Sliding-mode tracking control of piezo-actuated nanopositioners

Edardar, Mohamed; Tan, Xiaobo; Khalil, Hassan K.

doi:10.1109/acc.2012.6315559

Cited by 24 publications

(9 citation statements)

References 17 publications

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“…In Tables I and II, we list more experimental results for the proposed method (Scheme 3) and compare them with servo-compensator methods presented in [8] and Sliding-Mode-Control (SMC) presented in [23] that are implemented in the same nanopositioner used in this work. There are two designs for the servo-compensator:…”

Section: B Experimental Resultsmentioning

confidence: 99%

Tracking error analysis for singularly perturbed systems preceded by piecewise linear hysteresis

Edardar¹,

Tan²,

Khalil³

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-In this paper we introduce a new method for analyzing the closed-loop control system that involves a singularly perturbed plant preceded by hysteresis nonlinearity with piecewise linear characteristics, an example of which is a piezoactuated nanopositioners. Different methods are compared to quantify the tracking error and examine how the change in slopes from one segment to another interacts with the controller parameters and hence affects the tracking error. These methods all involve the combination of inverse hysteresis compensation and feedback control, but the points of insertion for the hysteresis inverse vary. A proportional-integral feedback controller is used throughout this comparison. The presented analysis is important because it provides an explicit expression for the tracking error, where the feedback controller parameters can be adjusted for the desired performance. Simulation and experimental results are presented for tracking control of a piezo-actuated nanopositioner, where the hysteresis is modeled with a Prandtl-Ishlinskii (PI) operator. The analysis carried out in this paper is applicable to other operators, such as the modified PI-operator and the Krasnoselskii-Porkovskii (KP) operator among others, since they all demonstrate piecewise linear hysteresis characteristics.

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Section: B Experimental Resultsmentioning

confidence: 99%

Tracking error analysis for singularly perturbed systems preceded by piecewise linear hysteresis

Edardar¹,

Tan²,

Khalil³

2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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show abstract

“…In practice, the equivalent internal resistance R 0 is usually assumed as R 0 = 0 [23], [25], [26], [28], [30]. Therefore, the electromechanical dynamic model (8) and (9) can be reduced to…”

Section: A Dynamic Modelingmentioning

confidence: 99%

“…This also explains why the tracking errors with the PID control and PBSMC are almost equal. For quantitatively comparing differences of them, the following definition DF is introduced with the control signal of the PID controller as the reference 30) where v pid and v pbsmc represent the control signals with the PID control and PBSMC, respectively.…”

Section: B Experimental Studiesmentioning

confidence: 99%

Proxy-Based Sliding-Mode Tracking Control of Piezoelectric-Actuated Nanopositioning Stages

Zhu

et al. 2015

IEEE/ASME Trans. Mechatron.

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In this paper, a proxy-based sliding-mode control (PBSMC) approach is proposed for robust tracking control of a piezoelectric-actuated nanopositioning stage composed of piezoelectric stack actuators and compliant flexure mechanisms. The essential feature of the PBSMC approach is the introduction of a virtual coupling proxy, which is controlled by the sliding-mode controller (SMC) to track the desired position. Simultaneously, due to the virtual coupling, a proportional-integral-derivative (PID) controller on the other side of the proxy ensures the position of the end-effector of the stage to follow the position of the proxy. Therefore, the PBSMC guarantees the end-effector to track the desired trajectory. The advantages of the developed PBSMC lie in the facts that 1) the discontinuous signum function in the traditional SMC is omitted without any approximation. Hence, the output of the PBSMC is continuous, which does not suffer from the chattering phenomenon; and 2) the PBSMC laws are developed without having the necessity to include the nominal system model, hysteresis model or the state observer. Hence, the PBSMC provides a novel effective yet simple control method, which permits to avoid the lack of performances from PID and the chattering from SMC, and permits to combine the advantages from them. The stability of the closed-loop control system is proved through Lyapunov analysis. Finally, comparative studies are performed on a custom-built piezo-actuated stage. Experimental results show that the tracking errors of the PBCM are reduced by 74.22%, as compared to the traditional PID controller, with the desired sinusoidal trajectory under the 50-Hz input frequency, which clearly demonstrates the superior tracking performance of the PBSMC.

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“…An extended survey of nanopositioning control [22] provides, among others, an overview of existing control methods for compensating the hysteresis. In the latest works [23], [24] on nanopositioning, two different control methods are proposed, both using an inverse Prandtl-Ishlinskii feedforward compensator. Further, the modeling and control of SMAactuated systems have been explicitly reported in [25], [26], and [27].…”

Section: Introductionmentioning

confidence: 99%

Control of Magnetic Shape Memory Actuators Using Observer-Based Inverse Hysteresis Approach

Ruderman

Bertram

2014

IEEE Trans. Contr. Syst. Technol.

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Magnetic shape memory (MSM) actuators belong to active material technologies with a high energy density and outstanding field-strain relation. Large-scale multivariate fieldstress-strain hysteresis effects, however, antagonize their broad use because of the inherent difficulties with control. In this brief, we describe and compare experimentally several MSM control strategies, including the observer-based inverse hysteresis approach proposed in the previous works and combined here with a linear feedback controller by connecting both in parallel. For a prototypic MSM actuator with return spring, it is shown that the actuator plant can be approximated by an appropriate hysteresis operator and a linear transfer function of residual dynamics. The positioning profiles with a bandwidth 0.1-10 Hz and amplitudes between 0.01 and 0.1 mm have been evaluated by the experiments.Index Terms-Control systems, hysteresis, inversion, magnetic shape memory (MSM), observer, Preisach model, smart actuators.

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Sliding-mode tracking control of piezo-actuated nanopositioners

Cited by 24 publications

References 17 publications

Tracking error analysis for singularly perturbed systems preceded by piecewise linear hysteresis

Tracking error analysis for singularly perturbed systems preceded by piecewise linear hysteresis

Proxy-Based Sliding-Mode Tracking Control of Piezoelectric-Actuated Nanopositioning Stages

Control of Magnetic Shape Memory Actuators Using Observer-Based Inverse Hysteresis Approach

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