Continuous time controller based on SMC and disturbance observer for piezoelectric actuators

Abstract – In this work, analog application for the Sliding Mode Control (SMC) to piezoelectric actuators (PEA) is presented. DSP application of the algorithm suffers from ADC and DAC conversions and mainly faces limitations in sampling time interval. Moreover piezoelectric actuators are known to have very large bandwidth close to the DSP operation frequency. Therefore, with the direct analog application, improvement of the performance and high frequency operation are expected. Design of an appropriate SMC together with a disturbance observer is suggested to have continuous control output and related experimental results for position tracking are presented with comparison of DSP and analog control application

Master of Science

thesisThe need for precise micro/nano-positioning has arisen in many fields of research and technology. Piezoelectric stick-slip actuators are widely used where precise positioning over a wide range of motion is required. Controlling manipulators that utilize piezoelectric stick-slip actuators is not a trivial task, as these actuators have a discrete stepping nature, with a step size that is influenced by a variety of factors such as actuator loading, temperature, and humidity. Absence of integrated joint sensors in manipulators that use piezoelectric stick-slip actuators (which is typical), as well as difficulty in using vision feedback for closed-loop control, has led to development of open-loop modeling methods to estimate the step size of the actuators. Prior work has failed to characterize and quantify the effects of various parameters on the displacement of such actuators to a degree as to be easily utilized in the control of an actual manipulator. In this thesis, we propose an empirically derived predictive open-loop model for the step size of the prismatic and rotary piezoelectric-stick-slip-actuated joints of a Kleindiek MM3A micromanipulator, based on static and inertial loads due to the mass of the manipulator's links as well as loads applied to the end-effector. The effects of various parameters on the step size of each joint are quantified and characterized. The results obtained are then fit into a model based on nonlinear regression via joint-specific parameters. Calibration routines are developed to quickly determine the joint-specific parameters for use in the derived predictive step-size model. Using the model obtained, we can predict the step size with an accuracy of 20% (100 nm) for the prismatic joint of the manipulator, and 2% (1 ^rad) for the rotary joints of the manipulator

Modeling and Control of Piezoelectric Actuators

Piezoelectric actuators (PEAs) utilize the inverse piezoelectric effect to generate fine displacement with a resolution down to sub-nanometers and as such, they have been widely used in various micro- and nanopositioning applications. However, the modeling and control of PEAs have proven to be challenging tasks. The main difficulties lie in the existence of various nonlinear or difficult-to-model effects in PEAs, such as hysteresis, creep, and distributive vibration dynamics. Such effects can seriously degrade the PEA tracking control performances or even lead to instability. This raises a great need to model and control PEAs for improved performance. This research is aimed at developing novel models for PEAs and on this basis, developing model-based control schemes for the PEA tracking control taking into account the aforementioned nonlinear effects. In the first part of this research, a model of a PEA for the effects of hysteresis, creep, and vibration dynamics was developed. Notably, the widely-used Preisach hysteresis model cannot represent the one-sided hysteresis of PEAs. To overcome this shortcoming, a rate-independent hysteresis model based on a novel hysteresis operator modified from the Preisach hysteresis operator was developed, which was then integrated with the models of creep and vibration dynamics to form a comprehensive model for PEAs. For its validation, experiments were carried out on a commercially-available PEA and the results obtained agreed with those from model simulations. By taking into account the linear dynamics and hysteretic behavior of the PEA as well as the presliding friction between the moveable platform and the end-effector, a model of the piezoelectric-driven stick-slip (PDSS) actuator was also developed in the first part of the research. The effectiveness of the developed model was illustrated by the experiments on the PDSS actuator prototyped in the author's lab. In the second part of the research, control schemes were developed based on the aforementioned PEA models for tracking control of PEAs. Firstly, a novel PID-based sliding mode (PIDSM) controller was developed. The rational behind the use of a sliding mode (SM) control is that the SM control can effectively suppress the effects of matched uncertainties, while the PEA hysteresis, creep, and external load can be represented by a lumped matched uncertainty based on the developed model. To solve the chattering and steady-state problems, associated with the ideal SM control and the SM control with boundary layer (SMCBL), the novel PIDSM control developed in the present study replaces the switching control term in the ideal SM control schemes with a PID regulator. Experiments were carried out on a commercially-available PEA and the results obtained illustrate the effectiveness of the PIDSM controller, and its superiorities over other schemes of PID control, ideal SM control, and the SMCBL in terms of steady state error elimination, chattering suppression, and tracking error suppression. Secondly, a PIDSM observer was also developed based on the model of PEAs to provide the PIDSM controller with state estimates of the PEA. And the PIDSM controller and the PIDSM observer were combined to form an integrated control scheme (PIDSM observer-controller or PIDSMOC) for PEAs. The effectiveness of the PIDSM observer and the PIDSMOC were also validated experimentally. The superiority of the PIDSMOC over the PIDSM controller with σ-β filter control scheme was also analyzed and demonstrated experimentally. The significance of this research lies in the development of novel models for PEAs and PDSS actuators, which can be of great help in the design and control of such actuators. Also, the development of the PIDSM controller, the PIDSM observer, and their integrated form, i.e., PIDSMOC, enables the improved performance of tracking control of PEAs with the presence of various nonlinear or difficult-to-model effects

Concept, modeling and experimental characterization of the modulated friction inertial drive (MFID) locomotion principle:application to mobile microrobots

A mobile microrobot is defined as a robot with a size ranging from 1 in3 down to 100 µm3 and a motion range of at least several times the robot's length. Mobile microrobots have a great potential for a wide range of mid-term and long-term applications such as minimally invasive surgery, inspection, surveillance, monitoring and interaction with the microscale world. A systematic study of the state of the art of locomotion for mobile microrobots shows that there is a need for efficient locomotion solutions for mobile microrobots featuring several degrees of freedom (DOF). This thesis proposes and studies a new locomotion concept based on stepping motion considering a decoupling of the two essential functions of a locomotion principle: slip generation and slip variation. The proposed "Modulated Friction Inertial Drive" (MFID) principle is defined as a stepping locomotion principle in which slip is generated by the inertial effect of a symmetric, axial vibration, while the slip variation is obtained from an active modulation of the friction force. The decoupling of slip generation and slip variation also has lead to the introduction of the concept of a combination of on-board and off-board actuation. This concept allows for an optimal trade-off between robot simplicity and power consumption on the one hand and on-board motion control on the other hand. The stepping motion of a MFID actuator is studied in detail by means of simulation of a numeric model and experimental characterization of a linear MFID actuator. The experimental setup is driven by piezoelectric actuators that vibrate in axial direction in order to generate slip and in perpendicular direction in order to vary the contact force. After identification of the friction parameters a good match between simulation and experimental results is achieved. MFID motion velocity has shown to depend sinusoidally on the phase shift between axial and perpendicular vibration. Motion velocity also increases linearly with increasing vibration amplitudes and driving frequency. Two parameters characterizing the MFID stepping behavior have been introduced. The step efficiency ηstep expresses the efficiency with which the actuator is capable of transforming the axial vibration in net motion. The force ratio qF evaluates the ease with which slip is generated by comparing the maximum inertial force in axial direction to the minimum friction force. The suitability of the MFID principle for mobile microrobot locomotion has been demonstrated by the development and characterization of three locomotion modules with between 2 and 3 DOF. The microrobot prototypes are driven by piezoelectric and electrostatic comb drive actuators and feature a characteristic body length between 20 mm and 10 mm. Characterization results include fast locomotion velocities up to 3 mm/s for typical driving voltages of some tens of volts and driving frequencies ranging from some tens of Hz up to some kHz. Moreover, motion resolutions in the nanometer range and very low power consumption of some tens of µW have been demonstrated. The advantage of the concept of a combination of on-board and off-board actuation has been demonstrated by the on-board simplicity of two of the three prototypes. The prototypes have also demonstrated the major advantage of the MFID principle: resonance operation has shown to reduce the power consumption, reduce the driving voltage and allow for simple driving electronics. Finally, with the fabrication of 2 × 2 mm2 locomotion modules with 2 DOF, a first step towards the development of mm-sized mobile microrobots with on-board motion control is made

DEVELOPMENT OF A NOVEL Z-AXIS PRECISION POSITIONING STAGE WITH MILLIMETER TRAVEL RANGE BASED ON A LINEAR PIEZOELECTRIC MOTOR

Piezoelectric-based positioners are incorporated into stereotaxic devices for microsurgery, scanning tunneling microscopes for the manipulation of atomic and molecular-scale structures, nanomanipulator systems for cell microinjection and machine tools for semiconductor-based manufacturing. Although several precision positioning systems have been developed for planar motion, most are not suitable to provide long travel range with large load capacity in vertical axis because of their weights, size, design and embedded actuators. This thesis develops a novel positioner which is being developed specifically for vertical axis motion based on a piezoworm arrangement in flexure frames. An improved estimation of the stiffness for Normally Clamped (NC) clamp is presented. Analytical calculations and finite element analysis are used to optimize the design of the lifting platform as well as the piezoworm actuator to provide maximum thrust force while maintaining a compact size. To make a stage frame more compact, the actuator is integrated into the stage body. The complementary clamps and the amplified piezoelectric actuators based extenders are designed such that no power is needed to maintain a fixed vertical position, holding the payload against the force of gravity. The design is extended to a piezoworm stage prototype and validated through several tests. Experiments on the prototype stage show that it is capable of a speed of 5.4 mm/s, a force capacity of 8 N and can travel over 16 mm

Development of a piezoelectric multi-axis stage based on stick-and-clamping actuation technology

This paper presents the design, analysis and fabrication of a piezoelectric multi-axis stage based on a new stick-and-clamping actuation technology for miniaturized machine tool systems, referred to as meso-scale machine tool (mMT) systems. In the stick-and-clamping actuation system, shearing/expanding piezoelectric actuators, an inertial mass and an advanced preload system are configured innovatively to generate the motion of an inertial mass. There are two operating modes in the stick-and-clamping actuation technology: (1) stick mode and (2) clamp mode. In stick mode, the ‘slow’ deformation of the shearing piezoelectric actuators drives an inertial mass, which is located on the tips of the shearing piezoelectric actuators, by means of the friction force at their contact interface. On the other hand, in clamp mode, the expanding piezoelectric actuators provide the clamping force to an inertial mass when the rapid backward deformation of the shearing piezoelectric actuators occurs. The stick-and-clamping actuation technology also enables two-degrees-of-freedom (DOF) motion of an inertial mass in a single plane by perpendicularly stacking two shearing piezoelectric actuators. The 2-DOF piezoelectric multi-axis stage is developed on the basis of the stick-and-clamping actuation technology, and the dynamic and static performance analyses are conducted. The LuGre friction model for the contact interfaces is introduced, and their dynamic behaviours are characterized. In the open-loop static performance test, linear, diagonal and circular motions of the developed piezoelectric multi-axis stage are generated, and their performances are evaluated. The dynamic characteristics and static performances of the developed 2-DOF piezoelectric multi-axis stage show its applicability and effectiveness for the precision positioning system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58149/2/sms7_6_040.pd

Performance-driven control of nano-motion systems

The performance of high-precision mechatronic systems is subject to ever increasing demands regarding speed and accuracy. To meet these demands, new actuator drivers, sensor signal processing and control algorithms have to be derived. The state-of-the-art scientific developments in these research directions can significantly improve the performance of high-precision systems. However, translation of the scientific developments to usable technology is often non-trivial. To improve the performance of high-precision systems and to bridge the gap between science and technology, a performance-driven control approach has been developed. First, the main performance limiting factor (PLF) is identified. Then, a model-based compensation method is developed for the identified PLF. Experimental validation shows the performance improvement and reveals the next PLF to which the same procedure is applied. The compensation method can relate to the actuator driver, the sensor system or the control algorithm. In this thesis, the focus is on nano-motion systems that are driven by piezo actuators and/or use encoder sensors. Nano-motion systems are defined as the class of systems that require velocities ranging from nanometers per second to millimeters per second with a (sub)nanometer resolution. The main PLFs of such systems are the actuator driver, hysteresis, stick-slip effects, repetitive disturbances, coupling between degrees-of-freedom (DOFs), geometric nonlinearities and quantization errors. The developed approach is applied to three illustrative experimental cases that exhibit the above mentioned PLFs. The cases include a nano-motion stage driven by a walking piezo actuator, a metrological AFM and an encoder system. The contributions of this thesis relate to modeling, actuation driver development, control synthesis and encoder sensor signal processing. In particular, dynamic models are derived of the bimorph piezo legs of the walking piezo actuator and of the nano-motion stage with the walking piezo actuator containing the switching actuation principle, stick-slip effects and contact dynamics. Subsequently, a model-based optimization is performed to obtain optimal drive waveforms for a constant stage velocity. Both the walking piezo actuator and the AFM case exhibit repetitive disturbances with a non-constant period-time, for which dedicated repetitive control methods are developed. Furthermore, control algorithms have been developed to cope with the present coupling between and hysteresis in the different axes of the AFM. Finally, sensor signal processing algorithms have been developed to cope with the quantization effects and encoder imperfections in optical incremental encoders. The application of the performance-driven control approach to the different cases shows that the different identified PLFs can be successfully modeled and compensated for. The experiments show that the performance-driven control approach can largely improve the performance of nano-motion systems with piezo actuators and/or encoder sensors