LMI-based digital redesign of linear time-invariant systems with state-derivative feedback

A simple method for designing a digital state-derivative feedback gain and a feedforward gain such that the control law is equivalent to a known and adequate state feedback and feedforward control law of a digital redesigned system is presented. It is assumed that the plant is a linear controllable, time-invariant, Single-Input (SI) or Multiple-Input (MI) system. This procedure allows the use of well-known continuous-time state feedback design methods to directly design discrete-time state-derivative feedback control systems. The state-derivative feedback can be useful, for instance, in the vibration control of mechanical systems, where the main sensors are accelerometers. One example considering the digital redesign with state-derivative feedback of a helicopter illustrates the proposed method. © 2009 IEEE.

On switched control design of linear time-invariant systems with polytopic uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure. © 2013 Wallysonn A. de Souza et al.

Controllability and stabilizability of linear time-varying distributed hereditary control systems

This paper is concerned with the controllability and stabilizability problem for control systems described by a time-varyinglinear abstract differential equation with distributed delay in the state variables. An approximate controllability propertyis established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operatorsassociated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptoticstability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximatecontrollability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes thesystem. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley &Sons, Ltd.

Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems

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

Robust state-derivative feedback LMI-based designs for multivariable linear systems

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix K. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.

Projeto, processo e produto: cartografia do design de conexões na televisão digital

Pós-graduação em Televisão Digital: Informação e Conhecimento - FAAC

Análise de Tópicos Relevantes em Programação Linear e Aplicações no Ensino de Engenharia

Pós-graduação em Engenharia Elétrica - FEIS

Design de Relações entre tecnologias amigáveis e sociabilidades virtuais: um novo campo de investigação para o Design

The Digital Age, with its new interactive and converging technologies, stimulates original forms of sociability, which are interconnected, intercommunicating and virtualized through hyperscreens. Another kind of interaction arises from the digitization and new speeds of contemporary communicative process. With the new order of knowledge, it is now possible to transgress the limits of physical space and linear time sequence, through the collective development of content through such telematics networks. Youth gives voice to a new type of user, or a social actor, whose thinking is connected to other communication habits, consolidating singular cultural standards, demanding new languages and skills. Here, we address the nature of this Design of new relations, interactions, behaviors and social systems that emerge in the so called Information Society.

Mitigation of symmetry condition in positive realness for adaptive control

Feasibility of nonlinear and adaptive control methodologies in multivariable linear time-invariant systems with state-space realization (A, B, C) is apparently limited by the standard strictly positive realness conditions that imply that the product CB must be positive definite symmetric. This paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric CB is only required to have a diagonal Jordan form and positive eigenvalues. The paper also shows that under the new condition any minimum-phase systems can be made strictly positive real via constant output feedback. The paper illustrates the usefulness of these extended properties with an adaptive control example. (C) 2006 Elsevier Ltd. All rights reserved.

Stabilizability and Disturbance Rejection with State-Derivative Feedback

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Utilização da relação potência-tempo até exaustão em testes de caminhada para avaliação da aptidão aeróbia

O objetivo do presente estudo foi avaliar a aptidão aeróbia em testes de caminhada com carga externa aplicada por meio da inclinação da esteira, a partir da relação não linear entre inclinação da esteira e tempo até a exaustão em velocidade fixa. Doze indivíduos do gênero masculino com 23,2 ± 2,7 anos de idade, 74,0 ± 7,9kg de massa corporal e 23,7 ± 2,5kg·(m²)-1 de IMC, realizaram duas etapas de testes de caminhada em esteira ergométrica com velocidade fixa de 5,5km·h-1 em todos os testes e sobrecarga de intensidade aplicada por meio de inclinação da esteira (%). A etapa 1 consistiu de três testes retangulares até a exaustão voluntária, nas intensidades de 18%, 20% e 22% de inclinação, para determinação dos parâmetros do modelo de potência crítica por dois modelos lineares e um hiperbólico. A etapa 2 consistiu na determinação da intensidade correspondente ao máximo estado estável de lactato sanguíneo (MEEL). ANOVA demonstrou que o modelo hiperbólico (15,4 ± 1,1%) resultou em estimativa significativamente menor que os outros dois modelos lineares inclinação-tempo-1 (16,0 ± 1,0%) e hiperbólico linearizado tempo-1-inclinação (15,9 ± 1,0%), porém, houve alta correlação entre os modelos. Os dois modelos lineares superestimaram a intensidade do MEEL (14,1 ± 1,4%), e o modelo hiperbólico, mesmo sem diferença estatística, apresentou fraca correlação, com baixa concordância em relação ao MEEL. Conclui-se que a relação inclinação-tempo até a exaustão, em testes de caminhada, não permitem a estimativa de intensidade de exercício suportável por longo período de tempo.

CONTROL OF UNCERTAIN DYNAMIC-SYSTEMS USING STRICTLY POSITIVE REAL SYSTEMS

This paper presents necessary and sufficient conditions to turn a linear time-invariant system with p outputs, m inputs, p greater-than-or-equal-to m and using only inputs and outputs measurements into a Strictly Positive Real (SPR).Two results are presented. In the first, the system compensation is made by two static compensators, one of which forward feeds the outputs and the second back feeds the outputs of the nominal system.The second result presents conditions for the Walcott and Zak variable structure observer-controller synthesis. In this problem, if the nominal system is given by {A,B,C}, then the compensated system is given by {A+GC,B,FC} where F and G are the constant compensation matrices. These results are useful in the control system with uncertainties.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.

Variable structure control of switched systems based on Lyapunov-Metzler-SPR systems

This paper presents two Variable Structure Controllers (VSC) for continuous-time switched plants. It is assumed that the state vector is available for feedback. The proposed control system provides a switching rule and also the variable structure control input. The design is based on Lyapunov-Metzler (LM) inequalities and also on Strictly Positive Real (SPR) systems stability results. The definition of Lyapunov-Metzler-SPR (LMS) systems and its direct application in the design of VSC for switched systems are introduced in this paper. Two examples illustrate the design of the proposed VSC, considering a plant given by a switched system with a switched-state control law and two linear time-invariant systems, that are not controllable and also can not be stabilized with state feedback. ©2008 IEEE.

Comparative study of LMI-based output feedback spr synthesis for plants with different numbers of inputs and outputs

New Linear Matrix Inequalities (LMI) conditions are proposed for the following problem, called Strictly Positive Real (SPR) synthesis: given a linear time-invariant plant, find a constant output feedback matrix Ko and a constant output tandem matrix F for the controlled system to be SPR. It is assumed that the plant has the number of outputs greater than the number of inputs. Some sufficient conditions for the solution of the problem are presented and compared. These results can be directly applied in the LMI-based design of Variable Structure Control (VSC) of uncertain plants. ©2008 IEEE.