Robust precision motion control of piezoelectric actuators using fast nonsingular terminal sliding mode with time delay estimation

Abstract

Background: Piezoelectric actuators are widely used in many micro/nano-manipulation applications, but their positioning accuracy are badly affected by their inherent nonlinear hysteresis and creep. To solve this problem, this paper presents a new robust motion-control method for piezoelectric actuators with fast nonsingular terminal sliding mode based on time delay estimation. Method: The proposed controller needs no detailed information about the hysteresis and other nonlinearities of the system, leading to a simple and model-free characteristic due to the time delay estimation and ensures fast convergence and high tracking accuracy thanks to the nonsingular terminal sliding-mode surface and fast terminal sliding mode -type reaching law. A robust exact differentiator is adopted to estimate the velocity and accelerationinformation online, and it overcomes the limitation of only available position measurements. The finite-time convergence and stability of the closed-loop system are proved by using a Lyapunov function. Results: Experimental results show that the proposed control strategy has faster convergence and higher tracking precision compared with a traditional time delay control. Conclusion: The proposed control strategy can be widely used as an effective control method for high-precision motion control of piezoelectric actuators.

Practical Tracking Control of Piezoelectric Actuators with Time-delay Estimation and Nonsingular Terminal Sliding Mode

“…Sliding mode control is one of the important discoveries in modern control theory and is an effective tool for solving nonlinear system control problems [15]. Sliding mode control is insensitive to model uncertainty, parameter changes, and external disturbances [16].…”

“…The nonsingular terminal sliding mode surface is adopted [15] q p e K e s    (5) where K is the parameter to be adjusted; p and q are positive parameters; and 2 1   q p . The input of the control law can be designed as follows: The TDE technology can be used to estimate the unknown terms ( P  ) as follows:…”

Precise robust motion control of cell puncture mechanism driven by piezoelectric actuators with fractional-order nonsingular terminal sliding mode control

“…In SMC, the displacement error and its derivatives are taken as the current state of the system [27]. The structure of the system continuously changes along with the current state and moves according to the predetermined "sliding mode" state trajectory [28]. Traditional SMC uses the linear sliding surface [29], which ensures that the state trajectory achieves progressive convergence [30].…”

Model-free robust finite-time force tracking control for piezoelectric actuators using time-delay estimation with adaptive fuzzy compensator

“…The main idea of the TDE is to estimate the lumped unknown dynamics of the system directly with the intentionally time-delayed states of the closed-loop systems, leading to an attractive model-free nature (Wang et al, 2016). Thanks to its efficiency and effectiveness, the TDE has been widely applied in various applications and obtains satisfactory performance even under large disturbances and parameter variations (Wang et al, 2016; Yu et al, 2019). However, the conventional TDC scheme exhibits two disadvantages.…”

“…To overcome this issue, recently, a nonlinear terminal sliding mode (TSM) has been selected as the DED injection term because of its finite-time stability, in place of the commonly used linear dynamics (Jin et al, 2009). In addition, several evolved versions of the TSM-type DED have also been proposed in the literatures, such as fast nonsingular TSM (FNTSM) (Yu et al, 2019), fractional-order NTSM (FONTSM) (Wang et al, 2016) and integal TSM (ITSM) (Lee et al, 2014a, 2019). Among these approaches, the ITSM-type DED does not require the second derivative of the feedback signal, which normally avoids the noise amplification in practical applications.…”