Precise tracking of a piezoelectric positioning stage via a filtering-type sliding-surface control with chattering alleviation

Digital controller design for absolute value function constrained nonlinear systems via scalar sign function approach

“…More details on the system can be found in Section 2.3. As is seen in both instances, absolute value function terms show either in a state equation as a state constraint like (2) or in a more complicated one like (3) where both state variable and control input have it. Traditionally, the typical way to deal with this type of constrained nonlinear systems is first to divide the state space into two or more subspaces based on the sign of the value in the absolute value function terms, and then do the further mathematic derivations for the control purpose in each subspace.…”

“…Due to the appearance of the absolute value function state constraints, the systems behave highly nonlinear. (b) In the model of piezoelectric actuators (PEA) that usually exhibit hysteresis behavior due to the piezoelectric materials used, the hysteresis can be represented as a state variable [3] x 4 = b 4 (x 4 , u) = k z1 u − k z2 |u|x 4 − k z3 u|x 4 |. (3) where x 4 is the hysteresis variable, u is input exciting voltage, and k z1 , k z2 and k z3 are given coefficients.…”

“…the output values cannot be determined without looking at the history of the input. This classic nonlinear behavior usually degrades the system accuracy and performance [3,14,15]. To accurately study and analyze hysteretic behavior, many proven successful techniques for hysteresis dynamic modeling have been developed.…”

“…To accurately study and analyze hysteretic behavior, many proven successful techniques for hysteresis dynamic modeling have been developed. The dynamics for piezoelectric actuators is represented by the differential equations of motion of two coupled systems [3,16]. One system is a mass-spring mechanical system having a linear viscous friction and a very large stiffness coefficient.…”

Unified hysteresis and creep compensation in AFM tip positioning with an extended PI model

“…An extended PI model was proposed by introducing a creep parameter into the hysteresis operator to compensate for inflexion creep effects only at the turning point of the single hysteretic loop, which significantly increased the tip positioning precision [22]. In addition, closed-loop control strategies, such as sliding-surface control [23], Dahl Model-based control [24], iterative control [25], [26], can be applied to compensate for hysteresis and creep nonlinearities. However, compared with the PI model based feedforward control systems for hysteresis and creep compensation, the closed-loop control systems need extra sensors for measuring the PZT displacements and hence cause new noises and vibration in dynamic driving curve.…”