Balancing of Flexible Rotors Using Convex Optimization Techniques: Optimum Min-Max LMI Influence Coefficient Balancing

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Costin D. Untaroiu ◽  
Paul E. Allaire ◽  
William C. Foiles
Keyword(s):  
Convex Optimization ◽  
Optimization Theory ◽  
Numerical Algorithms ◽  
Optimization Methods ◽  
Industrial Applications ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Influence Coefficient ◽  
Flexible Rotors ◽  
Optimum Solution

In some industrial applications, influence coefficient balancing methods fail to find the optimum vibration reduction due to the limitations of the least-squares optimization methods. Previous min-max balancing methods have not included practical constraints often encountered in industrial balancing. In this paper, the influence coefficient balancing equations, with suitable constraints on the level of the residual vibrations and the magnitude of correction weights, are cast in linear matrix inequality (LMI) forms and solved with the numerical algorithms developed in convex optimization theory. The effectiveness and flexibility of the proposed method have been illustrated by solving two numerical balancing examples with complicated requirements. It is believed that the new methods developed in this work will help in reducing the time and cost of the original equipment manufacturer or field balancing procedures by finding an optimum solution of difficult balancing problems. The resulting method is called the optimum min-max LMI balancing method.

scholarly journals Optimization for Software Implementation of Fractional Calculus Numerical Methods in an Embedded System

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 566
Author(s):  
Mariusz Matusiak
Keyword(s):  
Embedded System ◽  
Fractional Order ◽  
Numerical Algorithms ◽  
Computation Time ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Software Implementation ◽  
Software Optimization ◽  
Fractional Order Differential Equations ◽  
Non Locality

In this article, some practical software optimization methods for implementations of fractional order backward difference, sum, and differintegral operator based on Grünwald–Letnikov definition are presented. These numerical algorithms are of great interest in the context of the evaluation of fractional-order differential equations in embedded systems, due to their more convenient form compared to Caputo and Riemann–Liouville definitions or Laplace transforms, based on the discrete convolution operation. A well-known difficulty relates to the non-locality of the operator, implying continually increasing numbers of processed samples, which may reach the limits of available memory or lead to exceeding the desired computation time. In the study presented here, several promising software optimization techniques were analyzed and tested in the evaluation of the variable fractional-order backward difference and derivative on two different Arm® Cortex®-M architectures. Reductions in computation times of up to 75% and 87% were achieved compared to the initial implementation, depending on the type of Arm® core.

Design of water distribution systems using an intelligent simple benchmarking algorithm with respect to cost optimization and computational efficiency

2019 ◽  
Vol 19 (7) ◽  
pp. 1892-1898 ◽  
Author(s):  
Sachin Shende ◽  
K. W. Chau
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Heuristic Algorithms ◽  
Cost Optimization ◽  
Minimum Cost ◽  
Water Distribution Network ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Hydraulic Simulation ◽  
Optimum Solution

Abstract The increasing stress on the water distribution network (WDN) considering demand satisfaction with minimum cost has inspired designers to apply various optimization techniques to meet the consequent challenges. The traditional way of using optimization methods, e.g. stochastic meta-heuristic algorithms, have come along with various constraints to explore an optimum solution. In this study, a newly developed meta-heuristic algorithm called the Simple Benchmarking Algorithm (SBA) is used to optimize pipe size. A modified approach with SBA having interfaces with the EPANET 2.0 hydraulic simulation model is used to compute the minimum cost of the two-loop network and the Hanoi benchmark WDN. Results show that SBA is more efficient in obtaining the least possible cost with fast convergence.

Digital Control Design Via Convex Optimization

1993 ◽  
Vol 115 (4) ◽  
pp. 579-586 ◽  
Author(s):  
R. E. Avedon ◽  
B. A. Francis
Keyword(s):  
Convex Optimization ◽  
Operator Theory ◽  
Design Method ◽  
Numerical Algorithms ◽  
Optimization Techniques ◽  
Data Systems ◽  
Sampled Data ◽  
Design Heuristics ◽  
Stability Robustness ◽  
Data Design

A design method for sampled-data systems is presented incorporating robust control theory and convex optimization techniques. The technique is developed using operator theory applied to the relevant input-output operators for both performance and stability robustness. Numerical algorithms and an example for the SISO case are presented to explore some traditional sampled-data design heuristics.

scholarly journals Suboptimal Disturbance Observer Design Using All Stabilizing Q Filter for Precise Tracking Control

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh
Keyword(s):  
Design Method ◽  
Industrial Applications ◽  
Point Of View ◽  
Observer Design ◽  
Linear Matrix ◽  
External Disturbances ◽  
Closed Loop Systems ◽  
Control Target ◽  
The Stability ◽  
Unified Index

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.

scholarly journals Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

2015 ◽  
Vol 25 (4) ◽  
pp. 815-826 ◽  
Author(s):  
Máximo Ramírez ◽  
Raúl Villafuerte ◽  
Temoatzin González ◽  
Miguel Bernal
Keyword(s):  
Nonlinear Systems ◽  
Mimo System ◽  
Sufficient Conditions ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Exponential Estimates ◽  
Novel Approach ◽  
Guaranteed Cost ◽  
Stability And Stabilization ◽  
Twin Rotor Mimo System

Abstract This work introduces a novel approach to stability and stabilization of nonlinear systems with delayed multivariable inputs; it provides exponential estimates as well as a guaranteed cost of the system solutions. The result is based on an exact convex representation of the nonlinear system which allows a Lyapunov–Krasovskii functional to be applied in order to obtain sufficient conditions in the form of linear matrix inequalities. These are efficiently solved via convex optimization techniques. A real-time implementation of the developed approach on the twin rotor MIMO system is included.

scholarly journals Calibration of a Nonlinear DC Motor under Uncertainty Using Nonlinear Optimization Techniques

2021 ◽  
Vol 65 (1) ◽  
pp. 42-52
Author(s):  
Hamed Keshmiri Neghab ◽  
Hamid Keshmiri Neghab
Keyword(s):  
Nonlinear Optimization ◽  
Model Calibration ◽  
Optimization Methods ◽  
Dc Motor ◽  
Optimization Techniques ◽  
Unknown Parameters ◽  
Labview Software ◽  
Dc Motors ◽  
Industrial Software ◽  
Nonlinear Optimization Methods

The use of DC motors is increasingly high and it has more parameters which should be normalized. Now the calibration of each parameters is important for each motor, because it affects in its performance and accuracy. A lot of researches are investigated in this area. In this paper demonstrated how to estimate the parameters of a Nonlinear DC Motor using different Nonlinear Optimization techniques of fitting parameters to model, that called model calibration. First, three methods for calibration of a DC motor are defined, then unknown parameters of the mathematical model with the nonlinear optimization techniques for the fitting routines and model calibration process, are identified. In addition, three optimization techniques such as Levenberg-Marquardt, Constrained Nonlinear Optimization and Gauss-Newton, are compared. The goal of this paper is to estimate nonlinear parameters of a DC motor under uncertainty with nonlinear optimization methods by using LabVIEW software as an industrial software and compare the nonlinear optimization methods based on position, velocity and current. Finally, results are illustrated and comparison between these methods based on the results are made.

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