Adaptation‐Enhanced Model‐Based Control with Charge Feedback for Piezo‐Actuated Stage

Abstract

This paper proposes a new control design to compensate for the residual control error from charge feedback control. A part of the applied voltage is consumed by the hysteresis effect because of the nature of the piezoelectric material; moreover, this effect is difficult to overcome because it is rate dependent. This work utilizes a piezoelectric electromechanical model to propose a precompensation algorithm for a piezoelectric actuator. A nonlinear compensator can be used to treat both the hysteresis nonlinearity and the rate dependency of the system, and the adjustable parameters are specified through adaptive identification with only basic system information. The proposed design can position a piezoelectric stage with a magnifying mechanism within a few nanometers of a target, and the leftover hysteresis phenomenon is negligible.

Model-Free Output-Feedback Sliding-Mode Control Design for Piezo-Actuated Stage

“…The electrical subsystem is used to describe the system's reaction to an input voltage u, and the mechanical subsystem is used to describe the relationship between the driving force F p and elongation y p . In these two subsystems, q c is the charge flowing through an equivalent capacitance C; q p is the charge flowing through a transducer T em ; H(q) is the source of hysteresis with a charge flow q = q c + q p ; K p and Γ p are stiffness and damping constants, respectively; and M p is the mass of the actuator (Figure 1 [27]). The equivalent block structure of a piezo-actuated stage per the definition of these two subsystems is shown in Figure 2 In this study's proposed scheme, undesired hysteresis is treated as an unknown external disturbance, and the block diagram in Figure 2 can be transformed such that it has the structure illustrated in Figure 3, where d(t) = (T em − 1)u − T em H(q), q = (T em K −1 p + CT −1 em )F p .…”

“…[27]; G denotes the linear motion of the stage. The linear transfer function satisfies the relation G = C(sI − A)B, where s is the Laplace operator, and the matrices A, B, and C constitute the state-space realization ẋ = Ax + BF p (1) y = Cx, where x ∈ R n is an unknown state variable.…”

Design and Comparison of Reinforcement-Learning-Based Time-Varying PID Controllers with Gain-Scheduled Actions

“…In the closed loop of circuit, C is an equivalent internal capacitance, and T em is the transformation ratio for the connected mechanical and electrical subsystems. Based on the derivation in [36], a block diagram of a piezo-actuated stage is presented in Figure 3, where G is the linear, time-invariant transfer function of the mechanical stage body. On the basis of these preliminaries, the goal of this paper is to propose a reinforcement learning-based PID controller that drives the system output to track a reference signal despite the system being affected by nonlinear hysteresis H(q).…”