Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Root locus of fractional linear systems

In this paper an algorithm for the calculation of the root locus of fractional linear systems is presented. The proposed algorithm takes advantage of present day computational resources and processes directly the characteristic equation, avoiding the limitations revealed by standard methods. The results demonstrate the good performance for different types of expressions.

A method for plotting the complementary root locus using the root-locus (positive gain) rules

The root-locus method is a well-known and commonly used tool in control system analysis and design. It is an important topic in introductory undergraduate engineering control disciplines. Although complementary root locus (plant with negative gain) is not as common as root locus (plant with positive gain) and in many introductory textbooks for control systems is not presented, it has been shown a valuable tool in control system design. This paper shows that complementary root locus can be plotted using only the well-known construction rules to plot root locus. It can offer for the students a better comprehension on this subject. These results present a procedure to avoid problems that appear in root-locus plots for plants with the same number of poles and zeros.

On Complementary Root Locus of Biproper Transfer Functions

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

DIRECT EXPRESSIONS FOR OGATA LEAD-LAG DESIGN METHOD USING ROOT LOCUS

Direct expressions for the design of a lead-lag continuous compensator using the root locus method and the procedure described in the 1970 and 1990 books by Ogata are presented. These results are useful in the Ogata design method because they avoid the geometrical determination of poles and zeros, making it easier to create a computer-based design.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Proposta de um algoritmo GPC adaptativo com baixo custo computacional

Esta dissertação propõe um algoritmo do Controlador Preditivo Generalizado (GPC) com horizonte de controle igual a um para ser aplicado em plantas industriais com modelos variantes no tempo, simples o su ficiente para ser implementado em Controlador Lógico Programável (PLC). A solução explícita do controlador é obtida em função dos parâmetros do modelo e dos parâmetros de sintonia do GPC (horizonte nal de predição hp e o fator de supressão do sinal de controle ), além das entradas e saídas presentes e passadas. A sintonia do fator de supressão e do horizonte de previsão GPC é feita através do lugar das raízes da equação característica do sistema em malha fechada, sempre que os parâmetros do modelo da planta industrial (estável ou instável em malha aberta) forem modificados.

Controlo por computador de um sistema de levitação magnética

Ao longo deste projecto são efectuados vários passos para a realização de um sistema de levitação magnética controlado por computador. O objectivo deste projecto é a levitação de um objecto de material ferromagnético. Para a sua realização foi essencialmente necessário um electroíman, que exerce a força electromagnética sobre a bola, um circuito de potência para accionar o electroíman, um circuito sensor constituído por um LDR e por fim, o circuito constituído pelo PIC 18F4550. Para a comunicação entre o sistema e o PC foi estabelecida a comunicação série RS232. No que concerne ao controlo do sistema, foi aplicado um controlador PD e um controlador em avanço, ambos projectados directamente no domínio digital, através do método do Lugar de raízes. Posteriormente foi desenvolvida uma interface gráfica em ambiente MATLAB, para comunicação, via RS232, entre o PC e o sistema.

Controlo inteligente de um Sistema de Levitação Magnética

A levitação magnética tem sido um tema bastante investigado sobretudo devido à sua utilização em sistemas ferroviários de transportes. É o método ideal quando existe a necessidade em aplicações de restringir do contacto físico, ou a conveniência, em termos energéticos, de eliminar o atrito. O princípio de funcionamento é simples, um eletroíman cria uma força sobre um objeto ferromagnético que contraria a gravidade. Contudo um sistema de levitação por atração é instável e não linear, o que significa a necessidade de implementar um controlador para satisfazer as características de estabilidade desejadas. Ao longo deste projeto serão descritos os procedimentos teóricos e práticos que foram tomados na criação de um sistema de levitação eletromagnética. Desde a conceção física do sistema, como escolha do sensor, condicionamento de sinal ou construção do eletroíman, até aos procedimentos matemáticos que permitiram a modelação do sistema e criação de controladores. Os controladores clássicos, como o PID ou em avanço de fase, foram projetados através da técnica do Lugar Geométrico de Raízes. No projeto do controlador difuso, pelo contrário não se fez uso da modelação do sistema ou de qualquer relação matemática entre as variáveis. A utilização desta técnica de controlo destacou-se pela usa simplicidade e rapidez de implementação, fornecendo um bom desempenho ao sistema. Na parte final do relatório os resultados obtidos pelos diferentes métodos de controlo são analisados e apresentadas as respetivas conclusões. Estes resultados revelam que para este sistema, relativamente aos outros métodos, o controlador difuso apresenta o melhor desempenho tanto ao nível da resposta transitória, como em regime permanente.

Curving simulation and stability of a creep-controlled wheelset for high speed rail-vehicles

Higher travel speeds of rail vehicles will be possible by developing sophisticated top performance bogies having creep-controlled wheelsets. In this case the torque transmission between the right and the left wheel is realized by an actively controlled creep coupling. To investigate hunting stability and curving capability the linear equations of motion are written in state space notation. Simulation results are obtained with realistic system parameters from industry and various controller gains. The advantage of the „creep-controlled wheelset" is discussed by comparison the simulation results with the dynamic behaviour of the special cases „solid-axle wheelset" and „loose wheelset" (independent rotation of the wheels). The stability is also investigated with a root-locus analysis.

Metodologia para re-sintonia de controladores PID industriais

The present work has as objective to present a method of project and implementation of controllers PID, based on industrial instrumentation. An automatic system of auto-tunning of controllers PID will be presented, for systems of first and second order. The software presented in this work is applied in controlled plants by PID controllers implemented in a CLP. Software is applied to make the auto-tunning of the parameters of controller PID of plants that need this tunning. Software presents two stages, the first one is the stage of identification of the system using the least square recursive algorithm and the second is the stage of project of the parameters of controller PID using the root locus algorithm. An important fact of this work is the use of industrial instrumentation for the accomplishment of the experiments. The experiments had been carried through in controlled real plants for controllers PID implemented in the CLP. Thus has not only one resulted obtained with theoreticians experiments made with computational programs, and yes resulted obtained of real systems. The experiments had shown good results gotten with developed software

On lag controllers: Design and implementation

Sometimes it is inconvenient or expensive to open the loop of a system to insert lag controllers-for instance, when this system is an open-loop system. A new controller structure where the loop is not opened, and that allows the design of lag controllers as in the case where one can open the loop, is presented. This result can be used by educators in undergraduate courses that deal with classic control system theory, because it allows a better comprehension of the concept of lag compensation and provides a new method for its design and implementation. An example illustrates the application of the proposed method.

Digital controller design considering hardware constraints: application in a paraplegic patient

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

Comportamento dinâmico de suspensão eletromecânica: análise da resposta devido ao amortecimento e à rigidez não linear

Pós-graduação em Engenharia Elétrica - FEB

Estudo da estabilidade dinâmica e controle da aeronave AF-X da equipe AeroFEG

The present work aims to study the stability and control of the aircraft AF-X of AeroFEG team for AeroDesign to contribute with it in developing its theoretical project report for the competition and present the shortcomings of stability that it might measures for the practical test. In the first moment, it was presented forces and motion of the aircraft, so to define the equations of motion. After the equations of motion were calculated, the transfer functions were found and the aircraft response was analyzed under longitudinal stability and lateral-directional. We obtained responses from the aircraft and through the method of Root Locus the gains required to improve responses and reduce the overshoot, finally some changes and improvements for increased stability have been addressed. The study covered all the motions and control surfaces of the aircraft, showing the characteristics and behavior of the front disruptions, as well as opportunities for gains and improvementsThe present work aims to study the stability and control of the aircraft AF-X of AeroFEG team for AeroDesign to contribute with it in developing its theoretical project report for the competition and present the shortcomings of stability that it might measures for the practical test. In the first moment, it was presented forces and motion of the aircraft, so to define the equations of motion. After the equations of motion were calculated, the transfer functions were found and the aircraft response was analyzed under longitudinal stability and lateral-directional. We obtained responses from the aircraft and through the method of Root Locus the gains required to improve responses and reduce the overshoot, finally some changes and improvements for increased stability have been addressed. The study covered all the motions and control surfaces of the aircraft, showing the characteristics and behavior of the front disruptions, as well as opportunities for gains and improvements