Fractional-order integral resonant control of collocated smart structures
TL;DR: In this article, a fractional-order integral controller (FI) is proposed to improve the robustness of the closed-loop system to changes in the mass of the payload at the tip.
About: This article is published in Control Engineering Practice.The article was published on 2016-11-01. It has received 19 citations till now. The article focuses on the topics: Robust control & Robustness (computer science).
Citations
More filters
TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.
922 citations
TL;DR: The research carried out in the past five years, in the areas of modeling, and optimal positioning of piezoelectric actuators/sensors, for active vibration control, are covered.
Abstract: Considering the number of applications, and the quantity of research conducted over the past few decades, it wouldn't be an overstatement to label the piezoelectric materials as the cream of the crop of the smart materials. Among the various smart materials, the piezoelectric materials have emerged as the most researched material for practical applications. They owe it to a few key factors like low cost, large frequency bandwidth of operation, availability in many forms, and the simplicity offered in handling and implementation. For piezoelectric materials, from an application standpoint, the area of active control of vibration, noise, and flow, stands, alongside energy harvesting, as the most researched field. Over the past three decades, several authors have used piezoelectric materials as sensors and actuators, to (i) actively control structural vibrations, noise and aeroelastic flutter, (ii) actively reduce buffeting, and (iii) regulate the separation of flows. These studies are spread over several engineering disciplines-starting from large space structures, to civil structures, to helicopters and airplanes, to computer hard disk drives. This review is an attempt to concise the progress made in all these fields by exclusively highlighting the application of the piezoelectric material. The research carried out in the past five years, in the areas of modeling, and optimal positioning of piezoelectric actuators/sensors, for active vibration control, are covered. Along with this, investigations into different control algorithms, for the piezoelectric based active vibration control, are also reviewed. Studies reporting the use of piezoelectric modal filtering and self sensing actuators, for active vibration control, are also surveyed. Additionally, research on semi-active vibration control techniques like the synchronized switched damping (on elements like resistor, inductor, voltage source, negative capacitor) has also been covered
93 citations
TL;DR: In this paper, a fractional-order Positive Position Feedback (PPF) compensator is proposed, implemented and compared to the standard integer-order PPF, which is found to be more efficient in achieving the same performance with less actuation voltage.
50 citations
TL;DR: Comparative experimental results show that the proposed TDCLADRC possesses the best disturbance rejection and vibration suppression performance.
33 citations
TL;DR: In this article, a fractional order PD μ control of lattice grid beam with piezoelectric fiber composite face sheets is proposed, which can reduce the vibration amplitude more significantly and more rapidly.
23 citations
References
More filters
Book•
01 Jan 1999
TL;DR: In this article, the authors present a method for computing fractional derivatives of the Fractional Calculus using the Laplace Transform Method and the Fourier Transformer Transform of fractional Derivatives.
Abstract: Preface. Acknowledgments. Special Functions Of Preface. Acknowledgements. Special Functions of the Fractional Calculus. Gamma Function. Mittag-Leffler Function. Wright Function. Fractional Derivatives and Integrals. The Name of the Game. Grunwald-Letnikov Fractional Derivatives. Riemann-Liouville Fractional Derivatives. Some Other Approaches. Sequential Fractional Derivatives. Left and Right Fractional Derivatives. Properties of Fractional Derivatives. Laplace Transforms of Fractional Derivatives. Fourier Transforms of Fractional Derivatives. Mellin Transforms of Fractional Derivatives. Existence and Uniqueness Theorems. Linear Fractional Differential Equations. Fractional Differential Equation of a General Form. Existence and Uniqueness Theorem as a Method of Solution. Dependence of a Solution on Initial Conditions. The Laplace Transform Method. Standard Fractional Differential Equations. Sequential Fractional Differential Equations. Fractional Green's Function. Definition and Some Properties. One-Term Equation. Two-Term Equation. Three-Term Equation. Four-Term Equation. Calculation of Heat Load Intensity Change in Blast Furnace Walls. Finite-Part Integrals and Fractional Derivatives. General Case: n-term Equation. Other Methods for the Solution of Fractional-order Equations. The Mellin Transform Method. Power Series Method. Babenko's Symbolic Calculus Method. Method of Orthogonal Polynomials. Numerical Evaluation of Fractional Derivatives. Approximation of Fractional Derivatives. The "Short-Memory" Principle. Order of Approximation. Computation of Coefficients. Higher-order Approximations. Numerical Solution of Fractional Differential Equations. Initial Conditions: Which Problem to Solve? Numerical Solution. Examples of Numerical Solutions. The "Short-Memory" Principle in Initial Value Problems for Fractional Differential Equations. Fractional-Order Systems and Controllers. Fractional-Order Systems and Fractional-Order Controllers. Example. On Viscoelasticity. Bode's Analysis of Feedback Amplifiers. Fractional Capacitor Theory. Electrical Circuits. Electroanalytical Chemistry. Electrode-Electrolyte Interface. Fractional Multipoles. Biology. Fractional Diffusion Equations. Control Theory. Fitting of Experimental Data. The "Fractional-Order" Physics? Bibliography. Tables of Fractional Derivatives. Index.
3,962 citations
Book•
13 May 1980
TL;DR: This chapter discusses single-Input/Single-Output Relationships, nonstationary data analysis techniques, and procedures to Solve Multiple- Input/Multiple-Output Problems.
Abstract: Discusses engineering applications and recent developments based upon correlation and spectral analysis. Illustrations deal with applications to acoustics, mechanical vibrations, system identification, and fluid dynamics problems in aerospace, automotive, industrial noise control, civil engineering and oceanographic fields, as well as similar problems in other fields. Tackles problems and solutions, assuming reader has required hardware and software to compute estimates of correlation, spectra, coherence, and phase functions.
2,447 citations
01 Jan 2003
TL;DR: The author explains the design process and some concepts in structural dynamics, including Hamilton's principle, which guided the development of the piezoelectric beam actuator.
Abstract: Preface to the third edition.- Preface to the second edition.- Preface to the first edition.- 1 Introduction.- 1.1 Active versus passive.- 1.2 Vibration suppression.- 1.3 Smart materials and structures.- 1.4 Control strategies.- 1.4.1 Feedback.- 1.4.2 Feedforward.- 1.5 The various steps of the design.- 1.6 Plant description, error and control budget.- 1.7 Readership and Organization of the book.- 1.8 References.- 1.9 Problems.- 2 Some concepts in structural dynamics.- 2.1 Introduction.- 2.2 Equation of motion of a discrete system.- 2.3 Vibration modes.- 2.4 Modal decomposition.- 2.4.1 Structure without rigid body modes.- 2.4.2 Dynamic flexibility matrix.- 2.4.3 Structure with rigid body modes.- 2.4.4 Example.- 2.5 Collocated control system.- 2.5.1 Transmission zeros and constrained system.- 2.6 Continuous structures.- 2.7 Guyan reduction.- 2.8 Craig-Bampton reduction.- 2.9 References.- 2.10 Problems.- 3 Electromagnetic and piezoelectric transducers.- 3.1 Introduction.- 3.2 Voice coil transducer.- 3.2.1 Proof-mass actuator.- 3.2.2 Geophone.- 3.3 General electromechanical transducer.- 3.3.1 Constitutive equations.- 3.3.2 Self-sensing.- 3.4 Reaction wheels and gyrostabilizers.- 3.5 Smart materials.- 3.6 Piezoelectric transducer.- 3.6.1 Constitutive relations of a discrete transducer.- 3.6.2 Interpretation of k2.- 3.6.3 Admittance of the piezoelectric transducer.- 3.7 References.- 3.8 Problems.- 4 Piezoelectric beam, plate and truss.- 4.1 Piezoelectric material.- 4.1.1 Constitutive relations.- 4.1.2 Coenergy density function.- 4.2 Hamilton's principle.- 4.3 Piezoelectric beam actuator.- 4.3.1 Hamilton's principle.- 4.3.2 Piezoelectric loads.- 4.4 Laminar sensor.- 4.4.1 Current and charge amplifiers.- 4.4.2 Distributed sensor output.- 4.4.3 Charge amplifier dynamics.- 4.5 Spatial modalfilters.- 4.5.1 Modal actuator.- 4.5.2 Modal sensor.- 4.6 Active beam with collocated actuator-sensor.- 4.6.1 Frequency response function.- 4.6.2 Pole-zero pattern.- 4.6.3 Modal truncation.- 4.7 Admittance of a beam with a piezoelectric patch.- 4.8 Piezoelectric laminate.- 4.8.1 Two dimensional constitutive equations.- 4.8.2 Kirchhoff theory.- 4.8.3 Stiffness matrix of a multi-layer elastic laminate.- 4.8.4 Multi-layer laminate with a piezoelectric layer.- 4.8.5 Equivalent piezoelectric loads.- 4.8.6 Sensor output.- 4.8.7 Beam model vs. plate model.- 4.8.8 Additional remarks.- 4.9 Active truss.- 4.9.1 Open-loop transfer function.- 4.9.2 Admittance function.- 4.10 Finite element formulation.- 4.11 References.- 4.12 Problems.- 5 Passive damping with piezoelectric transducers.- 5.1 Introduction.- 5.2 Resistive shunting.- 5.3 Inductive shunting.- 5.4 Switched shunt.- 5.4.1 Equivalent damping ratio.- 5.5 References.- 5.6 Problems.- 6 Collocated versus non-collocated control.- 6.1 Introduction.- 6.2 Pole-zero flipping.- 6.3 The two-mass problem.- 6.3.1 Collocated control.- 6.3.2 Non-collocated control.- 6.4 Notch filter.- 6.5 Effect of pole-zero flipping on the Bode plots.- 6.6 Nearly collocated control system.- 6.7 Non-collocated control systems.- 6.8 The role of damping.- 6.9 References.- 6.10 Problems ..- 7 Active damping with collocated system.- 7.1 Introduction.- 7.2 Lead control.- 7.3 Direct velocity feedback (DVF).- 7.4 Positive Position Feedback (PPF).- 7.5 Integral Force Feedback(IFF).- 7.6 Duality between the Lead and the IFF controllers.- 7.6.1 Root-locus of a single mode.- 7.6.2 Open-loop poles and zeros.- 7.7 Actuator and sensor dynamics.- 7.8 Decentralized control with collocated pairs.- 7.8.1 Cross talk.- 7.8.2 Force actuator and displacement sensor.- 7.8.3 Displacement actuator and force sensor.- 7.9 References.- 7.10 Problems.- 8 Vibration isolation.- 8.1 Introduction.- 8.2 Relaxation isolator.- 8.2.1 Electromagnetic realization.- 8.3 Active isolation.- 8.3.1 Sky-hook damper.- 8.3.2 Integral Force Feedback.- 8.4 Flexible body.- 8.4.1 Free-free beam with isolator.- 8.5 Payload isolation in spacecraft.- 8.5.1 Interaction isolator/attitude control.- 8.5.2 Gough-Stewart platform.- 8.6 Six-axis isolator.- 8.6.1 Relaxation isolator.- 8.6.2 Integral Force Feedback.- 8.6.3 Spherical joints, modal spread.- 8.7 Active vs. passive.- 8.8 Car suspension.- 8.9 References.- 8.10 Problems.- 9 State space approach.- 9.1 Introduction.- 9.2 State space description.- 9.2.1 Single degree of freedom oscillator.- 9.2.2 Flexible structure.- 9.2.3 Inverted pendulum.- 9.3 System transfer function.- 9.3.1 Poles and zeros.- 9.4 Pole placement by state feedback.- 9.4.1 Example: oscillator.- 9.5 Linear Quadratic Regulator.- 9.5.1 Symmetric root locus.- 9.5.2 Inverted pendulum.- 9.6 Observer design.- 9.7 Kalman Filter.- 9.7.1 Inverted pendulum.- 9.8 Reduced order observer.- 9.8.1 Oscillator.- 9.8.2 Inverted pendulum.- 9.9 Separation principle.- 9.10 Transfer function of the compensator.- 9.10.1 The two-mass problem.- 9.11 References.- 9.12 Problems.- 10 Analysis and synthesis in the frequency domain.- 10.1 Gain and phase margins.- 10.2 Nyquist criterion.- 10.2.1 Cauchy's principle.- 10.2.2 Nyquist stability criterion.- 10.3 Nichols chart.- 10.4 Feedback specification for SISO systems.- 10.4.1 Sensitivity.- 10.4.2 Tracking error.- 10.4.3 Performance specification.- 10.4.4 Unstructured uncertainty.- 10.4.5 Robust performance and robust stability.- 10.5 Bode gain-phase relationships.- 10.6 The Bode Ideal Cutoff.- 10.7 Non-minimum phase systems.- 10.8 Usual compensators.- 10.8.1 System type.- 10.8.2 Lead compensator.- 10.8.3 PI compensator.- 10.8.4 Lag compensator.- 10.8.5 PID compensator.- 10.9 Multivariable systems.- 10.9.1 Performance specification.- 10.9.2 Small gain theorem.- 10.9.3 Stability robustness tests.- 10.9.4 Residual dynamics.- 10.10References.- 10.11Problems.- 11 Optimal control.- 11.1 Introduction.- 11.2 Quadratic integral.- 11.3 Deterministic LQR.- 11.4 Stochastic response to a white noise.- 11.4.1 Remark.- 11.5 Stochastic LQR.- 11.6 Asymptotic behavior of the closed-loop.- 11.7 Prescribed degree of stability.- 11.8 Gain and phase margins of the LQR.- 11.9 Full state observer.- 11.9.1 Covariance of the reconstruction error.- 11.10Kalman-Bucy Filter (KBF).- 11.11Linear Quadratic Gaussian (LQG).- 11.12Duality.- 11.13Spillover.- 11.13.1Spillover reduction.- 11.14Loop Transfer Recovery (LTR).- 11.15Integral control with state feedback.- 11.16Frequency shaping.- 11.16.1Frequency-shaped cost functionals.- 11.16.2Noise model ..- 11.17References.- 11.18Problems.- 12 Controllability and Observability.- 12.1 Introduction.- 12.1.1 Definitions.- 12.2 Controllability and observability matrices.- 12.3 Examples.- 12.3.1 Cart with two inverted pendulums.- 12.3.2 Double inverted pendulum.- 12.3.3 Two d.o.f. oscillator.- 12.4 State transformation.- 12.4.1 Control canonical form.- 12.4.2 Left and right eigenvectors.- 12.4.3 Diagonal form.- 12.5 PBH test.- 12.6 Residues.- 12.7 Example.- 12.8 Sensitivity.- 12.9 Controllability and observability Gramians.- 12.10Internally balanced coordinates.- 12.11Model reduction.- 12.11.1Transfer equivalent realization.- 12.11.2Internally balanced realization.- 12.11.3Example.- 12.12References.- 12.13Problems.- 13 Stability.- 13.1 Introduction.- 13.1.1 Phase portrait.- 13.2 Linear systems.- 13.2.1 Routh-Hurwitz criterion.- 13.3 Lyapunov's direct method.- 13.3.1 Introductory example.- 13.3.2 Stability theorem.- 13.3.3 Asymptotic stability theorem.- 13.3.4 Lasalle's theorem.- 13.3.5 Geometric interpretation.- 13.3.6 Instability theorem.- 13.4 Lyapunov functions for linear systems.- 13.5 Lyapunov's indirect method ..- 13.6 An application to controller design.- 13.7 Energy absorbing controls.- 13.8 References.- 13.9 Problems.- 14 Applications.- 14.1 Digital implementation.- 14.1.1 Sampling, aliasing and prefiltering.- 14.1.2 Zero-order hold, computational delay.- 14.1.3 Quantization.- 14.1.4 Discretization of a continuous controller.- 14.2 Active damping of a truss structure.- 14.2.1 Actuator placement.- 14.2.2 Implementation, experimental results.- 14.3 Active damping generic interface.- 14.3.1 Active damping.- 14.3.2 Experiment.- 14.3.3 Pointing and position control.- 14.4 Active damping of a plate.- 14.4.1 Control design.- 14.5 Active damping of a stiff beam.- 14.5.1 System design.- 14.6 The HAC/LAC strategy.- 14.6.1 Wide-band position control.- 14.6.2 Compensator design.- 14.6.3 Results.- 14.7 Vibroacoustics: Volume displacement sensors.- 14.7.1 QWSIS sensor.- 14.7.2 Discrete array sensor.- 14.7.3 Spatial aliasing.- 14.7.4 Distributed sensor.- 14.8 References.- 14.9 Problems.- 5 Tendon Control of Cable Structures.- 15.1 Introduction.- 15.2 Tendon control of strings and cables.- 15.3 Active damping strategy.- 15.4 Basic Experiment.- 15.5 Linear theory of decentralized active damping.- 15.6 Guyed truss experiment.- 15.7 Micro Precision Interferometer testbed.- 15.8 Free floating truss experiment.- 15.9 Application to cable-stayed bridges.- 15.10Laboratory experiment.- 15.11Control of parametric resonance.- 15.12Large scale experiment.- 15.13 References.- 16 Active Control of Large Telescopes.- 16.1 Introduction.- 16.2 Adaptive optics.- 16.3 Active optics.- 16.3.1 Monolithic primary mirror.- 16.3.2 Segmented primary mirror.- 16.4 SVD controller.- 16.4.1 Loop shaping of the SVD controller.- 16.5 Dynamics of a segmented mirror.- 16.6 Control-structure interaction.- 16.6.1 Multiplicative uncertainty.- 16.6.2 Additive uncertainty.- 16.6.3 Discussion.- 16.7 References.- 17 Semi-active control.- 17.1 Introduction.- 17.2 Magneto-rheological fluids.- 17.3 MR devices.- 17.4 Semi-active suspension.- 17.4.1 Semi-active devices.- 17.5 Narrow-band disturbance.- 17.5.1 Quarter-car semi-active suspension.- 17.6 References.- 17.7 Problems.- Bibliography.- Index.
1,107 citations
TL;DR: In this article, a method for tuning the PI λ D μ controller is proposed to fulfill five different design specifications, including gain crossover frequency, phase margin, and iso-damping property of the system.
881 citations
TL;DR: A review of the state of research on the chatter problem and classifications the existing methods developed to ensure stable cutting into those that use the lobbing effect, out-of-process or in-process, and those that, passively or actively, modify the system behavior as mentioned in this paper.
Abstract: Chatter is a self-excited vibration that can occur during machining operations and become a common limitation to productivity and part quality. For this reason, it has been a topic of industrial and academic interest in the manufacturing sector for many years. A great deal of research has been carried out since the late 1950s to solve the chatter problem. Researchers have studied how to detect, identify, avoid, prevent, reduce, control, or suppress chatter. This paper reviews the state of research on the chatter problem and classifies the existing methods developed to ensure stable cutting into those that use the lobbing effect, out-of-process or in-process, and those that, passively or actively, modify the system behaviour.
790 citations