Adaptive sliding mode control of a piezo-actuated bilateral teleoperated micromanipulation system

Piezoelectric actuators are widely used in micro manipulation applications. However, hysteresis nonlinearity limits the accuracy of these actuators. This paper presents a novel approach for utilizing a piezoelectric nano-stage as the slave manipulator of a teleoperation system based on a sliding mode controller. The Prandtl-Ishlinskii (PI) model is used to model actuator hysteresis in feedforward scheme to cancel out this nonlinearity. The presented approach requires full state and force measurements at both the master and slave sides. Such a system is costly and also difficult to implement. Therefore, sliding mode unknown input observer (UIO) is proposed for full state and force estimations. Furthermore, the effects of uncertainties in the constant parameters on the estimated external forces should be eliminated. So, a robust adaptive controller is proposed and its stability is guaranteed through the Lyapunov criterion. Performance of the proposed control architecture is verified through experiments.     

具有迟滞和蠕变特性压电作动器的模糊自适应逆控制方法

针对具有迟滞和蠕变特性的压电作动器非线性模型,提出了一种前馈控制和反馈控制相结合的自适应模糊逆控制方案。在前馈控制器中压电作动器的迟滞和蠕变非线性特性的逆模型由自适应模糊逻辑系统近似;在反馈控制器中比例控制器用来调节压电作动器的输出误差。该方法可以实时补偿压电作动器的迟滞和蠕变特性,减少作动器跟踪误差。仿真计算结果表明了该方法的有效性。     

Ultra-precise tracking control of piezoelectric actuators via a fuzzy hysteresis model

In this paper, a novel Takagi-Sugeno (T-S) fuzzy system based model is proposed for hysteresis in piezoelectric actuators. The antecedent and consequent structures of the fuzzy hysteresis model (FHM) can be, respectively, identified on-line through uniform partition approach and recursive least squares (RLS) algorithm. With respect to controller design, the inverse of FHM is used to develop a feedforward controller to cancel out the hysteresis effect. Then a hybrid controller is designed for high-performance tracking. It combines the feedforward controller with a proportional integral differential (PID) controller favourable for stabilization and disturbance compensation. To achieve nanometer-scale tracking precision, the enhanced adaptive hybrid controller is further developed. It uses real-time input and output data to update FHM, thus changing the feedforward controller to suit the on-site hysteresis character of the piezoelectric actuator. Finally, as to 3 cases of 50 Hz sinusoidal, multiple frequency sinusoidal and 50 Hz triangular trajectories tracking, experimental results demonstrate the efficiency of the proposed controllers. Especially, being only 0.35% of the maximum desired displacement, the maximum error of 50 Hz sinusoidal tracking is greatly reduced to 5.8 nm, which clearly shows the ultra-precise nanometer-scale tracking performance of the developed adaptive hybrid controller.     

Output characteristics and experiments of a novel low frequency rotary piezoelectric motor

In order to improve the output performance of a piezoelectric motor under low driving frequency, a novel rotary piezoelectric motor driven by two piezoelectric actuators is proposed that is actuated based on harmonic and friction driving mechanism. The motor uses two piezoelectric actuators to drive two amplifying mechanisms with π/2 phase difference to produce harmonic motion, and then drives the rotor to rotate through friction force. Based on the driving principle, the electromechanical coupling equations of the motor are established. And a test platform is built to test the output characteristics of the motor. The results show that fluctuation of harmonic force and output torque occurs when the motor operates at different positions. Under the driving voltage and frequency of 150 V and 5 Hz, the actual average output torque of the prototype is 3.08 Nmm. Moreover, fluctuation of harmonic force and output torque occurs when the motor operates at different positions.

     

Design and testing of a hybrid polymeric electrostrictive/piezoelectric beam with bang–bang control

Electrostrictive materials, hard ceramics and soft polymers, have been used as precision actuators in many engineering applications. This study is to examine bang–bang control performance of a hybrid Plexiglas beam laminated with polymeric electrostrictive (RTV 270) actuator and piezoelectric polyvinylidene fluoride (PVDF) sensor layers using both analytical and experimental techniques. Material characteristics are calibrated via static testing first; a hybrid beam model is then fabricated and an experiment set-up, consisting of a bang–bang controller, high-voltage amplifier, data acquisition system and the hybrid beam system, is designed to evaluate vibration control characteristics (i.e., damping ratio estimation) of the hybrid beam subjected to various control conditions. Due to the quadratic behaviour of electrostrictive materials, the controller activates the electrostrictive actuator only in upward motion of the beam, with reference to signals generated from the piezoelectric sensor. Base on constitutive equations and dynamic/control characteristics, a mathematic hybrid beam model is also derived from the electrostrictive thin shell theory and its dynamic responses, based on the finite difference discretization, are simulated to predict damping ratios resulting from control forces induced by the electrostrictive actuators. Dynamic responses (with and without control) of the physical beam model are measured and compared with simulation results. Favourable comparison suggests that the mathematical model describes the experimental model very well and its application to other advanced structures can be proceeded.     

Finite element based model predictive control for active vibration suppression of a one-link flexible manipulator

This paper presents a unique approach for active vibration control of a one-link flexible manipulator. The method combines a finite element model of the manipulator and an advanced model predictive controller to suppress vibration at its tip. This hybrid methodology improves significantly over the standard application of a predictive controller for vibration control. The finite element model used in place of standard modelling in the control algorithm provides a more accurate prediction of dynamic behavior, resulting in enhanced control. Closed loop control experiments were performed using the flexible manipulator, instrumented with strain gauges and piezoelectric actuators. In all instances, experimental and simulation results demonstrate that the finite element based predictive controller provides improved active vibration suppression in comparison with using a standard predictive control strategy.     

A comparative study on the use of black box modelling for piezoelectric actuators

In this article, different approaches of the use of black box modelling techniques for piezoelectric actuators are particularly addressed, regardless of the employed technique/algorithm. A modelling approach in this paper refers to two matters: the first, the role of black box techniques in modelling (i.e. if physics-based techniques are also involved in modelling; if so, how and to what extent). From this aspect, the spectrum of approaches ranges from those merged with/inspired by classical phenomenological models to an approach based on purely system identification-based techniques. The second aspect of modelling approaches, in this article, is the input variables to the model. Current and previous values of input voltage, previous values of the output (displacement), derivatives and extremum values of the system's input/output have been used as the inputs to the model so far. Both aforementioned aspects of modelling approaches are addressed appropriately in this article, and various modelling approaches in the literature are categorized and presented in a uniform and comparable manner, so that readers can easily identify research trends in this area and the gaps in the literature. One of the identified unanswered questions in the literature is whether the extremum values of the system's input/output should/should not be used as an input to black box models of piezoelectric actuators. There are works in the literature which have/have not used the aforementioned input variables, but there is no published investigation to evidently answer the proposed question. This article, in the last section, answers this question by reporting and discussing an experimental study.     

Hybrid controller of a linear piezoelectric walking stage relying on stack/shear piezoelectric actuators

This paper proposes a hybrid control strategy of a novel linear piezoelectric walking stage based on two sorts of piezoelectric actuators, which takes the load variation into account. The proposed stage consists of two parallel 4-bar lever amplification mechanisms with flexure hinges actuated by piezoelectric stacks to heighten the vertical distance (that is more tolerable to the assembly discrepancy), two compression springs (that is able to maintain a fixed linear position without powering), and two shear piezoelectric actuators (that can achieve longer and equivalent to walking motion) in a small form factor. The proposed stage has two operating modes, namely a coarse positioning mode with a more extensive travel range and a fine positioning mode with a nanometer-level resolution, to possess excellent performance for the linear piezoelectric walking stage of load variations. One multimodal switching controller and one feedforward-feedback controller conduct the coarse mode and fine mode, respectively. The optimal frequency for a specific load is obtained through a backpropagation neural network in the multimodal switching control. In the feedforward-feedback control, the inverse mathematical model based on the Bouc-Wen hysteresis model is used to mitigate the hysteresis effect in the feedforward part while the proportional–integral–derivative controller in the feedback part handles the external system disturbances. Experimental results show the proposed hybrid coarse/fine mode control strategy's effectiveness to satisfy an efficient and accurate positioning task.     

Practical and intuitive controller design method for precision positioning of a pneumatic cylinder actuator stage

The present paper describes a practical and intuitive controller design method for precision positioning of pneumatic cylinder actuator stages. Pneumatic actuators are easy to use and have numerous advantages, which has led to these actuators having a wide variety of applications. However, pneumatic actuators have notable nonlinear characteristics, which make precision positioning difficult to achieve. The purpose of the present study is to clarify a practical and intuitive controller design procedure for precision positioning of a pneumatic cylinder actuator. In addition to positioning performance, the present study focuses on the realization of easy controller design without the need for the exact model parameters or knowledge in control theory for general-industrial-use pneumatic cylinder actuators with friction characteristics. These considerations are important in order to fully exploit the advantages of pneumatic cylinder actuators in a wide variety of applications. As such, three elements are added to the conventional continuous-motion nominal characteristic trajectory following (CM NCTF) controller. A new design procedure of the improved CM NCTF controller for pneumatic cylinder actuator stages is introduced, and the positioning performance of the designed control system is examined experimentally under several conditions. The positioning results generally indicate a positioning error of 50 nm, which is equal to the sensor resolution.     

高频响伺服刀架的建模与控制

考虑目前应用压电陶瓷驱动器的伺服刀架只能提供单向驱动力,设计了一种基于双压电陶瓷驱动器的快速伺服刀架。涉及的两个压电陶瓷驱动器分别为刀具的进给和回复提供驱动力,其呈对称布置,用于有效提高刀架的整体刚度。为了对两个压电陶瓷驱动器进行联动协调控制,建立了PI迟滞模型和其逆模型,并设计了相应的联动协调控制方法。利用PI逆模型作为PID反馈控制的前馈环节构成复合控制用于调节快速伺服刀架的输出位移。实验验证了新型快速伺服刀架的响应频率、响应时间、位移响应特性和定位精度。结果显示:新型快速伺服刀架的响应频率为871.86 Hz,响应时间为0.000 45s;三角波信号的最大定位误差为3.366 1μm,误差百分数为7.63%,平均绝对误差为0.698 0μm,误差百分数为1.58%;正弦波信号的最大定位误差为3.244 4μm,误差百分数为7.67%,平均绝对误差为0.930 9μm,误差百分数为2.20%。     

一种新型两自由度柔性并联机械手的主动振动控制及其仿真

针对一种新型两自由度柔性并联机械手,在含有压电元件的有限元模型基础上,基于模态理论和滑模变结构理论,研究其振动主动控制问题。采用有限元法和模态理论建立系统的动力学模型。根据系统的性能要求,采用最优化方法确定滑移面,基于Lyapunov直接法设计滑模控制器。控制器能对系统的前几阶模态实施控制,实现机械手的振动主动控制。仿真结果表明,该控制器可有效地抑制柔性构件产生的弹性振动,减小并联机械手动平台的位置误差,从而验证了该控制器的可行性和有效性。     

Design and evaluation of a PEA-driven fast steering mirror with a permanent magnet preload force mechanism

This paper presents the design and evaluation of a high-bandwidth fast steering mirror (FSM) driven by a piezoelectric actuator (PEA) for applications in the scanning systems. To avoid additional dynamics induced by flexure hinges and to simplify the structure of the FSM, a preload force mechanism based on permanent magnets (PMs) is proposed. Actuators and sensors that can satisfy the required flatness and bandwidth are chosen, and the designs of the mirror and the preload force mechanism are completed with the aid of finite element analysis. A simple system model and controller design are achieved by analyzing the voltage transformation and the relationships between different displacements. To verify the feasibility of the design and evaluate the performance of the FSM, a series of experiments was carried out with voltage control, charge control, and charge plus notch filter control. The final experimental results show that the FSM reaches a high bandwidth of 8 kHz with charge plus notch filter control, demonstrating that design of an FSM with a PM preload force mechanism is feasible.     

Loop shaping design for tracking performance in machine axes

A modern interpretation of classical loop shaping control design methods is presented in the context of tracking control for linear motor stages. Target applications include noncontacting machines such as laser cutters and markers, water jet cutters, and adhesive applicators. The methods are directly applicable to the common PID controller and are pertinent to many electromechanical servo actuators other than linear motors. In addition to explicit design techniques a PID tuning algorithm stressing the importance of tracking is described. While the theory behind these techniques is not new, the analysis of their application to modern systems is unique in the research literature. The techniques and results should be important to control practitioners optimizing PID controller designs for tracking and in comparing results from classical designs to modern techniques. The methods stress high-gain controller design and interpret what this means for PID. Nothing in the methods presented precludes the addition of feedforward control methods for added improvements in tracking. Laboratory results from a linear motor stage demonstrate that with large open-loop gain very good tracking performance can be achieved. The resultant tracking errors compare very favorably to results from similar motions on similar systems that utilize much more complicated controllers.     

Frequency characteristics of non-contact ultrasonic motor with motion error correction

The purpose of this research is to achieve real time motion error correction of the rotor in a non-contact ultrasonic motor (non-contact USM). The rotor is installed in a cylindrical stator with a small gap and designed so that it has a resonant frequency of 22.2 kHz, the 8th flexural mode of vibration. The multi-layered piezoelectric actuators excite the flexural wave traveling in the circumference direction. The ultrasonic vibration produces a sound field that levitates the rotor, and the traveling wave induces a near-boundary streaming to rotate the rotor by viscous force. In this paper, we describe an experimental test of the performance of a non-contact USM. When the flexural vibration amplitude was 0.3 μm, the rotational speed was 4 rpm. The rotational speed and starting torque was proportional to the vibration amplitude. The starting performance to attain rotational speed had a time constant of 2 s for several different amplitudes hence the rotational torque is independent of the rotational speed and the resistance force on the rotor is governed by viscosity. In addition, the non-contact USM has the capability of contact-free micro positioning of the rotor by controlling the deformation of the piezoelectric actuators. The PI controller was constructed to correct the detected motion error of the rotor in the radial direction. As a consequence, a motion error of 0.8 μm for one rotor revolution was reduced to 0.1 μm.     

Constraint-force-based approach of modelling compliant mechanisms: Principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.     

Fluid-dynamic analysis and multi-objective design optimization of piezoelectric servo valves

This paper proposes an effective methodology for the fluid-dynamic design optimization of the main spool of a piezoelectric servo valve. The aim is to improve global performances of the piezoelectric servo valve by reducing the flow force acting on the main spool and the mass of the main spool. The main disturbance forces acting the main spool were analyzed. The steady-state flow force acting on the main spool was derived and the relationship between the flow force and the design parameters of the main spool was established. The design problem of the main spool was formulated mathematically as a multi-objective optimization problem. The minimum steady-state flow force and the minimum mass of main spool were considered as optimization objectives. The elitist non-dominated sorting genetic algorithm (NSGA-II) was applied and a set of Pareto-optimal solutions was calculated. The optimized results were analyzed and the final design parameters of the main spool were selected for the simulation analysis and experimental research. The computational fluid dynamics (CFD) simulation was employed to calculate the forces acting on the main spool. Simulation results show the flow force acting on the optimized main spool is significantly reduced. The unoptimized and optimized main spools were machined and experimental study was performed. Results show that the piezoelectric servo valve equipped with the optimized main spool has better response performance and dynamic bandwidth. The dynamic bandwidth is measured to 172 Hz under the amplitude attenuation of −3 dB. Compared with the piezoelectric servo valve with unoptimized main spool, the dynamic bandwidth of the piezoelectric servo valve with optimized main spool is increased by 26%.     

Observer-based sliding mode control with adaptive perturbation estimation for micropositioning actuators

Control of piezoelectric actuators is under the effects of hysteresis that could affect actuators micropositioning accuracy. In this paper a modified Prandtl-Ishlinskii (PI) operator and its inverse is utilized for both identification and real time compensation of the hysteresis effect. As a result, the actuator dynamic model would be transformed to the second order linear dynamic model. Considering the parametric uncertainties, PI estimation error and probably unmodeled dynamics, a variable structure controller coupled with adaptive perturbation estimation is proposed for trajectory tracking of the piezoelectric position. Considering the very noisy output of the actuator, a high-gain observer would estimate full states from the only measurable position trajectory. The stability of the controller in the presence of the estimated state is demonstrated with the Lyapunov criterion. Comparing to the widely used proportional-integral controller, the experimental results depicts that the proposed approach is greatly achieved in precisely tracking of multiple frequency trajectories.     

Active robust vibration control of flexible composite beams with parameter perturbations

In this paper, a time domain approach is presented to treat the problem of active controlling simultaneously the bending and torsional vibration of flexible composite beams under both mode truncations and parameter perturbations. In the proposed approach, the residual model, which is known as unstructured uncertainty, is viewed as an additive perturbation to the controlled model. Based on a state space model, which incorporates both bending and torsional deformation effects, of the flexible composite beam with piezoelectric sensors and actuators, a robust stability condition is derived to guarantee that both bending and torsional vibration of the flexible composite beam, which is subject to both mode truncation and linear time-varying parameter perturbations, can be actively controlled by an observer-based controller. The proposed robust stability condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effects and additive time-varying parameter perturbations. Finally, an active robust vibration control problem of a cantilevered flexible composite beam with piezoelectric sensors and actuators is provided for illustration.     

Active spindle system for a rotary planing machine

This paper presents the experimental validation of an active control approach to improve the damping of a spindle system for wood machining. The active control was implemented using piezoelectric actuators in push–pull configuration with real-time control capabilities. The adaptive control strategy based on the linear quadratic Gaussian is first modeled within MATLAB/Simulink and then implemented on the real spindle system. Experimental tests were performed on the small-scale planer prototype to validate the simulation models. Moreover a cutting force observer which can be used to continuously monitor the cutting process is also implemented and its performance is presented.     

Design and control of a decoupled two degree of freedom translational parallel micro-positioning stage

This paper presents a novel decoupled two degrees of freedom (2-DOF) translational parallel micro-positioning stage. The stage consists of a monolithic compliant mechanism driven by two piezoelectric actuators. The end-effector of the stage is connected to the base by four independent kinematic limbs. Two types of compound flexure module are serially connected to provide 2-DOF for each limb. The compound flexure modules and mirror symmetric distribution of the four limbs significantly reduce the input and output cross couplings and the parasitic motions. Based on the stiffness matrix method, static and dynamic models are constructed and optimal design is performed under certain constraints. The finite element analysis results are then given to validate the design model and a prototype of the XY stage is fabricated for performance tests. Open-loop tests show that maximum static and dynamic cross couplings between the two linear motions are below 0.5% and -45 dB, which are low enough to utilize the single-input-single-out control strategies. Finally, according to the identified dynamic model, an inversion-based feedforward controller in conjunction with a proportional-integral-derivative controller is applied to compensate for the nonlinearities and uncertainties. The experimental results show that good positioning and tracking performances are achieved, which verifies the effectiveness of the proposed mechanism and controller design. The resonant frequencies of the loaded stage at 2 kg and 5 kg are 105 Hz and 68 Hz, respectively. Therefore, the performance of the stage is reasonably good in term of a 200 N load capacity.