Applications of regulator theory are ubiquitous in control theory, encompassing almost all areas of systems and control engineering. Examples include active noise suppression [Banks et al., Decision and Control, Activ...
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Applications of regulator theory are ubiquitous in control theory, encompassing almost all areas of systems and control engineering. Examples include active noise suppression [Banks et al., Decision and Control, Active Noise Control: Piezoceramic Actuators in Fluid/structure Interaction Models, IEEE, Los Alamitos, CA (1991) 2328-2333], design and control of energy efficient buildings [Borggaard et al., Control, Estimation and Optimization of Energy Efficient Buildings. Riverfront, St. Louis, MO (2009) 837-841.] and control of heat exchangers [Aulisa et al., IFAC-PapersOnLine 49 (2016) 104-109.]. Numerous other examples can be found in [Aulisa and Gilliam, A Practical Guide to Geometric Regulation for Distributed Parameter Systems. Chapman and Hall/CRC, Boca Raton (2015).]. In the geometric approach to asymptotic regulation the main object of interest is a pair of operator equations called the regulator equations, whose solution provides a control solving the tracking/disturbance rejection regulation problem. In this paper we present an iterativealgorithm, called the beta-iteration method, which is based on the geometric methodology, and delivers accurate control laws for approximate asymptotic regulation. This iterative scheme has been successfully applied to a wide range of linear and nonlinear multi-physics examples and in practice only one or two iterations are usually required to deliver sufficiently accurate results. One drawback to these research efforts is that no proof was given of the convergence of the method. This work contains a detailed analysis of the error in the iterative scheme for a large class of linear distributed parameter systems. In particular we show that the iterative errors converge at a geometric rate. We demonstrate our estimates on three control problems in multi-physics applications.
This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory a...
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This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample's response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.
This study presents a new analytic approach to optimal coordination of directional overcurrent relays. This approach is based on the selection of optimum pickup current and time dial setting, in order to obtain minimu...
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This study presents a new analytic approach to optimal coordination of directional overcurrent relays. This approach is based on the selection of optimum pickup current and time dial setting, in order to obtain minimum operating time for the relays, while satisfying various coordination and boundary constraints. Based on the new optimal relay setting procedure, an iterativenumerical solution is proposed. The proposed numericalalgorithm converges to the global optimum values, which are independent of initial values and the order of relay setting. The proposed method is applied to three different test systems. The new method is compared with some previously proposed analytic and evolutionary approaches. The results demonstrate the advantages of the proposed method over the previous works.
The authors assume a linear equidistance antenna array as the receiver for a fixed frame-length multiple-access system, which employs variable-gain receiver power and repetition encoding. They propose a robust maximum...
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The authors assume a linear equidistance antenna array as the receiver for a fixed frame-length multiple-access system, which employs variable-gain receiver power and repetition encoding. They propose a robust maximum a posteriori probability (MAP) blind bit-rate detector (BBRD). This detector considers the rate detection (RD) as a multi-hypothesis test and maximises the likelihood functions (LFs) to find the true bit-rate, whereas the complex amplitude of the received signal, the noise variance and the direction of arrival are unknown parameters. First, assuming that the location parameter is known and the information sequence are independent and uniformly distributed random variables, the authors propose a hybrid likelihood ratio test (HLRT). The proposed HLRT requires to solve a set of non-linear equations that have no closed-form solution. Thus, an iterative numerical algorithm is proposed. In addition, a quasi-HLR detector which has a significantly lower computational complexity is also proposed. In the case of unknown location parameter, the authors develop two quasi-HLR methods. They use fast Fourier transform and search to estimate the unknown location. In Q-HLRT-Method-I, the non-linear equation similar to the one in known location parameter is iteratively solved. In Q-HLRT-Method-II, a low complexity solution is proposed. Simulation examples evaluate and compare the performances of the proposed BBRDs.
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