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

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

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

A Review of Modeling and Control of Piezoelectric Stick-Slip Actuators

Piezoelectric stick-slip actuators with high precision, large actuating force, and high displacement resolution are currently widely used in the field of high-precision micro-nano processing and manufacturing. However, the non-negligible, non-linear factors and complexity of their characteristics make its modeling and control quite difficult and affect the positioning accuracy and stability of the system. To obtain higher positioning accuracy and efficiency, modeling and control of piezoelectric stick-slip actuators are meaningful and necessary. Firstly, according to the working principle of stick-slip drive, this paper introduces the sub-models with different characteristics, such as hysteresis, dynamics, and friction, and presents the comprehensive modeling representative piezoelectric stick-slip actuators. Next, the control approaches suggested by different scholars are also summarized. Appropriate control strategies are adopted to reduce its tracking error and position error in response to the influence of various factors. Lastly, future research and application prospects in modeling and control are pointed out

Enhanced Piezoelectric Performance of Printed PZT Films on Low Temperature Substrates

Since piezoelectric effect was discovered in 1880, it has been widely used in micro-actuators, sensors, and energy harvesters. Lead Zirconate Titanate (PZT) is a commonly used piezoelectric material due to the high piezoelectric response. The basic PZT film fabrication process includes deposition, sintering, and poling. However, due to the high sintering temperature (\u3e 800 °C) of PZT, only high melting point material can be served as the substrate. Otherwise, complex film transfer approach is needed to achieve flexible and foldable PZT devices. The exploration is accordingly necessary to realize direct fabrication of PZT films on low melting point substrates without affecting the piezoelectric performance. In order to lower the PZT film sintering temperature, in this work, the effect of the powder size and sintering aid on the sintering temperature was studied. A maskless, CAD driven, non-contact direct printing system, aerosol jet printer, was used to deposit PZT thick films on the substrate. This technique allows creating features without masking and etching processes that are generally required for realizing designed features via conventional deposition approaches. Broadband, sub-millisecond, high intensity flash pulses were used to sinter the PZT films. The role of all sintering parameters was investigated to regulate the sintering quality of the PZT thick films. The photonically sintered films showed much lower substrate temperature increase mainly due to the extremely short pulse duration and temperature gradient through the film thickness. The superior piezoelectric property to thermally sintered group was also obtained. This process significantly shortens the processing duration and dramatically expands the possible substrate materials. It accordingly opens the possibility of processing PZT film directly on low melting point materials. A PZT energy harvester based on this process was directly fabricated on the polyethylene terephthalate (PET) substrate to demonstrate the capability. The relation between the load and the generated power was investigated to obtain the highest output power. Up to 0.1 μW was generated from this flexible energy harvester when connected with 10 MΩ resistive load. Photonic sintering of PZT film also creates the opportunity of processing poling during sintering. Different combinations of the sintering and poling techniques were studied. It was observed that the best piezoelectric property was obtained while performing poling during photonic sintering. Consequently, a new method of printing, sintering, and poling of micro-scaled PZT films was demonstrated in this work resulting in high performance films. This process provides the capability of realizing PZT devices on low temperature substrate, facilitates the fabrication of flexible piezoelectric devices, and enhances the piezoelectric property

Optimal Material Selection for Transducers

When selecting an active material for an application, it is tempting to rely upon prior knowledge or commercial products that fit the design criteria. While this method is time effective, it does not provide an optimal selection. The optimal material selection requires an understanding of the limitations of the active material, understanding of the function, constraints and objectives of the device, and rigorous decision making method to ensure rational and clear material selection can be performed. Therefore, this work looks into the three most researched active materials (piezoelectrics, magnetostrictives and shape memory alloys) and looks at how they work and their difficulties. The field of piezoelectrics is vast and contains ceramics, plastics and cellular structures that couple the mechanical and electrical domain. The difficulty with piezoelectric ceramics is their small strains and the dependence of their coefficients on the ferroelectric domains. Giant magnetostrictives materials couple the mechanical and magnetic domains. They are generally better suited for low-frequency operations since they properties deteriorate rapidly with heat. Shape memory alloys are materials that couple thermal and mechanical domains. They have large strain but are limited in their force output, fatigue life and cycle frequency. Optimal material selection requires a formalized material selection method. In mechanical material selection, the formal material selection method uses function, constraints and objectives of the designer to limit the parameter space and allow better decisions. Unfortunately, active materials figures of merit are domain dependent and therefore the mechanical material selection method needs to be adapted. A review of device selection of actuators, sensors and energy harvesters indicates a list of functions, constrains and objectives that the designer can use. Through the analysis of these devices figures of merit, it is realized that the issue is that the simplification that the figures of merit perform does not assist in decision making process. It is better to use decision making methods that have been developed in the field of operational research which assists complex comparative decision making. Finally, the decision making methods are applied to two applications: a resonant cantilever energy harvester and an ultrasound transducer. In both these cases, a review of selection methods of other designers provides guidance of important figures of merit. With these selection methods in consideration, figures of merit are selected and used to find the optimal material based upon the designer preference

Analog controller based on sliding mode control for piezoelectric actuators

Today, the digital implementation of the controllers is mainly preferred from reprogrammability point of view. Many important control problems can be effectively solved using a digital architecture in conjunction with analog-to-digital (ADC) and/or digital-to-analog conversion (DAC). Digital solutions offer two very attractive advantages: (1)-promise to shorten design cycles, and (2)-provide the freedom to reprogram the design in simple ways. This ease-of-change stands in sharp contrast to the great effort required to redesign a typical hard-wired analog implementation. However, depending on the complexity of the plant and the degrees of freedom (DOF) to be controlled, digital implementation of an algorithm may be demanding due to the high computational power requirement to run in real time. The necessity for the acquisition of the analog signals on the other hand requires ADC and DAC conversions that compel extra conditions on the system. Hence, multi-DOF systems may require either diminish in the systems operation frequency or additional hardware to run the algorithm in parallel for each DOF. This work aims to develop an analog motion controller for single input single output (SISO) plants of complex nature. As the control algorithm, Sliding Mode Control (SMC) like the well known robust nonlinear controller is selected as a design framework. Originally designed as a system motion for dynamic systems whose essential open-loop behavior can be sufficiently modeled with ordinary differential equations, Sliding Mode Control (SMC) is one of the effective nonlinear robust control approaches that provide system invariance to uncertainties once the sliding mode motion is enforced in the system. An important aspect of sliding mode is the discontinuous nature of the control action, which switches between two values to move the system motion on so-called “sliding mode” that exist in a manifold and therefore often referred as variable structure control (VSC). The resulting feedback system is called variable structure system (VSS). The position tracking of the piezoelectric actuators (PEA) is selected as the test bed for the designed system. Piezoelectricity, the ability of the material to become strained due to an electric field, gives the possibility to user those materials as actuator in sub-micrometer domain for a range of applications. Piezoelectric effect is a crystalline effect, and therefore, piezoelectric actuators do not suffer from “stick slip” effect mainly caused by the friction between elements of a mechanical system. This property theoretically offers an unlimited resolution, and therefore piezoelectric actuators are already used in many applications to provide sub-micrometer resolution. Still the achievable resolution in practice can be limited by a number of other factors such as the piezo control amplifier (electronic noise), sensor (resolution, noise and mounting precision) and control electronics (noise and sensitivity to EMI). As a result of this work, we are aiming an analog controller for SISO systems and by the use of this controller, improvement on the tracking performance for the plant we are studying and decrease on the possible computational load on digital controllers is targeted

Development and characterization of a novel piezoelectric-driven stick-slip actuator with anisotropic-friction surfaces

Piezoelectric actuators (PEA) hold the most promise for precision positioning applications due to their capability of producing extremely small displacements down to 10 pm (1 pm = 10-12 m) as well as their high stiffness and force output. The piezoelectric-driven stick-slip (PDSS) actuator, working on the friction-inertia concept, has the capacity of accomplishing an unlimited range of motion. It also holds the promises of simple configuration and low cost. On the other hand, the PDSS actuator has a relatively low efficiency and low loading capability, which greatly limits its applications. The purpose of this research is to improve the performance of the PDSS actuators by employing specially-designed working surfaces. The working surfaces, referred as anisotropic friction (AF) surfaces in this study, can provide different friction forces depending on the direction of relative motion of the two surfaces, and are used in this research to accomplish the aforementioned purpose. To fabricate such surfaces, two nanostructure technologies are employed: hot filament chemical vapour deposition (HFCVD) and ion beam etching (IBE). The HFCVD is used to deposit diamond on silicon substrates; and the IBE is used to etch the diamond crystalloid with a certain angle with respect to the coating surface to obtain an unsymmetrical-triangle microstructure. A PDSS actuator prototype containing the AF surfaces was developed in this study to verify the function of the AF surfaces and characterize the performance of PDSS actuators. The designed surfaces were mounted on the prototype; and the improvement in performance was characterized by conducting a set of experiments with both the normal isotropic friction (IF) surfaces and the AF surfaces, respectively. The results illustrate that the PDSS actuator with the AF surface has a higher efficiency and improved loading capability compared to the one with the IF surfaces. A model was also developed to represent the displacement of the novel PDSS actuator. The dynamics of the PEA and the platform were approximated by using a second order dynamic system. The pre-sliding friction behaviour involved was investigated by modifying the LuGre friction model, in which six parameters (Note that three parameters are used in the LuGre model) were employed to represent the anisotropic friction. By combining the PEA mechanism model, the modified friction model, and the dynamics of end-effector, a model for the PDSS actuator with the AF surface was developed. The model with the identified parameters was simulated in MATLAB Simulink and the simulation results obtained were compared to the experimental results to verify the model. The comparison suggests that the model developed in this study is promising to represent the displacement of the novel PDSS actuators with AF surfaces