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Robustness analysis and synthesis of a multi-PID controller based on an uncertain multimodel representation

COMPUTERS & CHEMICAL ENGINEERING 2006年第2期31卷 66-77页

作者： Toscano, R. Lyonnet, P. ENISE ECL CNRS UMR 5513 Lab Tribol & Dynam Syst F-42023 St Etienne 2 France

This paper presents an effective method for robustness analysis and synthesis of a multi-PID controller for non-linear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions. The robustness analysis problem is solved using an uncertain multimodel of the original non-linear system. The model of uncertainties used is an interval matrix modeled by a stochastic matrix which gives poor conservatism in the analysis of stability robustness. Moreover, the robust stability margin is interpreted as a smallest interval matrix that causes instability. This stability margin is evaluated using a random search algorithm. Simulation studies are used to demonstrate the effectiveness of the proposed method. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： PID controller multimodel multi-PID parametric uncertainties robust stability random search algorithm

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The peak load minimization problem in cyclic production

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COMPUTERS & OPERATIONS REsearch 2001年第14期28卷 1441-1460页

作者： Yao, MJ Tunghai Univ Dept Ind Engn Taichung 40407 Taiwan

The objective of this study is to determine a production schedule for a set of jobs so as to minimize the peak load for the entire planning horizon given the production duration and the cyclic frequencies of the jobs. We refer to this problem as the peak load minimization problem (PLMP). An efficient heuristic, viz. Proc. PLMP, is proposed to solve such class of problems. There are two parts for the Proc. PLMP: a greedy procedure that secures an initial production schedule and a schedule smoothing procedure that performs a local search to reduce the maximal load. Numerical experiments verify that Proc. PLMP is efficient, since its run time is of cubic order of the problem size, i.e., it is approximately an O(n(3)) algorithm. A major application of Proc. PLMP is to test the feasibility of a given set of a solution for the Economic Lot Scheduling Problem using the extended basic period approach.

关键词： scheduling random search algorithm cyclic production

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Robust Kalman smoother for EIV state space model based on multivariate least trimmed squares estimator

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IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION 2012年第1期29卷 23-32页

作者： AlMutawa, Jaafar King Fahd Univ Petr & Minerals Dept Math Sci Dhahran 31261 Saudi Arabia

This paper derives a robust Kalman smoother estimate for the errors-in-variables state space model that is less sensitive to outliers in the sense of the multivariate least trimmed squares (MLTS) method. Since the MLTS estimate is a combinatorial optimization problem, the randomized algorithm has been proposed. However, the uniform sampling method has a high computational cost and may lead to a biased estimate. Therefore, we apply the subsampling method. The algorithm presented here is both efficient and easy to implement. A Monte Carlo simulation result shows the efficiency of the proposed algorithm.

关键词： errors-in-variables state space model multivariate least trimmed squares Kalman filter and smoother outliers random search algorithm subsampling method

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Design optimization of offshore wind farms with multiple types of wind turbines

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APPLIED ENERGY 2017年 205卷 1283-1297页

作者： Feng, Ju Shen, Wen Zhong Tech Univ Denmark Dept Wind Energy DK-2800 Lyngby Denmark

Most studies on offshore wind farm design assume a uniform wind farm, which consists of an identical type of wind turbines. In order to further reduce the cost of energy, we investigate the design of non-uniform offshore wind farms, i.e., wind farms with multiple types of wind turbines and hub-heights. Given a set of different types of wind turbines with a different default hub height for each type, we can specify the design of a wind farm by the types of turbines, number of turbines for each type, and turbine locations. We consider the optimization of such design to minimize the levelized cost of energy, which is calculated using a capital cost model that covers the turbine cost and the balance of plant cost. An empirical wind turbine design cost and scaling model is utilized to model the cost of turbines with different sizes. Constraints on wind farm boundary, wind turbine proximity and total capacity are also included. We solve the problem with a newly developed extended random search algorithm and tested it in a realistic design optimization problem based on the Horns Rev 1 offshore wind farm in Denmark. The optimized non-uniform designs are compared with their uniform counterparts. We find that a non-uniform design can achieve a lower levelized cost of energy than its uniform counterparts, when the capital cost per MW is slightly lower for the smaller size turbine. Comparison with the mixed-discrete particle swarm optimization algorithm is also carried out for a non-uniform wind farm design problem with a fixed number of turbines, which shows the effectiveness and superiority of the proposed algorithm. Finally, the advantages and possible disadvantages of non-uniform design are also identified and discussed.

关键词： Offshore wind farm Non-uniform wind farm Layout optimization Design optimization random search algorithm Levelized cost of energy

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Robust synthesis of a PID controller by uncertain multimodel approach

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INFORMATION SCIENCES 2007年第6期177卷 1441-1451页

作者： Toscano, R. ENISE ECL CNRS UMR5513Lab Tribol & Dynam Syst F-42023 St Etienne 2 France

This paper presents an effective method to design a PID (or PI) controller for nonlinear systems where desirable robustness and performance properties must be maintained across a large range of operating conditions. For this purpose, an uncertain multimodel of the original nonlinear system is used. The uncertainties affecting the system are treated as stochastic matrices. Based on this multimodel representation a robust PID controller can be designed in order to obtain acceptable performance for all operating conditions. Numerical examples show the practical applicability of the proposed method. (c) 2006 Elsevier Inc. All rights reserved.

关键词： PID controller multimodel multi-PID parametric uncertainties robust stability random search algorithm

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Monte Carlo simulation via a numerical algorithm for solving a nonlinear inverse problem

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2010年第9期15卷 2436-2444页

作者： Farnoosh, R. Ebrahimi, M. Iran Univ Sci & Technol Narmak Sch Math Tehran 16846 Iran

This paper is intended to provide a numerical algorithm involving the combined use of the finite differences scheme and Monte Carlo method for estimating the diffusion coefficient in a one-dimensional nonlinear parabolic inverse problem. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. To modify the values of estimated coefficients of this polynomial form, we introduce a random search algorithm in Monte Carlo method for global optimization. A numerical test is performed in order to show the efficiency and accuracy of the present work. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Nonlinear inverse problem Finite differences scheme Monte Carlo optimization Diffusion coefficient random search algorithm

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A novel geometric model of breathing crack and its influence on rotor dynamics

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JOURNAL OF VIBRATION AND CONTROL 2022年第21-22期28卷 3411-3425页

作者： Ganguly, Krishanu Roy, Haraprasad Natl Inst Technol Dept Mech Engn Rourkela Orissa India

The present research focuses on performing the dynamic study of a cracked, internally damped, composite rotating shaft system with journal bearing end supports. A novel mathematical formulation is proposed to introduce a time-varying stiffness matrix for simulating the breathing behaviour of the crack. The random search algorithm is used as one of the metaheuristic processes to carry out the optimization and generate time-dependent geometric parameters of the cracked surface for one full rotation. The derived stiffness matrix is used in the composite shaft's higher order motion equation obtained through equivalent modulus theory, whose internal damping properties are incorporated using operator-based viscoelastic model. Eigenanalysis is carried out to perform a thorough study of dynamic characteristics of cracked shaft considering the crack depth and crack position as two important parameters. The effect of crack on stacking sequence as well as mode shapes of the heterogeneous laminated shaft is also studied.

关键词： Cracked composite shaft breathing crack model random search algorithm time-varying stiffness eigenanalysis

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ROBUST KALMAN FILTER AND SMOOTHER FOR ERRORS-IN-VARIABLES STATE SPACE MODELS WITH OBSERVATION OUTLIERS BASED ON THE MINIMUM-COVARIANCE DETERMINANT ESTIMATOR

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ASIAN JOURNAL OF CONTROL 2011年第4期13卷 513-521页

作者： Almutawa, Jaafar King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In this paper, we propose a robust Kalman filter and smoother for the errors-in-variables (EIV) state space models subject to observation noise with outliers. We introduce the EIV problem with outliers and then present the minimum covariance determinant (MCD) estimator which is a highly robust estimator in terms of protecting the estimate from the outliers. Then, we propose the randomized algorithm to find the MCD estimate. However, the uniform sampling method has a high computational cost and may lead to biased estimates, therefore we apply the sub-sampling method. A Monte Carlo simulation result shows the efficiency of the proposed algorithm.

关键词： Errors-in-variables model state space models minimum covariance determinant Kalman filter and smoother outliers random search algorithm sub-sampling method

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Multi-loop PI/PID controllers design for disturbance rejection based on non-parametric effective model and non-convex optimisation

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IET CONTROL THEORY AND APPLICATIONS 2014年第15期8卷 1499-1512页

作者： Jin, Qibing Liu, Qie Beijing Univ Chem Technol Coll Informat Sci & Technol Inst Automat Beijing 100029 Peoples R China

In this study, the authors address the design of the multi-loop controllers for multi-input and multi-output (MIMO) processes for disturbance rejection. Three types of disturbance rejection are analysed, and they demonstrate that those disturbance responses are directly related to the integral terms of the controllers. A concept of non-parametric effective model is introduced here to decompose a MIMO control system into several equivalent single-input and single-output control systems. Based on the effective model in each loop, a non-convex optimisation problem is established to obtain the optimal controller parameters with certain robustness indices. Considering the drawbacks of using random search algorithm, they develop a numerical algorithm to solve this non-convex optimisation problem. Simulation studies demonstrate that the proposed method improves the disturbance rejection compared with other decentralised controllers.

关键词： MIMO systems three-term control PI control control system synthesis concave programming optimal control search problems numerical analysis multiloop PI-PID controllers design disturbance rejection nonparametric effective model multi-input and multi-output processes disturbance responses MIMO control system nonconvex optimisation problem equivalent single-input and single-output control systems optimal controller parameters certain robustness indices random search algorithm numerical algorithm decentralised controllers

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Identification of errors-in-variables state space models with observation outliers based on minimum covariance determinant

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JOURNAL OF PROCESS CONTROL 2009年第5期19卷 879-887页

作者： AlMutawa, Jaafar King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In this paper, a subspace system identification algorithm for the errors-in-variables (EIV) state space models subject to observation noise with outliers has been developed. By using the minimum covariance determinant (MCD) estimator, the outliers have been identified and deleted. Then the classical EIV subspace system identification algorithms have been applied to estimate the parameters of the state space models. In order to solve the MCD problem for the EIV state space models, a random search algorithm has been proposed. A Monte-Carlo simulation results demonstrate the effectiveness of the proposed algorithm. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Subspace system identification Errors-in-variables State space models Outliers Minimum covariance determinant random search algorithm

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