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Journal ArticleDOI

Smith predictor based robust fractional order control: Application to water distribution in a main irrigation canal pool

TL;DR: In this article, the authors proposed a new methodology to design fractional integral controllers combined with Smith predictors, which are robust to high frequency model changes, in particular, special attention is paid to time delay changes.
About: This article is published in Journal of Process Control.The article was published on 2009-03-01. It has received 89 citations till now. The article focuses on the topics: Smith predictor & Model predictive control.
Citations
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Journal ArticleDOI
TL;DR: This review investigates its progress since the first reported use of control systems, covering the fractional PID proposed by Podlubny in 1994, and is presenting a state-of-the-art fractionalpid controller, incorporating the latest contributions in this field.

447 citations

Journal ArticleDOI
TL;DR: It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals, as a result, a limit cycle cannot be expected in the solution of these systems.

173 citations

Journal ArticleDOI
TL;DR: It is shown that the fractional-order derivatives of a periodic function with a specific period cannot be a periodicfunction with the same period, and based on this point it can be easily proved the absence of periodic responses in a wider class of fractional -order models.

116 citations

Journal ArticleDOI
TL;DR: The present paper attempts to address issues by reviewing recent literature in the field and by providing relevant analysis and recommendations on the benefit of using FOPID controllers.

101 citations


Additional excerpts

  • ...It was further investigated in, e.g., PommierBudinger et al. (2008); Feliu-Batlle et al. (2009); Sabatier et al. (2015); Beschi et al. (2015); Azarmi et al. (2016); Bettayeb et al. (2016)....

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Journal ArticleDOI
TL;DR: The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes.
Abstract: Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review.

89 citations


Cites background or methods from "Smith predictor based robust fracti..."

  • ...In [64], the idea in [63] is reiterated....

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  • ...In [63], a new methodology to design fractional order integral controllers combined with Smith predictors is proposed with the target of ensuring the robustness to high frequency model changes, especially changes in the time delay....

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References
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Book
01 Jan 1999

15,898 citations


"Smith predictor based robust fracti..." refers background in this paper

  • ...uðtÞ 1⁄4 K eðtÞ þ Ki D 1 t eðtÞ þ Kd D 1 t eðtÞ; ð4Þ can be generalized to a PIkDl fractional controller involving an integrator of order k and a differentiator of order l [22,26]....

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  • ...Several definitions of this operator have been proposed [22]....

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  • ...In the last years, fractional operators have been applied with satisfactory results to model and control processes with difficult dynamical behavior [22,23]....

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  • ...The limit value of expression (8) when T? 0 is called the Grundwald–Letnikov (GL) definition of the discretized fractional operator [22]....

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  • ...However, applying fractional order calculus to dynamic systems control is just a recent focus of interest [22]....

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Journal ArticleDOI
TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Abstract: Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel. >

5,272 citations

Journal ArticleDOI
TL;DR: In this article, a fractional-order PI/sup/spl lambda/D/sup /spl mu/controller with fractionalorder integrator and fractional order differentiator is proposed.
Abstract: Dynamic systems of an arbitrary real order (fractional-order systems) are considered. The concept of a fractional-order PI/sup /spl lambda//D/sup /spl mu//-controller, involving fractional-order integrator and fractional-order differentiator, is proposed. The Laplace transform formula for a new function of the Mittag-Leffler-type made it possible to obtain explicit analytical expressions for the unit-step and unit-impulse response of a linear fractional-order system with fractional-order controller for both open- and closed-loops. An example demonstrating the use of the obtained formulas and the advantages of the proposed PI/sup /spl lambda//D/sup /spl mu//-controllers is given.

2,479 citations

Book
30 Jun 2005
TL;DR: In this article, the authors present a set of control analysis methods for MIMO linear systems, including the phase plane method, M.S. Atherton, and A.R. Stubberud.
Abstract: FUNDAMENTALS OF CONTROL Mathematical Foundations Ordinary Linear Differential and Difference Equations, B.P. Lathi The Fourier, Laplace, and Z-Transforms, E.W. Kamen Matrices and Linear Algebra, B.W. Dickinson Complex Variables, C.W. Gray Models for Dynamical Systems Standard Mathematical Models Input-Output Models, W.S. Levine State Space, J. Gillis Graphical Models Block Diagrams, D.K. Frederick and C.M. Close Signal Flow Graphs, N.S. Nise Determining Models Modeling from Physical Principles, F.E. Cellier, H. Elmqvist, and M. Otter System Identification When Noise is Negligible, W.S. Levine Analysis and Design Methods for Continuous-Time Systems Analysis Methods Time Response of Linear Time-Invariant Systems, R.T. Stefani Controllability and Observability, W.A. Wolovich Stability Tests The Routh-Hurwitz Stability Criterion, R.H. Bishop and R.C. Dorf The Nyquist Stability Test, C.E. Rohrs Discrete-Time and Sampled-Data Stability Tests, M. Mansour Gain Margin and Phase Margin, R.T. Stefani Design Methods Specification of Control Systems, J.-S. Yang and W.S. Levine Design Using Performance Indices, R.C. Dorf and R.H. Bishop Nyquist, Bode, and Nichols Plots, J.J. D'Azzo and C.H. Houpis The Root Locus Plot, W.S. Levine PID Control, K.J. Astrom and T. Hagglund State Space - Pole Placement, K. Ogata Internal Model Control, R.D. Braatz Time-Delay Compensation - Smith Predictor and Its Modifications, Z.J. Palmor Digital Control Discrete-Time Systems, M.S. Santina and A.R. Stubberud Sampled-Data Systems, A. Feuer and G.C. Goodwin Discrete-Time Equivalents to Continuous-Time Systems, M.S. Santina and A.R. Stubberud Design Methods for Discrete-Time Linear Time-Invariant Systems, M.S. Santina and A.R. Stubberud Quantization Effects, M.S. Santina and A.R. Stubberud Sample-Rate Selection, M.S. Santina and A.R. Stubberud Real Time Software for Implementation of Digital Control, D.M. Auslander, J.R. Ridgely, and J. Jones Programmable Controllers, G. Olsson Analysis and Design Methods for Nonlinear Systems Analysis Methods The Describing Function Method, D.P. Atherton The Phase Plane Method, D.P. Atherton Design Methods Dealing with Actuator Saturation, R.H. Middleton Bumpless Transfer, A. Ahlen and S.F. Graebe Linearization and Gain-Scheduling, J.S. Shamma Software for Control System Analysis and Design Numerical and Computational Issues in Linear Control and System Theory, R.V. Patel, A.J. Laub, and P.M. Van Dooren Software for Modeling and Simulating Control Systems, M. Otter and F.E. Cellier Computer-Aided Control Systems Design, C.M. Rimvall and C.P Jobling ADVANCED METHODS OF CONTROL Analysis Methods for MIMO Linear Systems Multivariable Poles, Zeros, and Pole/Zero Cancellations, J. Douglas and M. Athans Fundamentals of Linear Time-Varying Systems, E.W. Kamen Geometric Theory of Linear Systems, F. Hamano Polynomial and Matrix Fraction Descriptions, D.F. Delchamps Robustness Analysis with Real Parametric Uncertainty, R. Tempo and F. Blanchini MIMO Frequency Response Analysis and the Singular Value Decomposition, S.D. Patek and M. Athans Stability Robustness to Unstructured Uncertainty for Linear Time-Invariant Systems, A. Chao and M. Athans Tradeoffs and Limitations in Feedback Systems, D.P. Looze and J.S. Freudenberg Modeling Deterministic Uncertainty, J. Raisch and B.A. Francis The Use of Multivariate Statistics in Process Control, M.J. Piovoso and K.A. Kosanovich Kalman Filter and Observers Linear Systems and White Noise, W.S. Levine Kalman Filter, M. Athans Riccati Equations and Their Solution, V. Kucera Observers, B. Friedland Design Methods for MIMO LTI Systems Eigenstructure Assignment, K.M. Sobel, E.Y. Shapiro, and A.N. Andry, Jr. Linear Quadratic Regulator Control, L. Lublin and M. Athans H2 (LQG) and H8 Control, L. Lublin, S. Grocott, and M. Athens Robust Control: Theory, Computation, and Design, M. Dahleh The Structured Singular Value (m) Framework, G.J. Balas and A. Packard Algebraic Design Methods, V. Kucera Quantitative Feedback Theory (QFT) Technique, C.H. Houpis The Inverse Nyquist Array and Characteristic Locus Design Methods, N. Munro and J.M. Edmunds Robust Servomechanism Problem, E.J. Davidson Numerical Optimization-Based Design, V. Balakrishnan and A.L. Tits Optimal Control, F.L. Lewis Decentralized Control, M.E. Sezer and D.D. Siljak Decoupling, T. Williams and P.J. Antsaklis Predictive Control, A.W. Pike, M.J. Grimble, M.A. Johnson, A.W. Ordys, and S. Shakoor Adaptive Control Automatic Tuning of PID Controllers, T. Hagglund and K.J. Astrom Self-Tuning Control, D.W. Clarke Model Reference Adaptive Control, P.A. Ioannou Analysis and Design of Nonlinear Systems Analysis Methods The Lie Bracket and Control, V. Jurdjevic Two Time Scale and Averaging Methods, H.K. Khalil Volterra and Fliess Series Expansion for Nonlinear Systems, F. Lamnabi-Lagarrique Stability Lyapunov Stability, H.K. Khalil Input-Output Stability, A.R. Teel, T.T. Georgiou, L. Praly, and E. Sontag Design Methods Feedback Linearization of Nonlinear Systems, A. Isidori and M.D. Di Benedetto Nonlinear Zero Dynamics, A. Isidori and C.I. Byrnes Nonlinear Output Regulation and Tracking, A. Isidori Lyapunov Design, R.A. Freeman and P.V. Kokotovic Variable Structure and Sliding Mode Controller Design, R.A. De Carlo, S.H. Zak, and S.V. Drakunov Control of Bifurcation and Chaos, E.H. Abed, H.O. Wang, and A. Tesi Open-Loop Control Using Oscillatory Inputs, J. Baillieul and B. Lehman Adaptive Nonlinear Control, M. Krstic and P.V. Kokotovic Intelligent Control, K.M. Passino Fuzzy Control, K.M. Passino and S. Yurkovich Neural Control, J.A. Farrell System Identification System Identification, L. Ljung Stochastic Control Discrete Time Markov Processes, A. Schwartz Stochastic Differential Equations, J.A. Gubner Linear Stochastic Input-Output Models, T. Soderstrom Minimum Variance Control, M.R. Katebi and A.W. Ordys Dynamic Programming, P.R. Kumar Stability of Stochastic Systems, K.O. Loparo and X. Feng Stochastic Adaptive Control, T.E. Duncan and B. Pasik-Duncan Control of Distributed Parameter Systems Controllability of Thin Elastic Beams and Plates, J.E. Lagnese and G. Leugering Control of the Heat Equation, T.I. Seidman Observability of Linear Distributed Parameter Systems, D.L. Russell APPLICATIONS OF CONTROL Process Control Water Level Control for the Toilet Tank: A Historical Perspective, B.G. Coury Temperature Control in Large Buildings, C.C. Federspiel and J.E. Seem Control of pH, F.G. Shinskey Control of the Pulp and Paper-Making Process, W.L. Bialkowski Control for Advanced Semiconductor Device Manufacturing: A Case History, T. Kailath, C. Schaper, Y. Cho, P. Gyugyi, S. Norman, P. Park, S. Boyd, G. Franklin, K. Saraswat, M. Modehi, and C. Davis Mechanical Control Systems Automotive Control Systems Engine Control, J.A. Cook, J.W. Grizzle, and J. Sun Adaptive Automotive Speed Control, M.K. Liubakka, D.S. Rhode, J.R. Winkelman, and P.V. Kokotovic Aerospace Controls Flight Control of Piloted Aircraft, M. Pachter and C.H. Houpis Spacecraft Attitude Control, V.T. Coppola and N.H. McClamroch Control of Flexible Space Structures, S.M. Joshi and A.G. Kelkar Line-of-Sight Pointing and Stabilization Control Systems, D.A. Haessig Control of Robots and Manipulators Motion Control of Robotic Manipulators, M.W. Spong Force Control of Robotic Manipulators, J. De Schutter and H. Bruyninckx Control of Nonholonomic Systems, J.T.-Y. Wen Miscellaneous Mechanical Control Systems Friction Compensation, B. Armstrong-Helouvry and C. Canudas de Wit Motion Control Systems, J. Tal Ultra-High Precision Control, T.R. Kurfess and H. Jenkins Robust Control of a Compact Disc Mechanism, M. Steinbuch, G. Schootstra, and O.H. Bosgra Electrical and Electronic Control Systems Power Electronic Controls Dynamic Modeling and Control in Power Electronics, G.C. Verghese Motion Control with Electric Motors by Input-Output Linearization, D.G. Taylor Control of Electric Generators, T. Jahns and R.W. De Doncker Control of Electrical Power Control of Electrical Power Generating Plants, H.G. Kwatny and C. Maffezzoni Control of Power Transmission, J.J. Paserba, J.J. Sanchez-Gasca, and E.V. Larsen Control Systems Including Humans Human-in-the-Loop Control, R.A. Hess Index

1,351 citations

Book
12 Aug 2008
TL;DR: Open-Channel Flow, Second Edition is written for students in senior-level undergraduate and graduate courses on steady and unsteady open-channel flow and for civil engineers needing up-to-date and relevant information on the latest developments and techniques in the field.
Abstract: Analysis of open-channel flow is essential for the planning, design, and operation of water-resource projects. The use of computers and the availability of efficient computational procedures has simplified such analysis, and made it possible to handle increasingly complex systems. In Open-Channel Flow, Second Edition, author Hanif Chaudhry draws upon years of practical experience and incorporates numerous examples and real life applications, to provide the reader with: A strong emphasis on the application of efficient solution techniques, computational procedures, and numerical methods suitable for computer analyses; Complete coverage of steady and unsteady flow techniques; A new chapter on sediment transport and updated chapters on uniform flow and two dimensional flow techniques; New and updated problem sets and exercises, a solutions manual for instructors, and a CD-ROM with short computer programs in FORTRAN that include the input data for sample problems and the associated computer output. Open-Channel Flow, Second Edition is written for students in senior-level undergraduate and graduate courses on steady and unsteady open-channel flow and for civil engineers needing up-to-date and relevant information on the latest developments and techniques in the field.

682 citations


Additional excerpts

  • ...[4,6])....

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