A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

Estudo da comunicação de um compensador série para rede de distribuição com o centro de controle utilizando tecnologia GPRS

Pós-graduação em Engenharia Elétrica - FEIS

Um novo sistema de refrigeração com controle de temperatura, compressor aberto, máquina de indução trifásica com velocidade variável e correção ativa do fator de potência do estágio de entrada

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Description of the attainable sets of one-dimensional differential inclusions

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

Optimal and robust modal control of a flexible structure using an active dynamic vibration absorber

This paper is concerned with feedback vibration control of a lightly damped flexible structure that has a large number of well-separated modes. A single active electrical dynamic absorber is used to reduce a particular single vibration mode selectively or multiple modes simultaneously. The absorber is realized electrically by feeding back the structural acceleration at one position to a collocated piezoceramic patch actuator via a controller consisting of one or several second order lowpass filters. A simple analytical method is presented to design a modal control filter that is optimal in that it maximally flattens the mobility frequency response of the target mode, as well as robust in that it works within a prescribed maximum control spillover of 2 dB at all frequencies. Experiments are conducted with a free-free beam to demonstrate its ability to control any single mode optimally and robustly. It is also shown that an active absorber with multiple such filters can effectively control multiple modes simultaneously.

Robust broadband vibration control of a flexible structure using an electrical dynamic absorber

This paper presents a simple but practical feedback control method to suppress the vibration of a flexible structure in the frequency range between 10 Hz and 1 kHz. A dynamic vibration absorber is designed for this, which has a natural frequency of 100 Hz and a normalized bandwidth (twice the damping ratio) of 9.9. The absorber is realized electrically by feeding back the structural acceleration at one position on the host structure to a collocated piezoceramic patch actuator via an analog controller consisting of a second-order lowpass filter. This absorber is equivalent to a single degree-of-freedom mechanical oscillator consisting of a serially connected mass-spring-damper system. A first-order lowpass filter is additionally used to improve stability at very high frequencies. Experiments were conducted on a free-free beam embedded with a piezoceramic patch actuator and an accelerometer at its center. It is demonstrated that the single absorber can simultaneously suppress multiple vibration modes within the control bandwidth. It is further shown that the control system is robust to slight changes in the plant. The method described can be applied to many other practical structures, after retuning the absorber parameters for the structure under control.

OUTPUT CONTROL WITH DYNAMIC COMPENSATORS AND STRICTLY POSITIVE REAL SYSTEMS

We present new results on the output control of uncertain dynamical systems. The design method uses dynamical compensators to turn the compensated plant into a strictly positive real system, and then chooses the control law-for example, a sliding mode control. This result is compared with another result from the literature which uses static compensators. An example is presented where the control with dynamic compensation works while a static compensation does not.

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.

Postural control in children: Coupling to dynamic somatosensory information

The purpose of this investigation was to determine whether the coupling between dynamic somatosensory information and body sway is similar in children and adults. Thirty children (4-, 6-, and 8-year-olds) and 10 adults stood upright, with feet parallel, and lightly contacting the fingertip to a rigid metal plate that moved rhythmically at 0.2, 0.5, and 0.8 Hz. Light touch to the moving contact surface induced postural sway in all participants. The somatosensory stimulus produced a broadband frequency response in children, while the adult response was primarily at the driving frequency. Gain, as a function of frequency, was qualitatively the same in children and adults. Phase decreased less in 4-year-olds than other age groups, suggesting a weaker coupling to position information in the sensory stimulus. Postural sway variability was larger in children than adults. These findings suggest that, even as young as age 6, children show well-developed coupling to the sensory stimulus. However, unlike adults, this coupling is not well focused at the frequency specified by the somatosensory signal. Children may be unable to uncouple from sensory information that is less relevant to the task, resulting in a broadband response in their frequency spectrum. Moreover, higher sway variability may not result from the sensory feedback process, but rather from the children's underdeveloped ability to estimate an internal model of body orientation.

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.

Ablation of the ability to control the right-to-left cardiac shunt does not affect oxygen uptake, specific dynamic action or growth in the rattlesnake Crotalus durissus

The morphologically undivided ventricle of the heart in non-crocodilian reptiles permits the mixing of oxygen-rich blood returning from the lungs and oxygen-poor blood from the systemic circulation. A possible functional significance for this intra-cardiac shunt has been debated for almost a century. Unilateral left vagotomy rendered the single effective pulmonary artery of the South American rattlesnake, Crotalus durissus, unable to adjust the magnitude of blood flow to the lung. The higher constant perfusion of the lung circulation and the incapability of adjusting the right-left shunt in left-denervated snakes persisted over time, providing a unique model for investigation of the long-term consequences of cardiac shunting in a squamate. Oxygen uptake recorded at rest and during spontaneous and forced activity was not affected by removing control of the cardiac shunt. Furthermore, metabolic rate and energetic balance during the post-prandial metabolic increment, plus the food conversion efficiency and growth rate, were all similarly unaffected. These results show that control of cardiac shunting is not associated with a clear functional advantage in adjusting metabolic rate, effectiveness of digestion or growth rates. © 2013. Published by The Company of Biologists Ltd.

Demonstration of non-collocated vibration control of a flexible manipulator using electrical dynamic absorbers

This paper describes an experimental study into the vibration control of a servo system comprising a servo motor and a flexible manipulator. Two modes of the system are controlled by using the servo motor and an accelerometer attached to the tip of the flexible manipulator. The control system is thus non-collocated. It consists of two electrical dynamic absorbers, each of which consists of a modal filter and, in case of an out-of-phase mode, a phase inverter. The experimental results show that each absorber acts as a mechanical dynamic vibration absorber attached to each mode and significantly reduces the settling time for the system response to a step input.

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)