Sliding Mode Control with Dynamical Correction for Time-Delay Piezoelectric Actuator Systems

Abstract

In piezoelectric actuators (PEAs), which suffer from inherent nonlinearities, sliding mode control (SMC) has proven to be a successful control strategy. Nonetheless, in micropositioning systems with time delay, integral proportional control (PI), and SMC, feedback control schemes have a tendency to overcompensate and, consequently, high controller gains must be rejected. This may produce a slow and inaccurate response. This paper presents a novel control strategy that deals with time-delay micropositioning systems aimed at achieving precise positioning by combining an open-loop control with a modified SMC scheme. The proposed SMC with dynamical correction (SMC-WDC) uses the dynamical system model to adapt the SMC inputs and avoid undesirable control response caused by delays. In order to develop the SMC-WDC scheme, an exhaustive analysis on the micropositioning system was first performed. Then, a mixed control strategy, combining inverse open-loop control and SMC-WDC, was developed. The performance of the presented control scheme was analyzed and compared experimentally with other control strategies (i.e., PI and SMC with saturation and hyperbolic functions) using different reference signals. It was found that the SMC-WDC strategy presents the best performance, that is, the fastest response and highest accuracy, especially against sudden changes of reference setpoints (frequencies >10 Hz). Additionally, if the setpoint reference frequencies are higher than 10 Hz, high integral gains are counterproductive (since the control response increases the delay), although if frequencies are below 1 Hz the integral control delay does not affect the system’s accuracy. The SMC-WDC proved to be an effective strategy for micropositioning systems, dealing with time delay and other uncertainties to achieve the setpoint command fast and precisely without chattering.

Experimental Validation of a Sliding Mode Control for a Stewart Platform Used in Aerospace Inspection Applications

“…SMC is a nonlinear control approach that drives the state trajectory of the system onto a specified sliding surface and maintains the trajectory on that surface for the subsequent time. However, in conventional SMC design, a priori knowledge of the bounds on system uncertainties must be acquired in order to calculate the sliding gain value that can surmount these uncertainties [23]. Perturbation estimation strategies were studied in the literature [23,30]: one common approach to estimating perturbation p est is as in Equation (15).…”

“…Sliding mode control (SMC) is a nonlinear control approach that drives the state trajectory of the system onto a specified sliding surface and maintains the trajectory on that surface for the subsequent time under system uncertainties and perturbations. However, in conventional SMC design, a priori knowledge of the bounds on system uncertainties must be acquired [23][24][25]. Several SMC-based strategies to control Stewart platforms are proposed and verified by simulations: SMC with perturbation estimation [26], integral SMC [5], continuous higher order SMC [27], and SMC with fuzzy tuning design [28].…”

Dynamics Modeling and Tension Control of Composites Winding System Based on ASMC

“…where k i is the constant. Define the state errors as x i =x i , x i , and (29) can be obtained by (28) minus (27).…”

“…Sliding mode control has strong robustness and good control effect on nonlinear system. However, the high frequency buffeting of sliding mode control affects the system structure, damages the sensors and excites the unmodeled dynamics of the system [23]- [27]. Approach law and boundary layer method are used to reduce chattering, but the control accuracy is reduced [28]- [30].…”

High-Performance Tracking for Piezoelectric Actuators Using Super-Twisting Algorithm Based on Artificial Neural Networks

“…In addition, other robust techniques as sliding mode control (SMC) had captured the interest due to its capability to reject the uncertainties [36,37]. Several approaches of first order SMC had been designed and used for PEAs, even though the chattering is an important drawback [38][39][40].…”