Novos resultados sobre a estabilidade e controle de sistemas nao-lineares utilizando modelos fuzzy e LMI

Relaxed conditions for the stability study of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed method provides better or at least the same results of the methods presented in the literature. Digital simulations exemplify this fact. These results are also used for the fuzzy regulators design. The nonlinear systems are represented by the fuzzy models proposed by Takagi and Sugeno. The stability analysis and the design of controllers are described by LMIs (Linear Matrix Inequalities), that can be solved efficiently by convex programming techniques. The specification of the decay rate, constraints on control input and output are also described by LMIs. Finally, the proposed design method is applied in the control of an inverted pendulum.

Lyapounov stability for impulsive dynamical systems

This article addresses the problem of stability of impulsive control systems whose dynamics are given by measure driven differential inclusions. One important feature concerns the adopted solution which allows the consideration of systems whose singular dynamics do not satisfy the so-called Frobenius condition. After extending the conventional notion of control Lyapounov pair for impulsive systems, some stability conditions of the Lyapounov type are given. Some conclusions follow the outline of the proof of the main result.

Control of thermal damage in grinding by digital signal processing of raw acoustic emission

Grinding process is usually the last finishing process of a precision component in the manufacturing industries. This process is utilized for manufacturing parts of different materials, so it demands results such as low roughness, dimensional and shape error control, optimum tool-life, with minimum cost and time. Damages on the parts are very expensive since the previous processes and the grinding itself are useless when the part is damaged in this stage. This work aims to investigate the efficiency of digital signal processing tools of acoustic emission signals in order to detect thermal damages in grinding process. To accomplish such a goal, an experimental work was carried out for 15 runs in a surface grinding machine operating with an aluminum oxide grinding wheel and ABNT 1045 e VC131 steels. The acoustic emission signals were acquired from a fixed sensor placed on the workpiece holder. A high sampling rate acquisition system at 2.5 MHz was used to collect the raw acoustic emission instead of root mean square value usually employed. In each test AE data was analyzed off-line, with results compared to inspection of each workpiece for burn and other metallurgical anomaly. A number of statistical signal processing tools have been evaluated.

Modeling of pre-regulator boost ZCS interleaved operating in critical conduction mode and with high power factor

This paper presents a new pre-regulator boost operating in the boundary area between the continuous and discontinuous conduction modes of the boost inductor current, where the switches and boost diode performing zero-current commutations during its turn-off, eliminating the disadvantages related to the reverse recovery losses and electromagnetic interference problems of the boost diode when operating in the continuous conduction mode. Additionally, the interleaving technique is applied in the power cell, providing a significant input current ripple reduction. It should be noticed that the main objective of this paper is to present a complete modeling for the converter operating in the critical conduction mode, allowing an improved design procedure for interleaved techniques with high input power factor, a complete dynamic analysis of the structure, and the possibility of implementing digital control techniques in closed loop.

Adaptive control charts for attributes

We develop a general model for adaptive c, np, u and p control charts in which one, two or three design parameters (sample size, sampling interval and control limit width) switch between two values, according to the most recent process information. For a given in-control average sampling rate and a given false alarm rate, the adaptive chart detects changes in the process much faster than a chart with fixed parameters. Moreover, this study also offers general guidance on how to choose an effective design.

The effect of actuator and sensor placement on the active control of rotor unbalance

This paper investigates both theoretically and experimentally the effect of the location and number of sensors and magnetic bearing actuators on both global and local vibration reduction along a rotor using a feedforward control scheme. Theoretical approaches developed for the active control of beams have been shown to be useful as simplified models for the rotor scenario. This paper also introduces the time-domain LMS feedforward control strategy, used widely in the active control of sound and vibration, as an alternative control methodology to the frequency-domain feedforward approaches commonly presented in the literature. Results are presented showing that for any case where the same number of actuators and error sensors are used there can be frequencies at which large increases in vibration away from the error sensors can occur. It is also shown that using a larger number of error sensors than actuators results in better global reduction of vibration but decreased local reduction. Overall, the study demonstrated that an analysis of actuator and sensor locations when feedforward control schemes are used is necessary to ensure that harmful increased vibrations do not occur at frequencies away from rotor-bearing natural frequencies or at points along the rotor not monitored by error sensors.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

Robust control to parametric uncertainties in smart structures 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 and aerospace 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. This article shows some steps that should be followed in the design of a smart structure. It is discussed: the optimal placement of actuators, the model reduction and the controller design through techniques involving linear matrix inequalities (LMI). It is considered as constraints in LMI: the decay rate, voltage input limitation in the actuators and bounded output peak (output energy). Two controllers robust to parametric variation are designed: the first one considers the actuator in non-optimal location and the second one the actuator is put in an optimal placement. The performance are compared and discussed. The simulations to illustrate the methodology are made with a cantilever beam with bonded piezoelectric actuators.

Defects location in power systems components through a dedicated genetic algorithm

In this work the problem of defects location in power systems is formulated through a binary linear programming (BLP) model based on alarms historical database of control and protection devices from the system control center, sets theory of minimal coverage (AI) and protection philosophy adopted by the electric utility. In this model, circuit breaker operations are compared to their expected states in a strictly mathematical manner. For solving this BLP problem, which presents a great number of decision variables, a dedicated Genetic Algorithm (GA), is proposed. Control parameters of the GA, such as crossing over and mutation rates, population size, iterations number and population diversification, are calibrated in order to obtain efficiency and robustness. Results for a test system found in literature, are presented and discussed. © 2004 IEEE.

PID stabilization of a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral plus derivative (PID) controllers concerning a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. © 2005 IEEE.

Active flutter suppression in a 2-D airfoil using linear matrix inequalities techniques

Flutter is an in-flight vibration of flexible structures caused by energy in the airstream absorbed by the lifting surface. This aeroelastic phenomenon is a problem of considerable interest in the aeronautic industry, because flutter is a potentially destructive instability resulting from an interaction between aerodynamic, inertial, and elastic forces. To overcome this effect, it is possible to use passive or active methodologies, but passive control adds mass to the structure and it is, therefore, undesirable. Thus, in this paper, the goal is to use linear matrix inequalities (LMIs) techniques to design an active state-feedback control to suppress flutter. Due to unmeasurable aerodynamic-lag states, one needs to use a dynamic observer. So, LMIs also were applied to design a state-estimator. The simulated model, consists of a classical flat plate in a two-dimensional flow. Two regulators were designed, the first one is a non-robust design for parametric variation and the second one is a robust control design, both designed by using LMIs. The parametric uncertainties are modeled through polytopic uncertainties. The paper concludes with numerical simulations for each controller. The open-loop and closed-loop responses are also compared and the results show the flutter suppression. The perfomance for both controllers are compared and discussed. Copyright © 2006 by ABCM.

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.

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

A structure excited by a DC motor of limited power supply and controlled by a pendulum like device

In this paper, a mathematical model is derived via Lagrange's Equation for a shear building structure that acts as a foundation of a non-ideal direct current electric motor, controlled by a mass loose inside a circular carving. Non-ideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure, not being a function of time only as in the ideal case. Thus, in this case, an additional equation of motion is written, related to the motor rotation, coupled to the equation describing the horizontal motion of the shear building. This kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure is reached, the better part of this energy is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. If additional increase steps in voltage are made, one may reach a situation where the rotor will jump to higher rotation regimes, no steady states being stable in between. As a device of passive control of both large amplitude vibrations and the Sommerfeld effect, a scheme is proposed using a point mass free to bounce back and forth inside a circular carving in the suspended mass of the structure. Numerical simulations of the model are also presented Copyright © 2007 by ASME.

A true programmable HPF hybrid three-phase rectifier

In this paper is proposed and analyzed a digital hysteresis modulation using a FPGA (Field Programmable Gate Array) device and VHDL (Hardware Description Language), applied at a hybrid three-phase rectifier with almost unitary input power factor, composed by parallel SEPIC controlled single-phase rectifiers connected to each leg of a standard 6-pulses uncontrolled diode rectifier. The digital control allows a programmable THD (Total Harmonic Distortion) at the input currents, and it makes possible that the power rating of the switching-mode converters, connected in parallel, can be a small fraction of the total average output power, in order to obtain a compact converter, reduced input current THD and almost unitary input power factor. The proposed digital control, using a FPGA device and VHDL, offers an important flexibility for the associated control technique, in order to obtain a programmable PFC (Power Factor Correction) hybrid three-phase rectifier, in agreement with the international standards (IEC, and IEEE), which impose limits for the THD of the AC (Alternate Current) line input currents. Finally, the proposed control strategy is verified through experimental results from an implemented prototype. ©2008 IEEE.