Sliding-mode control of a three-degrees-of-freedom nanopositioner
TL;DR: In this article, the sliding-mode control of a three-degrees-of-freedom nanopositioner (Z, X, Y) is presented, which is actuated by piezoelectric actuators.
Abstract: This paper presents the sliding-mode control of a three-degrees-of-freedom nanopositioner (Z, θx, θy). This nanopositioner is actuated by piezoelectric actuators. Capacitive gap sensors are used for position feedback. In order to design the feedback controller, the open-loop characteristics of this nanopositioner are investigated. Based on the results of the investigation, each pair of piezoelectric actuators and corresponding gap sensors is treated as an independent system and modeled as a first-order linear model coupled with hysteresis. When the model is identified and the hysteresis nonlinearity is linearized, a linear system model with uncertainty is used to design the controller. When designing the controller, the sliding-mode disturbance (uncertainty) estimation and compensation scheme is used. The structure of the proposed controller is similar to that of a proportional integral derivative controller. Thus, it can be easily implemented. Experimental results show that 3-nm tracking resolution can be obtained. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society
Citations
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TL;DR: The progresses of different modeling and control approaches for piezo-actuated nanopositioning stages are discussed and new opportunities for the extended studies are highlighted.
Abstract: Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.
458 citations
TL;DR: Experimental results demonstrate that the performance of proposed controller is superior to that of conventional SMCPE in both set-point regulation and motion tracking control and validates the feasibility of the proposed controller in the field of micro/nano scale manipulation as well.
Abstract: This paper proposes an improved sliding mode control with perturbation estimation (SMCPE) featuring a PID-type sliding surface and adaptive gains for the motion tracking control of a micromanipulator system with piezoelectric actuation One advantage of the proposed controller lies in that its implementation only requires the online estimation of perturbation and control gains without acquiring the knowledge of bounds on system uncertainties The dynamic model of the system with Bouc-Wen hysteresis is established and identified through particle swarm optimization (PSO) approach, and the controller is designed based on Lyapunov stability analysis A high-gain observer is adopted to estimate the full state from the only measurable position information Experimental results demonstrate that the performance of proposed controller is superior to that of conventional SMCPE in both set-point regulation and motion tracking control Moreover, a submicron accuracy tracking and contouring is achieved by the micromanipulator with dominant hysteresis compensated for a low magnitude level, which validates the feasibility of the proposed controller in the field of micro/nano scale manipulation as well
337 citations
Cites methods from "Sliding-mode control of a three-deg..."
...Besides, by considering the hysteresis as a disturbance or an uncertainty, sliding mode control (SMC) has been employed in the piezo-driven stage [15], [16] since SMC is an effective and simple way to deal with model imperfection and uncertainties for nonlinear systems [17]....
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TL;DR: Experimental results reveal that a submicron accuracy 1-D and 3-D positioning can be achieved by the system, which confirms the effectiveness of the proposed mechanism and controller design as well.
Abstract: This paper reports the design and development processes of a totally decoupled flexure-based XYZ parallel-kinematics micropositioning stage with piezoelectric actuation. The uniqueness of the proposed XYZ stage lies in that it possesses both input and output decoupling properties with integrated displacement amplifiers. The input decoupling is realized by actuation isolation using double compound parallelogram flexures with large transverse stiffness, and the output decoupling is implemented by employing two-dimensional (2-D) compound parallelogram flexures. By simplifying each flexure hinge as a two-degree-of-freedom (2-DOF) compliant joint, analytical models of kinematics, statics, and dynamics of the XYZ stage are established and then validated with finite-element analysis (FEA). The derived models are further adopted for optimal design of the stage through particle swarm optimization (PSO), and a prototype of XYZ stage is fabricated for performance tests. The nonsymmetric hysteresis behavior of the piezo-stage is identified with the modified Prandtl-Ishlinskii (MPI) model, and a control scheme combining the inverse model-based feedforward with feedback control is constructed to compensate the plant nonlinearity and uncertainty. Experimental results reveal that a submicron accuracy 1-D and 3-D positioning can be achieved by the system, which confirms the effectiveness of the proposed mechanism and controller design as well.
199 citations
Cites methods from "Sliding-mode control of a three-deg..."
...Specifically, both hysteresis model-based (e.g., Preisach model [21], Maxwell model [22], Prandtl-Ishlinskii model [23]–[25], and Bouc-Wen model [26]) and hysteresis model-free control schemes (e.g., inversion-based technique [27], [28], robust control [29], sliding mode control [ 30 ], and adaptive control [31]) have been exploited....
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TL;DR: In this article, an inversion-free predictive controller based on a dynamic linearized multilayer feedforward neural network (MFNN) model is proposed to deal with the physical constraints of the input voltage of PEAs.
Abstract: Piezoelectric actuators (PEAs) are widely used in high-precision positioning applications. However, the inherent hysteresis nonlinearity seriously deteriorates the tracking performance of PEAs. To deal with it, the compensation of the hysteresis by using its inverse model (called inversion-based) is the popular method in the literature. One major disadvantage of this method is that the tracking performance of PEAs highly relies on its inverse model. Meanwhile, the computational burden of obtaining the inverse model is overwhelming. In addition, the physical constraints of the input voltage of PEAs is hardly handled by the inversion-based method. This paper proposes an inversion-free predictive controller, which is based on a dynamic linearized multilayer feedforward neural network (MFNN) model. By the proposed method, the inverse model of the inherent hysteresis is not required, and the control law can be obtained in an explicit form. By using the technique of constrained quadratic programming, the proposed method still works well when dealing with the physical constraints of PEAs. Moreover, an error compensation term is introduced to reduce the steady-state error if the dynamic linearized MFNN cannot approximate the PEA's dynamical model satisfactorily. To verify the effectiveness of the proposed method, experiments are conducted on a commercial PEA. The experiment results show that the proposed method has a satisfactory tracking performance even with high-frequency references. Comparisons demonstrate that the proposed method outperforms some existing results.
90 citations
TL;DR: In this paper, a PID-based sliding mode observer (PIDSMO) is proposed to relax the observer matching condition as required in the use of unknown-input observers, which can accurately estimate the PEA states and achieve better tracking control performance compared to the PIDSMC with α-β filter control scheme.
Abstract: Tracking control of piezoelectric actuators (PEAs) has stimulated the development of various advanced control schemes that utilize the feedback of PEA system states for improved control performance. Among them, the one based on the concept of sliding mode has been shown promising due to its robustness to matched uncertainties, but leaving the required state estimation to be desired. Previous studies show that the PEA can be modeled as a linear dynamic system with matched uncertainties. On this basis, this paper presents the development of a novel observer based on the concept of proportional-integral-derivative-based (PID-based) sliding mode, in which the switching function is replaced by a PID regulator. The novel observer, referred to as the PID-based sliding mode observer (PIDSMO), relaxes the observer matching condition as required in the use of the unknown-input observers. The PIDSMO is then integrated with the PID-based sliding mode controller (PIDSMC) to form a novel integrated PID-based sliding mode observer-controller (PIDSMOC) for PEA tracking control. Experiments performed on a PEA showed that the PIDSMO can accurately estimate the PEA states and that the integrated PIDSMOC can achieve better tracking control performances as compared to the PIDSMC with α-β filter control scheme.
89 citations
References
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Book•
01 Jan 1999
TL;DR: Sliding mode control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems as mentioned in this paper, and is particularly useful for electro-mechanical systems because of its discontinuous structure.
Abstract: Sliding Mode Control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems. The strengths of sliding mode controllers result from the ease and flexibility of the methodology for their design and implementation. They provide inherent order reduction, direct incorporation of robustness against system uncertainties and disturbances, and an implicit stability proof. They also allow for the design of high performance control systems at low costs. SMC is particularly useful for electro-mechanical systems because of its discontinuous structure. In fact, since the hardware of many electro-mechanical systems (such as electric motors) prescribes discontinuous inputs, SMC has become the natural choice for direct implementation. The book is intended primarily for engineers and establishes an interdisciplinary bridge between control science, electrical and mechanical engineering.
2,593 citations
TL;DR: The results show that the tracking control performance is greatly improved by augmenting the feedback loop with a model of hysteresis in the feedforward loop.
Abstract: The tracking control accuracy of piezoceramic actuators is limited due to their inherent hysteresis nonlinearity. This paper presents a computer-based tracking control approach for a piezoceramic actuator based on incorporating a feedforward loop with a PID (proportional-integral-derivative) feedback controller. The hysteresis nonlinearity of the piezoceramic actuator is modeled in the feedforward loop by using the classical Preisach model. Experiments were performed on a stacked piezoceramic actuator for tracking sinusoidal waveforms with signal frequencies ranging from 0.1-20 Hz. A comparison was made between a feedforward control scheme, a regular PID feedback control scheme, and a PID feedback control scheme with hysteresis modeling in the feedforward loop. The results show that the tracking control performance is greatly improved by augmenting the feedback loop with a model of hysteresis in the feedforward loop. The maximum error in tracking a sinusoidal waveform is about half that obtained using a regular PID controller.
681 citations
"Sliding-mode control of a three-deg..." refers methods in this paper
...However, the result in [7] is valid only for a sinusoidal trajectory, and the method in [8] requires that the model is trained using reference input before the control can be started....
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...Ge and Jouaneh [7, 8] used a combination of a PID feedback controller and a feedforward controller that included the Preisach model of hysteresis....
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TL;DR: Simulations show that the use of the adaptive hysteresis inverse leads to major improvements of system performance.
Abstract: For a system with hysteresis, the authors present a parameterized hysteresis model and develop a hysteresis inverse. The authors then design adaptive controllers with an adaptive hysteresis inverse for plants with unknown hysteresis. A new adaptive controller structure is introduced which is capable of achieving a linear parameterization and a linear error model in the presence of a hysteresis nonlinearity. A robust adaptive law is used to update the controller parameters and hysteresis inverse parameters, which ensures the global boundedness of the closed-loop signals for a wide class of of hysteresis models. Simulations show that the use of the adaptive hysteresis inverse leads to major improvements of system performance. >
621 citations
"Sliding-mode control of a three-deg..." refers background in this paper
...Tao and Kokotovic [ 11 ] developed an adaptive hysteresis inverse and cascaded it with the system so that the effects of hysteresis nonlinearity could be reduced....
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01 Mar 1997-Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology
TL;DR: In this article, a generalized Preisach model is proposed to relax the congruency requirement on the hysteresis loops of a piezoceramic actuator.
Abstract: This paper presents a new approach for modeling the hysteresis nonlinearity of a piezoceramic actuator using a modified generalized Preisach model, and the use of this model in a linearizing control scheme. The developed generalized Preisach model relaxes the congruency requirement on the hysteresis loops of a piezoceramic actuator, which must be satisfied when using the classical Preisach model. The congruency property is experimentally proved to not hold when running the actuator on a minor hysteresis loop. A numerical expression of the model is derived in terms of first- and second-order reversal curve experimental datasets. Output prediction using this model is performed on both an exponentially decayed sinusoidal input signal and an arbitrary input signal, and the results show that the model can accurately reproduce the hysteresis response with an error of less than 2.7%. A tracking control system for a piezoceramic actuator is also developed by combining a PID feedback controller with a hysteresis linearizing scheme in a feed-forward loop. The results show that this new control system can achieve 0.25 μm tracking control accuracy, which is 80 and 50% less than that obtained when using an open-loop controller and a regular feedback control system, respectively.
368 citations
"Sliding-mode control of a three-deg..." refers methods in this paper
...However, the result in [7] is valid only for a sinusoidal trajectory, and the method in [8] requires that the model is trained using reference input before the control can be started....
[...]
...Ge and Jouaneh [7, 8] used a combination of a PID feedback controller and a feedforward controller that included the Preisach model of hysteresis....
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TL;DR: A method for the design of compensators able to reduce hysteresis in transducers, as well as two measures to quantify and compare controller performance are described.
Abstract: The paper describes a method for the design of compensators able to reduce hysteresis in transducers, as well as two measures to quantify and compare controller performance. Rate independent hysteresis, as represented by the Preisach model of hysteresis, is seen as an input-output phase lag. The compensation is based on controllers derived from the "phaser," a unitary gain operator that shifts a periodic signal by a single phase angle. A "variable phaser" is shown to be able to handle minor hysteresis loops. Practical implementations of these controllers are given and discussed. Experimental results exemplify the use of these techniques.
153 citations
"Sliding-mode control of a three-deg..." refers methods in this paper
...Cruz-Hernandez and Hayward [9] proposed a variable-phase method....
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