Linear-quadratic optimal control of descriptor systems

In recent years the analysis and synthesis of (mechanical) control systems in descriptor form has been established. This general description of dynamical systems is important for many applications in mechanics and mechatronics, in electrical and electronic engineering, and in chemical engineering as well. This contribution deals with linear mechanical descriptor systems and its control design with respect to a quadratic performance criterion. Here, the notion of properness plays an important role whether the standard Riccati approach can be applied as usual or not. Properness and non-properness distinguish between the cases if the descriptor system is exclusively governed by the control input or by its higher-order time-derivatives additionally. In the unusual case of non-proper systems a quite different problem of optimal control design has to be considered. Both cases will be solved completely.

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Active control in flexible plates with piezoelectric actuators using linear matrix inequalities

The study of algorithms for active vibrations control in flexible structures became an area of enormous interest, mainly due to the countless demands of an optimal performance of mechanical systems as aircraft, aerospace and automotive structures. Smart structures, formed by a structure base, coupled with piezoelectric actuators and sensor are capable to guarantee the conditions demanded through the application of several types of controllers. The actuator/sensor materials are composed by piezoelectric ceramic (PZT - Lead Zirconate Titanate), commonly used as distributed actuators, and piezoelectric plastic films (PVDF-PolyVinyliDeno Floride), highly indicated for distributed sensors. The design process of such system encompasses three main phases: structural design; optimal placement of sensor/actuator (PVDF and PZT); and controller design. Consequently, for optimal design purposes, the structure, the sensor/actuator placement and the controller have to be considered simultaneously. This article addresses the optimal placement of actuators and sensors for design of controller for vibration attenuation in a flexible plate. Techniques involving linear matrix inequalities (LMI) to solve the Riccati's equation are used. The controller's gain is calculated using the linear quadratic regulator (LQR). The major advantage of LMI design is to enable specifications such as stability degree requirements, decay rate, input force limitation in the actuators and output peak bounder. It is also possible to assume that the model parameters involve uncertainties. LMI is a very useful tool for problems with constraints, where the parameters vary in a range of values. Once formulated in terms of LMI a problem can be solved efficiently by convex optimization algorithms.

Non-linear Control of an Autonomous Ground Vehicle

In this paper, in order to select a speed controller for a specific non-linear autonomous ground vehicle, proportional-integral-derivative (PID), Fuzzy, and linear quadratic regulator (LQR) controllers were designed. Here, in order to carry out the tuning of the above controllers, a multicomputer genetic algorithm (MGA) was designed. Then, the results of the MGA were used to parameterize the PID, Fuzzy and LQR controllers and to test them under laboratory conditions. Finally, a comparative analysis of the performance of the three controllers was conducted.

Equilibrium existence in the circle model with linear quadratic transport cost

We treat the problem of existence of a location-then-price equilibrium in the circle model with a linear quadratic type of transportation cost function which can be either convex or concave. We show the existence of a unique perfect equilibrium for the concave case when the linear and quadratic terms are equal and of a unique perfect equilibrium for the convex case when the linear term is equal to zero. Aside from these two cases, there are feasible locations by the firms for which no equilibrium in the price subgame exists. Finally, we provide a full taxonomy of the price equilibrium regions in terms of weights of the linear and quadratic terms in the cost function.

Study on the development of an autonomous mobile robot

Dissertação para obtenção do Grau de Mestre em Engenharia Eletrotécnica e de Computadores

Balance-bot

Research on inverted pendulum has gained momentum over the last decade on a number of robotic laboratories over the world; due to its unstable proprieties is a good example for control engineers to verify a control theory. To verify that the pendulum can balance we can make some simulations using a closed-loop controller method such as the linear quadratic regulator or the proportional–integral–derivative method. Also the idea of robotic teleoperation is gaining ground. Controlling a robot at a distance and doing that precisely. However, designing the tool to takes the best benefit of the human skills while keeping the error minimal is interesting, and due to the fact that the inverted pendulum is an unstable system it makes a compelling test case for exploring dynamic teleoperation. Therefore this thesis focuses on the construction of a two-wheel inverted pendulum robot, which sensor we can use to do that, how they must be integrated in the system and how we can use a human to control an inverted pendulum. The inverted pendulum robot developed employs technology like sensors, actuators and controllers. This Master thesis starts by presenting an introduction to inverted pendulums and some information about related areas such as control theory. It continues by describing related work in this area. Then we describe the mathematical model of a two-wheel inverted pendulum and a simulation made in Matlab. We also focus in the construction of this type of robot and its working theory. Because this is a mobile robot we address the theme of the teleoperation and finally this thesis finishes with a general conclusion and ideas of future work.

System identification and active vibration control of a flexible structure

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Short and long period optimization of drug doses in the treatment of AIDS

Técnicas de otimização numérica são úteis na solução de problemas de determinação da melhor entrada para sistemas descritos por modelos matemáticos e cujos objetivos podem ser expressos de uma maneira quantitativa. Este trabalho aborda o problema de otimizar as dosagens dos medicamentos no tratamento da AIDS em termos de um balanço entre a resposta terapêutica e os efeitos colaterais. Um modelo matemático para descrever a dinâmica do vírus HIV e células CD4 é utilizado para calcular a dosagem ótima do medicamento no tratamento a curto prazo de pacientes com AIDS por um método de otimização direta utilizando uma função custo do tipo Bolza. Os parâmetros do modelo foram ajustados com dados reais obtidos da literatura. Com o objetivo de simplificar os procedimentos numéricos, a lei de controle foi expressa em termos de uma expansão em séries que, após truncamento, permite obter controles sub-ótimos. Quando os pacientes atingem um estado clínico satisfatório, a técnica do Regulador Linear Quadrático (RLQ) é utilizada para determinar a dosagem permanente de longo período para os medicamentos. As dosagens calculadas utilizando a técnica RLQ , tendem a ser menores do que a equivalente terapia de dose constante em termos do expressivo aumento na contagem das células T+ CD4 e da redução da densidade de vírus livre durante um intervalo fixo de tempo.

Optimal placement of sensors/actuators in truss structures with known disturbances

An important stage in the solution of active vibration control in flexible structures is the optimal placement of sensors and actuators. In many works, the positioning of these devices in systems governed for parameter distributed is, mainly, based, in controllability approach or criteria of performance. The positions that enhance such parameters are considered optimal. These techniques do not take in account the space variation of disturbances. An way to enhance the robustness of the control design would be to locate the actuators considering the space distribution of the worst case of disturbances. This paper is addressed to include in the formulation of problem of optimal location of sensors and piezoelectric actuators the effect of external disturbances. The paper concludes with a numerical simulation in a truss structure considering that the disturbance is applied in a known point a priori. As objective function the C norm system is used. The LQR (Linear Quadratic Regulator) controller was used to quantify performance of different sensors/actuators configurations.

Identification of structural parameters for active vibration control

The study of algorithms for active vibration control in flexible structures became an area of enormous interest for some researchers due to the innumerable requirements for better performance in mechanical systems, as for instance, aircrafts and aerospace structures. Intelligent systems, constituted for a base structure with sensors and actuators connected, are capable to guarantee the demanded conditions, through the application of diverse types of controllers. For the project of active controllers it is necessary, in general, to know a mathematical model that enable the representation in the space of states, preferential in modal coordinates to permit the truncation of the system and reduction in the order of the controllers. For practical applications of engineering, some mathematical models based in discrete-time systems cannot represent the physical problem, therefore, techniques of identification of system parameters must be used. The techniques of identification of parameters determine the unknown values through the manipulation of the input (disturbance) and output (response) signals of the system. Recently, some methods have been proposed to solve identification problems although, none of them can be considered as being universally appropriate to all the situations. This paper is addressed to an application of linear quadratic regulator controller in a structure where the damping, stiffness and mass matrices were identified through Chebyshev's polynomial functions.

Controle com Estrutura Variável e Modos Deslizantes Aplicado em Sistema de Suspensão Ativa

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Diagnose de trincas em sistemas rotativos, utilizando modelos de falhas através da metodologia dos observadores de estados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Diagnose de falhas em sistemas rotativos com excitações desconhecidas, através da metodologia dos observadores de estado

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controle ativo de vibrações em estruturas espaciais tipo treliças usando controladores IMSC

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)