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Simplified structure of a multilayer piezoelectric bimorph. (a) Detailed view of a single piezoelectric layer between two electrodes. The directions of the polarization p and of the electric field E are indicated. (b) Piezoelectric stack consisting of N l layers. Electrical connections between the electrodes and two voltage sources are indicated. (c) Stack dimensions. (d) Bimorph element consisting of two stacks (A and B) connected to independent voltage sources and a common ground.
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Piezoelectric actuators are becoming a viable alternative to electrodrives in terms of size, speed and stall force characteristics. In this paper, a novel dynamic model of a contemporary linear piezoelectric actuator is presented. The model is based on physically meaningful parameters and macroscopically measured data for the fully assembled state....
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... employed in the PiezoLegs actuator are tape-cast multilayer bimorphs with interdigital electrode configuration [44]. Figure 2 shows a simplified structure of such a bimorph element while the construction and fabrication details for similar structures can be found in [8,36]. To a good approximation the bimorph consists of a series of N l soft-type ceramic (EDO EC-76) layers which alternate in the direction of polarization p (figure 2(a)) and together constitute a stack of height L. The ceramic layers are separated with screen-printed electrodes which are connected to two external voltage sources U + and U − in such a way that the resulting potentials coincide in polarity with the polarization p in the corresponding layers and cause their elongation. ...
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Citations
... Figure 5c illustrates the equivalent model of the piezoelectric actuator, from which a mathematical model can be derived. Due to space limitations, this paper does not provide the specific derivation process [20]. ...
... According to Equations (19) and (20), the impact of disturbance d on the output depends on the sensitivity function S(s), and the effect of sensor noise on the output depends on the complementary sensitivity function T(s). Meanwhile, based on the small gain theorem (see Equation (14)), the robust stability conditions of the closed-loop system also depend on T(s). ...
... ( ) ( )‖ < 1 in Equation(21) represents the performance evaluation function for disturbance rejection. According to Equation(20) with T(s), the evaluation function can be expressed as: ...
During the operation of space gravitational wave detectors, the constellation configuration formed by three satellites gradually deviates from the ideal 60° angle due to the periodic variations in orbits. To ensure the stability of inter-satellite laser links, active compensation of the breathing angle variation within the constellation plane is achieved by rotating the optical subassembly through the telescope pointing mechanism. This paper proposes a high-performance robust composite control method designed to enhance the robust stability, disturbance rejection, and tracking performance of the telescope pointing system. Specifically, based on the dynamic model of the telescope pointing mechanism and the disturbance noise model, an H∞ controller has been designed to ensure system stability and disturbance rejection capabilities. Meanwhile, employing the method of an H∞ norm optimized disturbance observer (HODOB) enhances the nonlinear friction rejection ability of the telescope pointing system. The simulation results indicate that, compared to the traditional disturbance observer (DOB) design, utilizing the HODOB method can enhance the tracking accuracy and pointing stability of the telescope pointing system by an order of magnitude. Furthermore, the proposed composite control method improves the overall system performance, ensuring that the stability of the telescope pointing system meets the 10 nrad/Hz1/2 @0.1 mHz~1 Hz requirement specified for the TianQin mission.
... Piezoelectric actuator is a device that converts electrical energy into mechanism motion through the anti-piezoelectric effect. It has been widely applied in micro/nano operation [1,2] and other high-precision instruments, such as optical alignment [3,4], microsurgical instrument [5,6], and lithography [7,8]. Consequently, it has attracted the attention of many researchers in related fields. ...
Backward motion commonly exists in the stick-slip linear piezoelectric actuator, resulting in deterioration of the output performance and limiting their applications. To solve the problem, a stick-slip linear piezoelectric actuator with suppressed backward motion, achieved using an active-locking mechanism (ALM) with two mechanisms, is proposed in this paper. One mechanism involves stick-slip driving, while the other actively suppresses backward motion by clamping the slider during the backward driving process through efficient control. A prototype actuator was designed and manufactured to verify the feasibility of this method, and an experimental system was established to obtain the detailed parameters. Also, to verify the feasibility and effectiveness of the suppression effect on backward motion of the proposed actuator, the output performance of the traditional stick-slip actuator and the actuator with the ALM were compared. Based on the results, we demonstrate that the maximum output speed and maximum output force of the prototype are 2.26 mm s-1 and 1.6 N under a voltage of 100 V, respectively.
... Besides, the cycloid pattern has the ability to track the string-like feature for local scan [9]. In this paper, a modified cycloid trajectory is proposed for long-range scanning by the integration of the xy-piezoelectric scanner and the long traveling range nano-positioning stage (LTRPS) [10], [11]. In this way, the xy-piezoelectric scanner is just repeatedly forced to follow the elliptical trajectory which only contains one scanning frequency, and in the meanwhile, LTRPS is continuously to follow the ramp signal for long-range scanning. ...
... Furthermore, some parallel stages operating in the resonance, inertial or clamping and feeding actuation modes [115][116][117][118][119][120][121] were presented. Deng et al. [112] proposed an planar stage composed of four bending-bending hybrid sandwich transducers in parallel, as shown in Fig. 17, the planar motions could be obtained by the coordination of the four transducers, the maximum linear and rotary speeds of 19.8 mm/s and 0.266 rad/s were obtained when operating at bending-bending compound vibration mode. ...
Multi-degree-of-freedom (Multi-DOF) piezoelectric motion stage is an important part of modern manufacturing industry. In order to perform high precision outputs in a large travel range, various multi-DOF piezoelectric motion stages have been proposed and applied for decades. This work is concentrated on reviewing the research on piezoelectric motion stage. It involves the major components, operating principles of different actuation modes, design schemes and structures of the multi-DOF piezoelectric motion stages. In this review, the summary and classification of the actuation modes used in the multi-DOF piezoelectric motion stages are presented, mainly including the resonance actuation mode, inertial actuation mode, clamping and feeding actuation mode and direct actuation mode; the multi-DOF piezoelectric motion stage is divided into multi-actuator type and single-actuator type according to the number of actuators used in the motion stage, in which the multi-actuator type includes series, parallel and series-parallel types from the viewpoint of structure mechanism; in addition, the output performances of the stages are compared, and the state of arts of the stages are discussed and summarized, the further efforts and future research perspectives are highlighted.
... Each leg produces an elliptic trajectory during activation. Gray color denotes legs currently in contact with the drive rod.46 c IOP Publishing 2012. ...
... According to present studies, the 2-DOF linear PIDM can be regarded as two spring-mass-damper systems. The simplified system of the PIDM is shown in Figure 1b, where m px is the equivalent mass of the PA and stage in the x-axis, x p is the distance of the PA in the x-axis, x s is the distance of the slider in the x-axis, k x is the stiffness of the PA and stage in the x-axis, c x is the damper of the PA and stage in the x-axis, F px (t) is the equivalent driving force of the PA in the x-axis, f x is the friction force in the x-axis, m sx is the mass of the slider in the x-axis, m py is the equivalent mass of the PA and stage in the y-axis, y p is the distance of the PA in the y-axis, y s is the distance of the slider in the y-axis k y is the stiffness of the PA and stage in the y-axis, c y is the damper of the PA and stage in the y-axis, F py (t) is the equivalent driving force of the PA in the y-axis, f y is the friction force in the y-axis, and m sy is the mass of the slider in the y-axis [32,33]. achieved multi-DOF motions by avoiding coupled motions [4,5,16]. ...
... According to present studies, the 2-DOF linear PIDM can be regarded as two spring-mass-damper systems. The simplified system of the PIDM is shown in Figure 1b, where mpx is the equivalent mass of the PA and stage in the x-axis, xp is the distance of the PA in the x-axis, xs is the distance of the slider in the x-axis, kx is the stiffness of the PA and stage in the x-axis, cx is the damper of the PA and stage in the x-axis, Fpx(t) is the equivalent driving force of the PA in the x-axis, fx is the friction force in the x-axis, msx is the mass of the slider in the x-axis, mpy is the equivalent mass of the PA and stage in the y-axis, yp is the distance of the PA in the y-axis, ys is the distance of the slider in the y-axis ky is the stiffness of the PA and stage in the y-axis, cy is the damper of the PA and stage in the y-axis, Fpy(t) is the equivalent driving force of the PA in the y-axis, fy is the friction force in the y-axis, and msy is the mass of the slider in the y-axis [32,33]. Kinematics equations of the 2-DOF orthogonal motions in the parallel 2-DOF PIDM can be extended from the 1-DOF PIDM model [34] and expressed as ...
A two-degrees-of-freedom (2-DOF) linear piezoelectric impact drive mechanism (PIDM) is actuated by two independent piezoelectric actuators (PAs). The coupled motion interactions of a two orthogonal DOF linear PIDM with a single friction interface are introduced and analyzed. A complete dynamic model of the 2-DOF PIDM is established with the Karnopp friction model considering the distribution of friction in the x-axis and y-axis. The output displacements of the 2-DOF PIDM and two corresponding independent 1-DOF PIDMs are investigated numerically. When the two input exciting signals of a 2-DOF PIDM have the same driving voltage of 100 V with a duty ratio of 98% at 10 Hz and two 1-DOF PIDMs are driving under the same conditions, the step displacements in the two axes of 2-DOF PIDM are improved compared to the corresponding 1-DOF PIDM. When the two input exciting signals of a 2-DOF PIDM have the same driving voltages of 100 V with a duty ratio of 98% but the driving frequency is 10 Hz in the x-axis and 20 Hz in the y-axis, the results show that the displacement of high frequency achieves a slight decrease and displacement of low frequency shows a large increase compared to the two corresponding 1-DOF PIDMs.
... The elastic rotor driven by an elliptical motion trajectory of a contact point was modeled as a linear spring. Szufnarowski [21] proposed a contact dynamics model that describes the frictional interaction between multiple piezoelectric legs and a ceramic rod. In this model, the interaction interface between the ceramic surfaces of the drive rod and the legs are represented as effective stiffness. ...
... Equation (21) expresses the steady state velocity of the sliding clipper. Substituting equation (21) into equation (11), characteristic phase angle in steady state form can be written as -> is satisfied, the steady state solution of t p i w exists and can be expressed as α+2πi. ...
... Equation (21) expresses the steady state velocity of the sliding clipper. Substituting equation (21) into equation (11), characteristic phase angle in steady state form can be written as -> is satisfied, the steady state solution of t p i w exists and can be expressed as α+2πi. In this paper, equivalent steady phase angle α is calculated based on adequate a and b to evaluate the output force and the x-directional velocity of the sliding clipper. ...
Piezoelectric actuators have been widely used in positioning stages because of their compact size, stepping controllability, and holding force. This study proposes a piezoelectric-driven stage composed of a bi-electrode piezoelectric slab, capacitive position sensor, and capillary filling detector for filling liquid samples into nanopipettes using capillary flow. This automatic sample-filling device is suitable for transmission electron microscopy image-based quantitative analysis of aqueous products with added nanoparticles. The step length of the actuator is adjusted by a pulse width modulation signal that depends on the stage position; the actuator stops moving once the capillary filling has been detected. A novel dynamic model of the piezoelectric-driven stage based on collision interactions between the piezoelectric actuator and the sliding clipper is presented. Unknown model parameters are derived from the steady state solution of the equivalent steady phase angle. The output force of the piezoelectric actuator is formulated using the impulse and momentum principle. Considering the applied forces and related velocity between the sliding clipper and the piezoelectric slab, the stage dynamic response is confirmed with the experimental results. Moreover, the model can be used to explain the in-phase slanted trajectories of piezoelectric slab to drive sliders, but not elliptical trajectories. The maximum velocity and minimum step length of the piezoelectric-driven stage are 130 mm s⁻¹ and 1 μm respectively.
... For a detailed dynamic modeling of the motor, the reader is advised to consider study [27] where developed model is based on the physically meaningful parameters and macroscopically measured data for the fully assembled state of the motor. Fig. 2 shows the free body diagram of the Piezo LEGS motor. ...
In this paper implementation of a control system for high precision applications is presented. The control system is developed for a Piezo LEGS motor, which is a walking piezo motor that can be employed in nanometric precision applications. In the control system structure, two main components are digital signal controller which executes control algorithm and power driver that is generating driving voltages for the motor. The waveforms of the driving voltages are designed using a recently presented coordinate transformation. This transformation enables synthesis of driving waveforms according to design requirements regarding force imposed to the motor's rod and rod's x-direction trajectory profile. In this work, the waveforms are selected to ensure no relative motion between the motor's legs and rod, and constant velocity of the rod within one step. Control algorithm is named as virtual time control. Despite its simplicity, the algorithm allows high precision positioning which is very close to theoretically achievable one.
... Discussion on the operating principle and dynamic behavior of a Piezo LEGS motor in this study will be concise, including only the information necessary for the reader to understand the proposed method for driving the motor. For a detailed dynamic modeling of the motor, the reader is advised to consider study [25] where developed model is based on the physically meaningful parameters and macroscopically measured data for the fully assembled state of the motor. ...
... Force F y is generated once the nonzero sum of voltages is applied to the legs. In the study [25], this force is denoted as normal force. The rod moves in the direction of this force when its magnitude becomes larger than the magnitude of F p . ...
... It is already noted that the motor's legs are working in pairs of two. These pairs will be called pair 1 and pair 2. In the studies where the waveforms of driving voltages were discussed [16], [10], [25], the authors proposed different types of the waveforms. Each has its advantages and disadvantages regarding the motor's speed within one step and the y-direction interaction force (normal force [25]) imposed on the rod by the legs. ...
This paper offers a new approach for specifying the waveforms of driving voltages for a Piezo LEGS motor. A novel idea of coordinate transformation to define the waveforms of driving voltages, based on the motor static model, is presented. This transformation defines driving voltages according to the desired motion of the motor legs in the x- and y-directions. The approach allows a user to first define force acting on the motor rod in the y-direction and define the rod's x-direction trajectory profile. Waveforms of the driving voltages are subsequently defined to meet these requirements. The proposed approach also enables the possibility of defining the desired step shape for the motor and, according to that definition, producing driving voltages. Based on the given coordinate transformation, a simple method for Piezo LEGS motor control, identified as virtual time control, is presented. This method results in overshoot-free high precision positioning.
... Hence, more intricate model including dynamic behavior of the piezoelectric legs and driving rod is needed. Piezo LEGS motor dynamical behavior is described by authors in [26]. Model in this work is extensive and describes normal force and frictional interaction between piezoelectric legs and ceramic rod. ...
... In this paper notion of what is the driving principle behind Piezo LEGS is given and furthermore certain measurements are provided that show how accurate is approximation of motor behavior from (1) and (2). Considering these equations and model developed in [26] driving principle of Piezo LEGS motor can be summarized as below. Let us assume that leg is at first moving freely in space. ...
... Important advantage is that y-direction interaction force and x-direction trajectory profile can be independently set. Different approaches for driving waveforms definition are suggested in [13], [8], [26], but none of them has this flexibility. ...
This paper describes FPGA based control system for a piezoelectric motor, commercially available Piezo LEGS motor. Driving voltages waveforms are defined as a combination of linear functions. This definition provides possibility for easy implementation on very simple hardware. Linear functions parameters allow forming of the driving voltages according to desired trajectory of motor's legs. Considering that FPGA technology offers many advantages over the classical microprocessor based systems, it is used as control system implementation hardware. Realized control system can be very easily expanded to control multiple motors, if hardware resources are big enough. Also modularity is provided, making the future application very simple. In the paper control system structure is described in detail along with a very simple control algorithm for Piezo LEGS motor positioning control. Experimental results are given to validate designed control system. They showed satisfying control performance, responses with no overshoot and expected steady state error.
