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Active Vibration Suppression of nonlinear Cantilever Beam using Shape Memory Alloy Actuators

IFAC-PapersOnLine 2018年第1期51卷 130-135页

作者： Vishal, Prateek Kaliperumal, Dhanalakshmi Padhi, Radhakant National Institute of Technology Tiruchirapalli India Indian Institute of Science Bangalore India

This paper presents the active vibration suppression of a cantilever beam using shape memory alloy (SMA) wires as actuator. The cantilever beam is modelled as a nonlinear distributed parameter system (DPS) following the Euler Bernoulli Beam theory. Sensors and actuators are optimally placed at discrete locations along the cantilever beam. Controllability Gramians are evaluated to determine the optimal locations for the actuator placement. Modal analysis is used to determine the optimal locations for the sensor placement. The desired system response is obtained by designing a nonlinear controller using the concepts of dynamic inversion and optimal control. This methodology is based on the Design Then Approximate (DTA) philosophy. Optimal Dynamic Inversion is used as the control technique to ensure suppression of vibration along the length of the beam. This approach of control design can be used for any randomly generated initial profile of the beam. Experimental setup is designed using discrete sensors such as LASER sensor and Piezoelectric Sensor and the actuation is done using SMA based wire actuators. The control algorithm is verified experimentally and theoretically for vibration suppression. © 2018

关键词： Shape memory effect Cantilever beams Continuum mechanics Location Modal analysis Nanocantilevers Piezoelectric actuators Active vibration controls Active vibration suppression Controllability gramian Euler Bernoulli beam theory nonlinear cantilever beams nonlinear distributed parameter system Optimal dynamics Shape memory alloy actuators

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Active Vibration Suppression of nonlinear Cantilever Beam using Shape Memory Alloy Actuators

Active Vibration Suppression of Nonlinear Cantilever Beam us...

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5th IFAC Conference on Advances in Control and Optimization of Dynamical systems (ACODS)

作者： Vishal, Prateek Kaliperumal, Dhanalakshmi Padhi, Radhakant Natl Inst Technol Tiruchirappalli India Indian Inst Sci Bangalore Karnataka India

关键词： Shape Memory Alloy nonlinear distributed parameter system Active Vibration Control Controllability Gramian Design-Then-Approximate Optimal Dynamic Inversion

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An Adaptive Model Predictive Control Strategy for nonlinear distributed parameter systems using the Type-2 Takagi-Sugeno Model

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INTERNATIONAL JOURNAL OF FUZZY systemS 2016年第5期18卷 792-805页

作者： Wang, Mengling Paulson, Joel A. Yan, Huaicheng Shi, Hongbo East China Univ Sci & Technol Minist Educ Key Lab Adv Control & Optimizat Chem Proc 130 Meilong Rd Shanghai 200237 Peoples R China MIT Dept Chem Engn 77 Massachusetts Ave Cambridge MA 02139 USA

This paper proposes an adaptive model predictive control (MPC) strategy for nonlinear distributed parameter systems (DPSs) based on the online-tuning interval Type-2 Takagi-Sugeno (IT2 T-S) model. First, the infinite dimension DPS is approximated in a finite dimensional space via the finite difference method, and from this model, training data are generated. Principal component analysis is then used to project the finite, but still high, dimensional spatiotemporal training data into a low-dimensional time series using spatial basis functions. Next, an online-tuning IT2 T-S fuzzy model is proposed to predict the low-dimensional time series with a high accuracy by computing an optimal time-varying weight parameter. Furthermore, a new method for simplifying controller design is presented by transforming the control objective from the high-dimensional spatial outputs reaching their set points to the lower dimensional time outputs reaching their set points. These novel contributions increase the accuracy of the prediction model (thus improving control performance) and reduce the computational cost of the underlying MPC optimization. Lastly, simulations are presented on a typical DPS to demonstrate the accuracy and effectiveness of the proposed methods.

关键词： Interval Type-2 fuzzy T-S model nonlinear distributed parameter system Time/space separation modeling approach Model predictive control

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Optimal Port Allocation for nonlinear distributed parameter systems. This work was supported by JSPS Grants-in-Aid for Scientific Research (C) No. 264204f 5, and JSPS Grants-in-Aid for Challenging Exploratory Research No. 26630197. N. Sakamoto was supported by Nanzan University Pache Research Subsidy I-A-2 for the 2015 academic year

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IFAC-PapersOnLine 2016年第8期49卷 284-289页

作者： Nishida, Gou Sakamoto, Noboru Graduate School of Information Science and Engineering Tokyo Institute of Technology 2-12-1 W8-1 O-okayama TokyoMeguro-ku152-8552 Japan Department of Mechatronics Faculty of Science and Engineering Nanzan University 18 Yamazato-cho NagoyaShyowa-ku466-8673 Japan

This paper proposes an optimal way of allocating collocated input-output pairs for stabilizing distributed parameter systems. We first introduce a finite-dimensional reduced model from sampled initial responses of the systems via the POD (Proper Orthogonal Decomposition)-Galerkin method. Next, optimal gains of the stabilizing controller for the reduced systems are designed by the stable manifold method that is an exact numerical solver of Hamilton-3Jacobi equations. Finally, we present three allocation methods derived from state shape matching, dissipation enhancement, and their mixed evaluation, and we show that the optimal allocations can be associated with energy controls in terms of port representations. © 2016

关键词： distributed parameter control systems Galerkin methods nonlinear equations nonlinear systems Numerical methods Principal component analysis distributed parameter systems Hamilton Jacobi equations Model reduction nonlinear distributed parameter system Optimal controls Proper orthogonal decompositions Scientific researches Stabilizing controllers

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Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems

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IET SCIENCE MEASUREMENT & TECHNOLOGY 2014年第6期8卷 537-545页

作者： Sadeghi, Mokhtar Sha Vafamand, Navid Babaei, Mohammad Sadegh Shiraz Univ Technol Elect & Elect Dept Shiraz Iran Shiraz Univ E Learning Dept Shiraz Iran

In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi-Sugeno fuzzy-partial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study, non-quadratic Lyapunov function is utilised and some slack matrices are introduced to derive stability conditions in terms of linear matrix inequalities (LMIs). The proposed approach has three main features. First, stability conditions are not derived in the form of spatial differential LMI. Second, conservativeness of LMI conditions is reduced. Third, there is no restriction on the form of semi-linear hyperbolic PDE systems and therefore more semi-linear systems classes can be stabilised. Also, the proposed approach is more suitable for practical implementation compared with the recently published papers.

关键词： partial differential equations nonlinear differential equations hyperbolic equations fuzzy control control system synthesis nonlinear control systems distributed parameter systems Lyapunov methods linear matrix inequalities asymptotic stability nonquadratic exponential stabilisation nonlinear hyperbolic partial differential equation systems fuzzy controller design systematic approach TakagiaEuro"Sugeno fuzzy partial differential equation TS fuzzy-PDE system nonlinear distributed parameter system first order semilinear hyperbolic PDE nonquadratic Lyapunov function stability conditions linear matrix inequalities LMI

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Optimal spatial sampling scheme for parameter estimation of nonlinear distributed parameter systems

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COMPUTERS & CHEMICAL ENGINEERING 2012年 45卷 38-49页

作者： Alana, Jorge E. Theodoropoulos, Constantinos Univ Manchester Sch Chem Engn & Analyt Sci Manchester M13 9PL Lancs England Univ Zulia Fac Ingn Escuela Ingn Quim Maracaibo 4011 Zulia Venezuela

In this paper a methodology for the estimation of parameters of distributed parameter systems based on optimal spatial measurements is discussed. The concept of the covariance matrix for sampling design is exploited and D-optimality criteria concerning relevant metrics are linked with the computation of optimal measurement locations. These are obtained at the points where sensitivity functions reach their extrema values and coincide with the locations where system eigenmodes obtained by proper orthogonal decomposition (POD) are maximised or minimised as has been shown in a recent work (Alana & Theodoropoulos, 2011). A tubular reactor with recycle is used as illustrative example to demonstrate the sampling methodology, including cases where the system behaviour is unstable exhibiting sustained oscillations. The estimates with the highest deviation from the nominal parameter values are the ones with the lowest (absolute) sensitivity coefficients. Using a POD-based reduced model can significantly reduce computational costs and in addition improve the estimation procedure by using measurements at the locations where the POD modes extrema occur. The results are strongly influenced by experimental noise, and filtering techniques are needed to mitigate the related uncertainties. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Covariance matrix Sensitivity coefficients Measurement points Proper orthogonal decomposition Empirical eigenfunctions nonlinear distributed parameter system

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Optimal combination of spatial basis functions for the model reduction of nonlinear distributed parameter systems

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COMMUNICATIONS IN nonlinear SCIENCE AND NUMERICAL SIMULATION 2012年第12期17卷 5240-5248页

作者： Jiang, Mian Deng, Hua Cent S Univ Sch Mech & Elect Engn Changsha 410083 Peoples R China State Key Lab High Performance & Complex Mfg Changsha 410083 Peoples R China

Spectral methods are among the most extensively used techniques for model reduction of distributed parameter systems in various fields, including fluid dynamics, quantum mechanics, heat conduction, and weather prediction. However, the model dimension is not minimized for a given desired accuracy because of general spatial basis functions. New spatial basis functions are obtained by linear combination of general spatial basis functions in spectral method, whereas the basis function transformation matrix is derived from straightforward optimization techniques. After the expansion and truncation of spatial basis functions, the present spatial basis functions can provide a lower dimensional and more precise ordinary differential equation system to approximate the dynamics of the systems. The numerical example shows the feasibility and effectiveness of the optimal combination of spectral basis functions for model reduction of nonlinear distributed parameter systems. (C) 2012 Elsevier B.V. All rights reserved.

关键词： nonlinear distributed parameter system Spectral method Spatial basis function Optimal combination Model reduction

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Inferential MIMO predictive control of the particle size distribution in emulsion polymerization

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COMPUTERS & CHEMICAL ENGINEERING 2012年 38卷 115-125页

作者： da Silva, Bruno Dufour, Pascal Sheibat-Othman, Nida Othman, Sami Univ Lyon 1 CNRS UMR 5007 LAGEP F-69622 Villeurbanne France Univ Lyon F-69622 Villeurbanne France

A new inferential 2-step multiple input/multiple output (MIMO) model predictive control (MPC) of the particle size distribution (PSD) in emulsion polymerization processes is proposed. The bulk-like model describing the PSD is used with the material balances of initiator, radicals, monomer and surfactant. The inferential 2-step control strategy uses two measurements available online (without delay): the concentration of surfactant in the aqueous phase by conductimetry, and the concentration of monomer by calorimetry. In a first step, the optimal trajectory of surfactant concentration leading to the target PSD is calculated offline. In a second step, a multivariable model predictive control manipulates online the monomer and surfactant flow rates in order to track the precalculated surfactant concentration trajectory and to maximise the monomer concentration in the polymer particles in a constrained set-point tracking. Two control strategies are compared (nonlinear MPC and linearized MPC) with and without modelling errors. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Model predictive control nonlinear distributed parameter system Emulsion polymerization Particle size distribution Inferential control

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MPC as control strategy for pasta drying processes

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COMPUTERS & CHEMICAL ENGINEERING 2009年第1期33卷 50-57页

作者： De Temmerman, J. Dufour, P. Nicolai, B. Ramon, H. Katholieke Univ Leuven BIOSYST MeBioS B-3001 Louvain Belgium Univ Lyon F-69003 Lyon France Univ Lyon 1 CNRS UMR 5007 LAGEP Lab Proc Control & Chem Engn F-69100 Villeurbanne France

This study focuses on the drying process of pasta in a convectional air drying oven. A model predictive control algorithm is designed, based on a dynamic model describing the mass transfer between pasta and the surrounding air. The multiple input single output control algorithm minimizes a cost function over a prediction horizon which represents the deviation of the process from a desired reference track, thereby incorporating the working limitations of the oven. The performance of the controller and the influence of the prediction horizon are examined in this paper, showing minimal deviation between process and reference track. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Drying process Model predictive control nonlinear distributed parameter system First principle model Moisture content

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Optimal dynamic inversion control design for a class of nonlinear distributed parameter systems with continuous and discrete actuators

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IET CONTROL THEORY AND APPLICATIONS 2007年第6期1卷 1662-1671页

作者： Padhi, R. Balakrishnan, S. N. Indian Inst Technol Dept Aerosp Engn Bangalore Karnataka India Univ Missouri Dept Mech & Aerosp Engn Rolla MO USA

Combining the principles of dynamic inversion and optimisation theory, two stabilising state-feedback control design approaches are presented for a class of nonlinear distributed parameter systems. One approach combines the dynamic inversion with variational optimisation theory and it can be applied when there is a continuous actuator in the spatial domain. This approach has more theoretical significance in the sense that it does not lead to any singularity in the control computation and the convergence of the control action can be proved. The other approach, which can be applied when there are a number of discrete actuators located at distinct places in the spatial domain, combines dynamic inversion with static optimisation theory. This approach has more relevance in practice, since such a scenario appears naturally in many practical problems because of implementation concern. These new techniques can be classified as 'design-then-approximate' techniques, which are in general more elegant than the 'approximate-then-design' techniques. However, unlike the existing design-then-approximate techniques, the new techniques presented here do not demand involved mathematics (like infinite-dimensional operator theory, inertial manifold theory and so on). To demonstrate the potential of the proposed techniques, a real-life temperature control problem for a heat transfer application is solved, first assuming a continuous actuator and then assuming a set of discrete actuators.

关键词： variational optimisation theory spatial domain stabilising state-feedback control stability temperature control heat transfer application static optimisation theory continuous actuator actuators state feedback nonlinear distributed parameter system optimal dynamic inversion control discrete actuator optimal control nonlinear systems

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