A study on high accuracy discrete-time sliding mode control

In this paper a Discrete-Time Sliding-Mode based controller design for high accuracy motion control systems is presented. The controller is designed for a general SISO system with nonlinearity and external disturbance. Closed-Loop behavior of the general system with the proposed control and Lyapunov stability is shown and the error of the closed loop system is proven to be within an o(T2). The proposed controller is applied to a stage driven by a piezo drive that is known to suffer from hysteresis nonlinearity in the control gain. Proposed SMC controller is proven to offer chattering-free motion and rejection of the disturbances represented by hysteresis and the time variation of the piezo drive parameters. As a separate idea to enhance the accuracy of the closed loop system a combination of disturbance rejection method and the SMC controller is explored and its effectiveness is experimentally demonstrated. Closed-loop experiments are presented using PID controller with and without disturbance compensation and Sliding-Mode Controller with and without disturbance compensation for the purpose of comparison

Scaled bilateral teleoperation using discrete-time sliding mode controller

In this paper, the design of a discrete-time slidingmode controller based on Lyapunov theory is presented along with a robust disturbance observer and is applied to a piezostage for high-precision motion. A linear model of a piezostage was used with nominal parameters to compensate the disturbance acting on the system in order to achieve nanometer accuracy. The effectiveness of the controller and disturbance observer is validated in terms of closed-loop position performance for nanometer references. The control structure has been applied to a scaled bilateral structure for the custom-built telemicromanipulation setup. A piezoresistive atomic force microscope cantilever with a built-in Wheatstone bridge is utilized to achieve the nanonewtonlevel interaction forces between the piezoresistive probe tip and the environment. Experimental results are provided for the nanonewton-range force sensing, and good agreement between the experimental data and the theoretical estimates has been demonstrated. Force/position tracking and transparency between the master and the slave has been clearly demonstrated after necessary scalin

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, ANALYSIS AND CONTROL OF FLEXIBLE SOLID-STATE HYSTERETIC ACTUATORS

A distributed parameters modeling and control framework for flexible solid-state hysteretic actuator is presented in this work. For the simplicity of analysis, the actuator dynamic behavior is decoupled and treated separately from the hysteresis nonlinearity. To include the effects of widely-used flexural mechanisms, a mass-spring-damper boundary condition is considered for system. Moreover, the effect of electromechanical actuation is included as a concentrate force at the boundary. The problem is then divided into two parts: first part deals with free motion analysis of system in order to obtain eigenvalues and eigenfunctions using the expansion theorem and a standard eigenvalue problem procedure. The effects of different boundary mass and spring values on the natural frequencies and mode shapes are demonstrated, which indicate their significant contribution to system performance. In the second part, forced motion analysis of system and its state-space representation are presented. A frequency based control strategy utilizing widely used Lyapunov theorem is designed to obtain an accurate control over the actuator motion. A robust variable structure control is incorporated into the developed controller for compensation of ever-present plant structural uncertainties. A full order state feedback observer is designed to accurately mimic the states of an unobservable plant. An optimization algorithm is developed to compute the optimal observer gain matrix. Various frequency tracking simulations are performed using feedback controller-observer model to observe the effect of modes deficiency on the tracking frequency bandwidth of the controller. Finally, for the accurate prediction of nonlinear multi-loop hysteresis effect, a major source of inaccuracies at quasi-static frequency, a recently developed hysteresis model based on three hysteric properties of piezoelectric material namely targeting of turning points, curve alignment and the wiping-out effect is used. Initially, the hysteresis nonlinearity is decoupled from the looping effect and modeled separately using an exponential function. The obtained exponential function is then utilized in a nonlinear mapping procedure, where it is mapped between consequent turning points recorded in model memory unit. This mapping also uses four constant shaping parameters - two for the ascending and two for the descending hysteresis trajectories. A proportional integral (PI) controller is used for the compensation of hysteresis nonlinearity. Performance of PI controller is validated using several numerical simulations. Finally, the method of combining robust feedback control strategy with the feedforward hysteresis compensation technique is presented to accomplish the precise control over actuator motion

Dynamics and Control of Smart Structures for Space Applications

Smart materials are one of the key emerging technologies for a variety of space systems ranging in their applications from instrumentation to structural design. The underlying principle of smart materials is that they are materials that can change their properties based on an input, typically a voltage or current. When these materials are incorporated into structures, they create smart structures. This work is concerned with the dynamics and control of three smart structures: a membrane structure with shape memory alloys for control of the membrane surface flatness, a flexible manipulator with a collocated piezoelectric sensor/actuator pair for active vibration control, and a piezoelectric nanopositioner for control of instrumentation. Shape memory alloys are used to control the surface flatness of a prototype membrane structure. As these actuators exhibit a hysteretic nonlinearity, they need their own controller to operate as required. The membrane structures surface flatness is then controlled by the shape memory alloys, and two techniques are developed: genetic algorithm and proportional-integral controllers. This would represent the removal of one of the main obstacles preventing the use of membrane structures in space for high precision applications, such as a C-band synthetic aperture radar antenna. Next, an adaptive positive position feedback law is developed for control of a structure with a collocated piezoelectric sensor/actuator pair, with unknown natural frequencies. This control law is then combined with the input shaping technique for slew maneuvers of a single-link flexible manipulator. As an alternative to the adaptive positive position feedback law, genetic algorithms are investigated as both system identification techniques and as a tool for optimal controller design in vibration suppression. These controllers are all verified through both simulation and experiments. The third area of investigation is on the nonlinear dynamics and control of piezoelectric actuators for nanopositioning applications. A state feedback integral plus double integral synchronization controller is designed to allow the piezoelectrics to form the basis of an ultra-precise 2-D Fabry-Perot interferometer as the gap spacing of the device could be controlled at the nanometer level. Next, an output feedback linear integral control law is examined explicitly for the piezoelectric actuators with its nonlinear behaviour modeled as an input nonlinearity to a linear system. Conditions for asymptotic stability are established and then the analysis is extended to the derivation of an output feedback integral synchronization controller that guarantees global asymptotic stability under input nonlinearities. Experiments are then performed to validate the analysis. In this work, the dynamics and control of these smart structures are addressed in the context of their three applications. The main objective of this work is to develop effective and reliable control strategies for smart structures that broaden their applicability to space systems

Robust fractional-order fast terminal sliding mode control with fixed-time reaching law for high-performance nanopositioning

Open Access via the Wiley Agreement ACKNOWLEDGEMENTS This work is supported by the China Scholarship Council under Grant No. 201908410107 and by the National Natural Science Foundation of China under Grant No. 51505133. The authors also thank the anonymous reviewers for their insightful and constructive comments.Peer reviewedPublisher PD

Advanced Control of Piezoelectric Actuators.

168 p.A lo largo de las últimas décadas, la ingeniería de precisión ha tenido un papel importante como tecnología puntera donde la tendencia a la reducción de tamaño de las herramientas industriales ha sido clave. Los procesos industriales comenzaron a demandar precisión en el rango de nanómetros a micrómetros. Pese a que los actuadores convencionales no pueden reducirse lo suficiente ni lograr tal exactitud, los actuadores piezoeléctricos son una tecnología innovadora en este campo y su rendimiento aún está en estudio en la comunidad científica. Los actuadores piezoeléctricos se usan comúnmente en micro y nanomecatrónica para aplicaciones de posicionamiento debido a su alta resolución y fuerza de actuación (pueden llegar a soportar fuerzas de hasta 100 Newtons) en comparación con su tamaño. Todas estas características también se pueden combinar con una actuación rápida y rigidez, según los requisitos de la aplicación. Por lo tanto, con estas características, los actuadores piezoeléctricos pueden ser utilizados en una amplia variedad de aplicaciones industriales. Los efectos negativos, como la fluencia, vibraciones y la histéresis, se estudian comúnmente para mejorar el rendimiento cuando se requiere una alta precisión. Uno de los efectos que más reduce el rendimiento de los PEA es la histéresis. Esto se produce especialmente cuando el actuador está en una aplicación de guiado, por lo que la histéresis puede inducir errores que pueden alcanzar un valor de hasta 22%. Este fenómeno no lineal se puede definir como un efecto generado por la combinación de acciones mecánicas y eléctricas que depende de estados previos. La histéresis se puede reducir principalmente mediante dos estrategias: rediseño de materiales o algoritmos de control tipo feedback. El rediseño de material comprende varias desventajas por lo que el motivo principal de esta tesis está enfocado al diseño de algoritmos de control para reducir la histéresis. El objetivo principal de esta tesis es el desarrollo de estrategias de control avanzadas que puedan mejorar la precisión de seguimiento de los actuadores piezoeléctricos comerciale

Fuzzy PID Feedback Control of Piezoelectric Actuator with Feedforward Compensation

Piezoelectric actuator is widely used in the field of micro/nanopositioning. However, piezoelectric hysteresis introduces nonlinearity to the system, which is the major obstacle to achieve a precise positioning. In this paper, the Preisach model is employed to describe the hysteresis characteristic of piezoelectric actuator and an inverse Preisach model is developed to construct a feedforward controller. Considering that the analytical expression of inverse Preisach model is difficult to derive and not suitable for practical application, a digital inverse model is established based on the input and output data of a piezoelectric actuator. Moreover, to mitigate the compensation error of the feedforward control, a feedback control scheme is implemented using different types of control algorithms in terms of PID control, fuzzy control, and fuzzy PID control. Extensive simulation studies are carried out using the three kinds of control systems. Comparative investigation reveals that the fuzzy PID control system with feedforward compensation is capable of providing quicker response and better control accuracy than the other two ones. It provides a promising way of precision control for piezoelectric actuator

Robust motion control SMC point of view

In this paper the robust motion control systems in the sliding mode framework are discussed. Due to the fact that a motion control system with n d.o.f may be mathematically formulated in a unique way as a system composed of n second order systems, design of such a system may be formulated in a unique way as a requirement that the generalized coordinates must satisfy certain algebraic constraint. Such a formulation leads naturally to sliding mode framework to be applied. In this approach constraint manifolds are selected to coincide with desired constraints on the generalized coordinates. It has been shown that the CMC can be interpreted as a realization of the acceleration controller thus possessing all robust properties of the acceleration controller framework. The possibility to treat both unconstrained motion (the motion without contact with environment) and constrained motion in the same way is shown