A Novel Passivity-Based Controller for a Piezoelectric Beam

This paper presents a new passivity property for distributed piezoelectric devices with integrable port-variables. We present two new control methodologies by exploiting the integrability property of the port-variables. The derived controllers have a Proportional-Integral (PI) like structure. Finally, we present the simulation results and an in-depth analysis on the tuning gains explaining their transient and the steady-state behaviors

Modeling and Control of MEMS-based Multi-layered Prestressed Piezoelectric Cantilever Beam

Piezoelectric materials are the preferred smart materials for sensing and actuation in the form of micro and nano-engineering structures like beams and plates. Cantilever beams play a significant role as key components in atomic force microscopy and bio and chemical sensors. Adding an active layer such as lead zirconate titanate (PZT) thin-film to form smart cantilever beams with sensing and actuation capabilities is highly desirable to facilitate miniaturization, enhance performance and functionali- ties such as enabling on-chip high-speed parallel AFM. During the micro-fabrication process, residual stresses develop in the different layers of the cantilever beam, causes initial deflection. The residual stress in the different layers of the cantilever beam and the application of voltage to the PZT thin-film affects their dynamics. This the- sis investigates the dynamic behaviour and develops a control technique and a novel charge readout circuit to improve the performance of a micro-fabricated multi-layer prestressed piezoelectric cantilever beam as an actuator and a deflection sensor. Firstly, the fabrication process of a unimorph PZT cantilever beam is explained. A low thermal budget Ultra-high vacuum e-beam evaporated polysilicon thin-film (UHVEEpoly) process is used for the fabrication of multi-layered PZT cantilever beam in d31 mode. The sharp peaks at resonant frequencies in the frequency response of the PZT cantilever beam show very little damping and a large settling time of the cantilever beam. Secondly, the dynamic behaviour of the prestressed PZT cantilever beam is in- vestigated subjected to change in driving voltage. Experimental investigations show a shift in resonant frequencies of a PZT cantilever beam. However, there is no reported mathematical model that predicts the shift in resonance frequencies of a multi-layered prestressed piezoelectric cantilever beam subjected to a change in driving voltage. This work developed a mathematical model with experimental val- idation to estimate the shift in resonance frequencies of such cantilever beams with the change in the driving voltage. A very good agreement between the model predic- tions and experimental measurements for the frequency response of the cantilever beam at different driving voltages has been obtained. A novel linear formulation has been developed to predict the shift in resonance frequencies of the PZT can- i tilever beam for a wide range of driving voltages. The formulation shows that the shift in resonance frequencies of a multi-layered prestressed piezoelectric cantilever beam per unit of applied voltage is dependent on geometric parameters and material properties. Thirdly, a robust resonant controller has been designed and implemented to re- duce the settling time of a highly vibrating PZT cantilever beam. The controller design is based on a mixed negative-imaginary, passivity, and a small-gain approach. The motivation to design a resonant controller using the above-mentioned analyti- cal framework is its bandpass nature and the use of velocity feedback, as the charge collected from a vibrating PZT cantilever beam gives the velocity information of the beam. The proposed controller design results in finite gain stability for a pos- itive feedback interconnection between two stable linear systems with a large gain and phase margin. Experimental results demonstrate that the designed resonant controller is able to effectively damp the first resonant mode of a cantilever, signifi- cantly reducing settling time from 528 ms to 32 ms. The robustness of the designed resonant controller is tested against changes in the cantilever beam dynamics due to residual stress variation and or stress variation due to driving voltage. Finally, to facilitate the miniaturization of on-chip sensors and parallel high- speed AFM, a single layer of a PZT thin-film in a cantilever beam is used as a deflection sensor and an actuator instead of bulky optical deflection sensors. A novel charge readout circuit is designed for deflection sensing by capturing the electrical charge generated due to the vibration of the PZT beam. The signal-to-noise ratio and sensitivity analysis of the readout circuit shows similar results compared to the commercially available optical deflection sensors. Our work highlights very important aspects in the dynamic behaviour and perfor- mance of a multi-layered prestressed piezoelectric cantilever beam. The agreement between the proposed theoretical formulation and experimental investigations in modeling, control design, and a novel readout circuit will provide the platform for further the development and miniaturization of microcantilever-based technologies, including on-chip parallel HS-AFM

Twenty years of distributed port-Hamiltonian systems:A literature review

The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups

Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures with Free Body Motion

Negative imaginary (NI) systems play an important role in the robust control of highly resonant flexible structures. In this paper, a generalized NI system framework is presented. A new NI system definition is given, which allows for flexible structure systems with colocated force actuators and position sensors, and with free body motion. This definition extends the existing definitions of NI systems. Also, necessary and sufficient conditions are provided for the stability of positive feedback control systems where the plant is NI according to the new definition and the controller is strictly negative imaginary. The stability conditions in this paper are given purely in terms of properties of the plant and controller transfer function matrices, although the proofs rely on state space techniques. Furthermore, the stability conditions given are independent of the plant and controller system order. As an application of these results, a case study involving the control of a flexible robotic arm with a piezo-electric actuator and sensor is presented

TIP trajectory tracking of flexible-joint manipulators

In most robot applications, the control of the manipulator’s end-effector along a specified desired trajectory is the main concern. In these applications, the end-effector (tip) of the manipulator is required to follow a given trajectory. Several methods have been so far proposed for the motion control of robot manipulators. However, most of these control methods ignore either joint friction or joint elasticity which can be caused by the transmission systems (e.g. belts and gearboxes). This study aims at development of a comprehensive control strategy for the tip-trajectory tracking of flexible-joint robot manipulators. While the proposed control strategy takes into account the effect of the friction and the elasticity in the joints, it also provides a highly accurate motion for the manipulator’s end-effector. During this study several approaches have been developed, implemented and verified experimentally/numerically for the tip trajectory tracking of robot manipulators. To compensate for the elasticity of the joints two methods have been proposed; they are a composite controller whose design is based on the singular perturbation theory and integral manifold concept, and a swarm controller which is a novel biologically-inspired controller and its concept is inspired by the movement of real biological systems such as flocks of birds and schools of fishes. To compensate for the friction in the joints two new approaches have been also introduced. They are a composite compensation strategy which consists of the non-linear dynamic LuGre model and a Proportional-Derivative (PD) compensator, and a novel friction compensation method whose design is based on the Work-Energy principle. Each of these proposed controllers has some advantages and drawbacks, and hence, depending on the application of the robot manipulator, they can be employed. For instance, the Work-Energy method has a simpler form than the LuGre-PD compensator and can be easily implemented in industrial applications, yet it provides less accuracy in friction compensation. In addition to design and develop new controllers for flexible-joint manipulators, another contribution of this work lays in the experimental verification of the proposed control strategies. For this purpose, experimental setups of a two-rigid-link flexible-joint and a single-rigid-link flexible-joint manipulators have been employed. The proposed controllers have been experimentally tested for different trajectories, velocities and several flexibilities of the joints. This ensures that the controllers are able to perform effectively at different trajectories and speeds. Besides developing control strategies for the flexible-joint manipulators, dynamic modeling and vibration suppression of flexible-link manipulators are other parts of this study. To derive dynamic equations for the flexible-link flexible-joint manipulators, the Lagrange method is used. The simulation results from Lagrange method are then confirmed by the finite element analysis (FEA) for different trajectories. To suppress the vibration of flexible manipulators during the manoeuvre, a collocated sensor-actuator is utilized, and a proportional control method is employed to adjust the voltage applied to the piezoelectric actuator. Based on the controllability of the states and using FEA, the optimum location of the piezoelectric along the manipulator is found. The effect of the controller’s gain and the delay between the input and output of the controller are also analyzed through a stability analysis

A Robust Finite-Difference Model Reduction for the Boundary Feedback Stabilization of Fully-dynamic Piezoelectric Beams

Piezoelectric materials exhibit electric responses to mechanical stress, and mechanical responses to electric stress. The PDE model, describing the longitudinal oscillations on the beam, with two boundary feedback controllers is known to have exponentially stable solutions. However, the reduced model by the semi-discretized Finite Elements is shown to lack of exponential stability uniformly as the discretization parameter tends to zero. This is due to the loss of uniform gap among the high-frequency eigenvalues. In this paper, an alternate Finite-Difference based model reduction is investigated by cleverly reducing the order of the model together with the consideration of equidistant grid points and averaging operators. This new model reduction successfully retains the exponential stability uniformly as the discretization parameter tends to zero. Moreover, it does not need a further numerical Fourier filtering. Our results are based on a careful construction of a Lyapunov function. The numerical simulations are provided to compare reduced models and to show the strength of introduced results.Comment: 8 figures, 2 table