Transient Optimization of an Electrically-Damped Cantilever-Supported Microactuator and the Pull-In Analysis

2000 ◽  
Author(s):  
Yijian Chen ◽  
Yashesh Shroff ◽  
William G. Oldham
Keyword(s):  
Optimal Control ◽  
Simple Model ◽  
Dynamic System ◽  
Perturbation Method ◽  
Performance Index ◽  
Transient Behavior ◽  
Linear Control ◽  
Control Parameters ◽  
Linear Control Theory ◽  
The Stability

Abstract Analytic modeling of the transient behavior of an electrically-damped cantilever-supported microactuator using the perturbation method and linear control theory is presented. Five control parameters are identified and the transient optimization of the dynamic system to reduce the overshoot and settling time is carried out. With the ITAE performance index minimized, the optimal control parameters are obtained and the resultant optimized transient behavior is shown. We apply the Routh-Hurwitz criterion to analyze the stability of the dynamic system and three inequality relations for a stable system are derived. The pull-in phenomenon for a short-cantilever actuator is investigated with this simple model.

Parasitic-Capacitance-Induced Degradation of the Transient Behavior of Electrically-Damped Microactuators

2000 ◽  
Author(s):  
Yijian Chen ◽  
Yashesh Shroff ◽  
William G. Oldham
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Perturbation Method ◽  
Transient Behavior ◽  
Parasitic Capacitance ◽  
Linear Control ◽  
Control Parameters ◽  
Analytic Modeling ◽  
Linear Control Theory ◽  
Capacitance Effect

Abstract The influence of the parasitic capacitance on the transient behavior of two electrically-damped microactuators is investigated. Analytic modeling of the parasitic-capacitance effect is performed using the perturbation method and linear control theory. We show that the optimal control parameters are changed by the parasitic capacitance. The resultant degradation of the optimal transient behavior of two actuators is observed.

A Generalization of the Bang-Bang Principle of Linear Control Theory*

1965 ◽  
Vol 8 (6) ◽  
pp. 783-789
Author(s):  
Richard Datko
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Matrix Function ◽  
Linear Time ◽  
Time Optimal Control ◽  
Linear Control ◽  
Dimensional Vector ◽  
R Matrix ◽  
Linear Control Theory ◽  
Time Optimal

In a paper by LaSalle [l] on linear time optimal control the following lemma is proved:Let Ω be the set of all r-dimensional vector functions U(τ) measurable on [ 0, t] with |ui(τ)≦1. Let Ωo be the subset of functions uo(τ) with |uoi(τ) = 1. Let Y(τ) be any (n × r ) matrix function in L1([ 0, t]).

Bifurcation Control of in Morris-Lecar Neuron Model via Washout Filter with a Linear Term Based on Filter-Aided Dynamic Feedback

2012 ◽  
Vol 485 ◽  
pp. 600-603 ◽  
Author(s):  
Hai Long Duan ◽  
Cheng Kun Cui ◽  
Chun Xiao Han ◽  
Yan Qiu Che
Keyword(s):  
Electrical Stimulation ◽  
Stability Criterion ◽  
Neuron Model ◽  
Linear Control ◽  
Control Parameters ◽  
Dynamic Feedback ◽  
Hurwitz Stability ◽  
Washout Filter ◽  
Simulation Results ◽  
The Stability

In this paper, based on Routh-Hurwitz stability criterion, the linear control term of washout filter-aided dynamic feedback controller is added to the Morris-Lecar (ML) system to stabilize the bifurcation. We deduce the linear control parameters according to the stability criterion, and the simulation results indicate that the controller is effective to stabilize ML model. In addition, electrical stimulation is selected as an output of the controller, thus it may provide theoretical guidance for clinical diagnosis and therapy of dynamical diseases.

scholarly journals Stabilization and Analytic Approximate Solutions of an Optimal Control Problem

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 476-487 ◽  
Author(s):  
Camelia Pop ◽  
Camelia Petrişor ◽  
Remus-Daniel Ene
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Equilibrium Points ◽  
Approximate Solutions ◽  
Linear Control ◽  
Runge Kutta Method ◽  
The Stability ◽  
Stability Results

Abstract This paper analyses a dynamical system derived from a left-invariant, drift-free optimal control problem on the Lie group SO(3) × ℝ3 × ℝ3 in deep connection with the important role of the Lie groups in tackling the various problems occurring in physics, mathematics, engineering and economic areas [1, 2, 3, 4, 5]. The stability results for the initial dynamics were inconclusive for a lot of equilibrium points (see [6]), so a linear control has been considered in order to stabilize the dynamics. The analytic approximate solutions of the resulting nonlinear system are established and a comparison with the numerical results obtained via the fourth-order Runge-Kutta method is achieved.

Asymptotic Treatment of Non-Classically Damped Linear Systems

1995 ◽  
Vol 48 (11S) ◽  
pp. S111-S117
Author(s):  
W. Fang ◽  
J.-G. Tseng ◽  
J. A. Wickert
Keyword(s):  
Eigenvalue Problem ◽  
Dynamic System ◽  
Perturbation Method ◽  
Quadratic Forms ◽  
Vibration Modes ◽  
Discrete Dynamic System ◽  
Damped System ◽  
Base Solution ◽  
The Stability ◽  
Dissipative Terms

The presence of non-classical dissipation in a general discrete dynamic system is investigated through a perturbation method for the eigenvalues and vectors. Results accurate to second-order are obtained, with corrections to the base solution being expressed in terms of readily-calculated quadratic forms. Exact solutions, and the derived asymptotic ones, are compared with the predictions of the so-called method of approximate decoupling, in which certain non-classical dissipative terms are omitted from calculations in the eigenvalue problem. The perturbation method is discussed through its application in several examples, indicating circumstances in which a non-classically damped system can be well-approximated by an “equivalent” classically damped one. Somewhat surprisingly, the addition of non-classical damping does not necessarily increase the stability of all vibration modes, and the perturbation method is shown to be useful in identifying those critical modes.

OPTIMAL LINEAR CONTROL APPLIED IN A ENERGY HARVESTING DYNAMIC SYSTEM WITH PERIODIC EXCITATION

2019 ◽  
Author(s):  
Estevão Fuzaro de Almeida ◽  
Fabio Roberto Chavarette ◽  
Douglas da Costa Ferreira
Keyword(s):  
Energy Harvesting ◽  
Dynamic System ◽  
Linear Control ◽  
Periodic Excitation ◽  
Optimal Linear

scholarly journals Dynamical system of the growth of COVID-19 with controller

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Dania Altulea ◽  
Rafida M. Elobaid
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Growth Rate ◽  
Dynamic System ◽  
Unique Solution ◽  
Population Dynamic ◽  
Integral Control ◽  
The Social ◽  
Social Separation ◽  
Strong Control

AbstractRecently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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