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

Sliding-mode control of a flexure based mechanism using piezoelectric actuators

The position control of designed 3 PRR flexure based mechanism is examined in this paper. The aims of the work are to eliminate the parasitic motions of the stage, misalignments of the actuators, errors of manufacturing and hysteresis of the system by having a redundant mechanism with the implementation of a sliding mode control and a disturbance observe. x-y motion of the end-effector is measured by using a laser position sensor and the necessary references for the piezoelectric actuators are calculated using the pseudo inverse of the transformation matrix coming from the experimentally determined kinematics of the mechanism. The effect of the observer and closed loop control is presented by comparing the results with open loop control. The system is designed to be redundant to enhance the position control. In order to see the effects of the redundant system firstly the closed loop control for active 2 piezoelectric actuators experiments then for active 3 piezoelectric actuators experiments are presented. As a result, our redundant mechanism tracks the desired trajectory accurately and its workspace is bigger

Modeling and Control of Piezoactive Micro and Nano Systems

Piezoelectrically-driven (piezoactive) systems such as nanopositioning platforms, scanning probe microscopes, and nanomechanical cantilever probes are advantageous devices enabling molecular-level imaging, manipulation, and characterization in disciplines ranging from materials science to physics and biology. Such emerging applications require precise modeling, control and manipulation of objects, components and subsystems ranging in sizes from few nanometers to micrometers. This dissertation presents a comprehensive modeling and control framework for piezoactive micro and nano systems utilized in various applications. The development of a precise memory-based hysteresis model for feedforward tracking as well as a Lyapunov-based robust-adaptive controller for feedback tracking control of nanopositioning stages are presented first. Although hysteresis is the most degrading factor in feedforward control, it can be effectively compensated through a robust feedback control design. Moreover, an adaptive controller can enhance the performance of closed-loop system that suffers from parametric uncertainties at high-frequency operations. Comparisons with the widely-used PID controller demonstrate the effectiveness of the proposed controller in tracking of high-frequency trajectories. The proposed controller is then implemented in a laser-free Atomic Force Microscopy (AFM) setup for high-speed and low-cost imaging of surfaces with micrometer and nanometer scale variations. It is demonstrated that the developed AFM is able to produce high-quality images at scanning frequencies up to 30 Hz, where a PID controller is unable to present acceptable results. To improve the control performance of piezoactive nanopositioning stages in tracking of time-varying trajectories with frequent stepped discontinuities, which is a common problem in SPM systems, a supervisory switching controller is designed and integrated with the proposed robust adaptive controller. The controller switches between two control modes, one mode tuned for stepped trajectory tracking and the other one tuned for continuous trajectory tracking. Switching conditions and compatibility conditions of the control inputs in switching instances are derived and analyzed. Experimental implementation of the proposed switching controller indicates significant improvements of control performance in tracking of time-varying discontinuous trajectories for which single-mode controllers yield undesirable results. Distributed-parameters modeling and control of rod-type solid-state actuators are then studied to enable accurate tracking control of piezoactive positioning systems in a wide frequency range including several resonant frequencies of system. Using the extended Hamilton\u27s principle, system partial differential equation of motion and its boundary conditions are derived. Standard vibration analysis techniques are utilized to formulate the truncated finite-mode state-space representation of the system. A new state-space controller is then proposed for asymptotic output tracking control of system. Integration of an optimal state-observer and a Lyapunov-based robust controller are presented and discussed to improve the practicability of the proposed framework. Simulation results demonstrate that distributed-parameters modeling and control is inevitable if ultra-high bandwidth tracking is desired. The last part of the dissertation, discusses new developments in modeling and system identification of piezoelectrically-driven Active Probes as advantageous nanomechanical cantilevers in various applications including tapping mode AFM and biomass sensors. Due to the discontinuous cross-section of Active Probes, a general framework is developed and presented for multiple-mode vibration analysis of system. Application in the precise pico-gram scale mass detection is then presented using frequency-shift method. This approach can benefit the characterization of DNA solutions or other biological species for medical applications

Design and control of a 6-degree-of-freedom precision positioning system

This paper presents the design and test of a6-degree-of-freedom (DOF) precision positioning system, which is assembledby two different 3-DOF precision positioning stages each driven by three piezoelectric actuators (PEAs). Based on the precision PEAs and flexure hinge mechanisms, high precision motion is obtained.The design methodology and kinematic characteristics of the6-DOF positioning system areinvestigated. According to an effective kinematic model, the transformation matrices are obtained, which is used to predict the relationship between the output displacement from the system arrangement and the amountof PEAsexpansion. In addition, the static and dynamic characteristics of the 6-DOF system have been evaluated by finite element method (FEM) simulation andexperiments. The design structure provides a high dynamic bandwidth withthe first naturalfrequency of 586.3 Hz.Decoupling control is proposed to solve the existing coupling motion of the 6-DOF system. Meanwhile, in order to compensate for the hysteresis of PEAs, the inverse Bouc-Wen model was applied as a feedforward hysteresis compensator in the feedforward/feedback hybrid control method. Finally, extensive experiments were performed to verify the tracking performance of the developed mechanism

PKM mechatronic clamping adaptive device

This study proposes a novel adaptive fixturing device based on active clamping systems for smart micropositioning of thin-walled precision parts. The modular architecture and the structure flexibility make the system suitable for various industrial applications. The proposed device is realized as a Parallel Kinematic Machine (PKM), opportunely sensorized and controlled, able to perform automatic error-free workpiece clamping procedures, drastically reducing the overall fixturing set-up time. The paper describes the kinematics and dynamics of this mechatronic system. A first campaign of experimental trails has been carried out on the prototype, obtaining promising results

Model reference control for ultra-high precision positioning systems

Due to the increasing demands of high-density semiconductors, molecular biology, optoelectronics, and MEMS/NEMS in the past decades, control of ultra-high precision positioning using piezoelectricity has become an important area because of its high displacement resolution, wide bandwidth, low power consumption, and potential low cost. However, the relatively small displacement range limits its application. This work proposed a practical ultra-high precision piezoelectric positioning system with a complementary high displacement range actuation technology. Solenoids are low cost, high speed electromagnetic actuators which are commonly used in on-off mode only because of the inherent high nonlinear force-stroke characteristics and unipolar forces (push/pull) generated by the magnetic fields. In this work, an integrated positioning system based on a monolithic piezoelectric positioner and a set of push-pull dual solenoid actuators is designed for high speed and high precision positioning applications. The overall resolution can be sub-nanometer while the moving range is in millimeters, a three order of magnitude increase from using piezoelectric positioner alone. The dynamic models of the dual solenoid actuator and piezoelectric nanopositioner are derived. The main challenge of designing such positioning systems is to maintain the accuracy and stability in the presence of un-modeled dynamics, plant variations, and parasitic nonlinearities, specifically in this work, the friction and forcestroke nonlinearities of the dual solenoid actuator, and the friction, hysteresis and coupling effects of piezoelectric actuator, which are impossible to be modeled accurately and even time-varying. A model reference design approach is presented to attenuate linear as well as nonlinear uncertainties, with a fixed order controller augmenting a reference model that embeds the nominal dynamics of the plant. To improve transient characteristics, a Variable Model Reference Zero Vibration (VMRZV) control is also proposed to stabilize the system and attenuate the adverse effect of parasitic nonlinearities of micro-/nano- positioning actuators and command-induced vibrations. The speed of the ultra-high precision system with VMRZV control can also be quantitatively adjusted by systematically varying the reference model. This novel control method improves the robustness and performance significantly. Preliminary experimental data on dual solenoid system confirm the feasibility of the proposed method

Control of a 3D piezo-actuating table by using an adaptive sliding-mode controller for a drilling process

AbstractRecently, the micropositioner has become an important developing target for achieving the requirements of precision machinery. The piezo-actuating device plays a very important role in this application area. In this paper, a model-free adaptive sliding-mode controller is proposed for a 3D piezo-actuating system because of the system’s hysteresis nonlinearity and time-varying characteristics. This control strategy employs the functional approximation technique to establish the unknown function for releasing the model based requirements of the sliding-mode control. The update laws for the coefficients of the Fourier series function parameters are derived from a Lyapunov function to guarantee the control system stability. To verify the effectiveness of the proposed controller, drilling process control using the designed controller is investigated in this paper

Micro position control of a designed 3-PRR compliant mechanism using experimental models

A new compliant stage based on 3-PRR kinematic structure is designed to be used as a planar micro positioner. The mechanism is actuated by using piezoelectric actuators and center position of the stage is measured using a dual laser position sensor. It's seen that manufactured mechanism has unpredictable motion errors due to manufacturing and assembly faults. Thus, sliding mode control with disturbance observer is chosen to be implemented as position control in x-y axes of the center of the mechanism. Instead of piezoelectric actuator models, experimental models are extracted for each actuation direction in order to be used as nominal plants for the disturbance observer. The position control results are compared with the previous position control using linear piezoelectric actuator models and it's seen that the implemented control methodology is better in terms of errors in x and y axes. Besides, the position errors are lowered down to ±0.06 microns, which is the accuracy of the dual laser position sensor

Micro position control of a 3-RRR compliant mechanism

A 3-RRR compliant mechanism is designed to be used as a micro positioning stage. The stage displacements are analyzed by using structural FEA. However the experimental results for the manufactured mechanism are not compatible with the FEA which are mostly accepted as ideal while designing. A position control using Sliding Mode Control with Disturbance Observer is proposed for the reference tracking of the center of the stage. The motion of the center is measured by using a laser position sensor and the necessary references for the piezoelectric actuators are calculated using the pseudo inverse of the transformation matrix coming from the experimentally determined kinematics of the mechanism. Piezoelectric actuator linear models are used for disturbance rejection. Finally, the position control of the mechanism is succeeded although it has big errors in manufacturing, assembly etc