Short Comments on an Energy Pumping Levels in a MEMS Gyroscope Vibrating Problem, by Using of an Global and Local Optimal Linear Control Design

This paper deals with an energy pumping that occurs in a (MEMS) Gyroscope nonlinear dynamical system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We also developed a linear optimal control design for reducing the oscillatory movement of the nonlinear systems to a stable point.

An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A model for optimal chemical control of leaf area damaged by fungi population - Parameter dependence

We present a model to study a fungi population submitted to chemical control, incorporating the fungicide application directly into the model. From that, we obtain an optimal control strategy that minimizes both the fungicide application (cost) and leaf area damaged by fungi population during the interval between the moment when the disease is detected (t = 0) and the time of harvest (t = t(f)). Initially, the parameters of the model are considered constant. Later, we consider the apparent infection rate depending on the time (and the temperature) and do some simulations to illustrate and to compare with the constant case.

Necessary conditions for optimal impulsive control problems

A Maximum Principle is derived for a class of optimal control problems arising in midcourse guidance, in which certain controls are represented by measures and, the state trajectories are functions of bounded variation. The optimality conditions improves on previous optimality conditions by allowing nonsmooth data, measurable time dependence, and a possibly time varying constraint set for the conventional controls.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

A new sufficient condition for optimal impulsive control problems

In this article we introduce the concept of MP-pseudoinvexity for general nonlinear impulsive optimal control problems whose dynamics are specified by measure driven control equations. This is a general paradigm in that, both the absolutely continuous and singular components of the dynamics depend on both the state and the control variables. The key result consists in showing the sufficiency for optimality of the MP-pseudoinvexity. It is proved that, if this property holds, then every process satisfying the maximum principle is an optimal one. This result is obtained in the context of a proper solution concept that will be presented and discussed. © 2012 IEEE.

Optimal linear control to parametric uncertainties in a micro electro mechanical system

This paper, a micro-electro-mechanical systems (MEMS) with parametric uncertainties is considered. The non-linear dynamics in MEMS system is demonstrated with a chaotic behavior. We present the linear optimal control technique for reducing the chaotic movement of the micro-electromechanical system with parametric uncertainties to a small periodic orbit. The simulation results show the identification by linear optimal control is very effective. © 2013 Academic Publications, Ltd.

Vibration Control Applied in a Semi-Active Suspension using Magneto Rheological Damper and Optimal Linear Control Design

In this paper we study the behavior of a semi-active suspension witch external vibrations. The mathematical model is proposed coupled to a magneto rheological (MR) damper. The goal of this work is stabilize of the external vibration that affect the comfort and durability an vehicle, to control these vibrations we propose the combination of two control strategies, the optimal linear control and the magneto rheological (MR) damper. The optimal linear control is a linear feedback control problem for nonlinear systems, under the optimal control theory viewpoint We also developed the optimal linear control design with the scope in to reducing the external vibrating of the nonlinear systems in a stable point. Here, we discuss the conditions that allow us to the linear optimal control for this kind of non-linear system.

Optimal current control for sub-unity power factor correction

Switching mode power supplies (SMPS) are subject to low power factor and high harmonic distortions. Active power-factor correction (APFC) is a technique to improve the power factor and to reduce the harmonic distortion of SMPSs. However, this technique results in double frequency output voltage variation which can be reduced by using a large output capacitance. Using large capacitors increases the cost and size of the converter. Furthermore, the capacitors are subject to frequent failures mainly caused by evaporation of the electrolytic solution which reduce the converter reliability. This thesis presents an optimal control method for the input current of a boost converter to reduce the size of the output capacitor. The optimum current waveform as a function of weighing factor is found by using the Euler Lagrange equation. A set of simulations are performed to determine the ideal weighing which gives the lowest possible output voltage variation as the converter still meets the IEC-61000-3-2 class-A harmonics requirements with a power factor of 0.8 or higher. The proposed method is verified by the experimental work. A boost converter is designed and it is run for different power levels, 100 W, 200 W and 400 W. The desired output voltage ripple is 10 V peak to peak for the output voltage of 200 Vdc. This ripple value corresponds to a ± 2.5% output voltage ripple. The experimental and the simulation results are found to be quite matching. A significant reduction in capacitor size, as high as 50%, is accomplished by using the proposed method.

Optimal game theoretic distributed control methodologies in small scale power systems

This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.

A Bayesian perspective on stochastic neurocontrol

Control design for stochastic uncertain nonlinear systems is traditionally based on minimizing the expected value of a suitably chosen loss function. Moreover, most control methods usually assume the certainty equivalence principle to simplify the problem and make it computationally tractable. We offer an improved probabilistic framework which is not constrained by these previous assumptions, and provides a more natural framework for incorporating and dealing with uncertainty. The focus of this paper is on developing this framework to obtain an optimal control law strategy using a fully probabilistic approach for information extraction from process data, which does not require detailed knowledge of system dynamics. Moreover, the proposed control method framework allows handling the problem of input-dependent noise. A basic paradigm is proposed and the resulting algorithm is discussed. The proposed probabilistic control method is for the general nonlinear class of discrete-time systems. It is demonstrated theoretically on the affine class. A nonlinear simulation example is also provided to validate theoretical development.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

Optimal Controller Designs for Rotating Machines - Penalising the Rate of Change of Control Forcing

In the context of active control of rotating machines, standard optimal controller methods enable a trade-off to be made between (weighted) mean-square vibrations and (weighted) mean-square currents injected into magnetic bearings. One shortcoming of such controllers is that no concern is devoted to the voltages required. In practice, the voltage available imposes a strict limitation on the maximum possible rate of change of control force (force slew rate). This paper removes the aforementioned existing shortcomings of traditional optimal control.

Efficient control of an autonomous underwater vehicle while accounting for thruster failure

This paper is concerned with the design and implementation of control strategies onto a test-bed vehicle with six degrees-of-freedom. We design our trajectories to be efficient in time and in power consumption. Moreover, we also consider cases when actuator failure can arise and discuss alternate control strategies in this situation. Our calculations are supplemented by experimental results.