the hysteresis and achieving high-precision control in the presence of model uncertainties. An inversion-based adaptive conditional servocompensator (ACS) is first proposed, where a nanopositioning system represented as a linear system preceded with a hysteresis nonlinearity modeled with a Modified Prandtl-Ishlinskii (MPI) operator. With an approximate inverse MPI operator as a compensator, the resulting system takes a semi-affine form. The proposed controller consists of two parts, a continuously-implemented sliding mode control (SMC) law followed by an ASC. The hysteresis inversion error is treated as a matched disturbance and its analytical bound is used to minimize the conservativeness of the SMC design. Under mild assumptions, the well-posedness and periodic stability of the closed-loop system are established. The second part of the dissertation focuses on designing an inversion-free ACS to achieve precise tracking control of systems with hysteresis, without requiring explicit inversion of the hysteresis. To facilitate the control design, the MPI operator is rearranged into a form comprised of three parts: a linear term, a nominal hysteretic term represented by a classical Prandtl-Ishlinskii (PI) operator, and a hysteretic perturbation. The bound on the hysteretic perturbation is further derived based on the parameter uncertainty of the MPI operator. To properly ``cancel'' the nominal hysteresis effect without inversion, a technique involving a low-pass filter is introduced. It is shown that, with persistent excitation, the closed-loop variables are ultimately bounded and the tracking error approaches a neighborhood of zero, where the neighborhood can be made arbitrarily small via the choice of the SMC boundary layer width parameter and the servocompensator order. In the third part, an output feedback-based hysteresis compensation approach is used using dynamic inversion and extended high-gain observers. With mild assumptions on the properties of the hysteresis nonlinearity, the system can be represented as an uncertain, non-affine, nonlinear system containing a hysteretic perturbation. Dynamic inversion is used to deal with the non-affine input, uncertainties, and the hysteretic perturbation, where the latter two are estimated using an extended high-gain observer. Analysis of the closed-loop system under output feedback shows that the tracking error converges to a small neighborhood near the origin, which can be made arbitrarily small via proper choice of time-scale parameters of dynamic inversion and the observer, respectively. The efficacy of the three proposed controllers is verified experimentally on a commercial nanopositioning device under different types of periodic reference inputs, via comparison with multiple inversion-based and inversion-free approaches.
Read
