About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system.

Auto-weighted minimum-variance self-tuning controller

A self-tuning controller which automatically assigns weightings to control and set-point following is introduced. This discrete-time single-input single-output controller is based on a generalized minimum-variance control strategy. The automatic on-line selection of weightings is very convenient, especially when the system parameters are unknown or slowly varying with respect to time, which is generally considered to be the type of systems for which self-tuning control is useful. This feature also enables the controller to overcome difficulties with non-minimum phase systems.

A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Single-phase current-source-boost inverter for renewable energy sources

This paper presents a new methodology for the operation and control of a single-phase current-source (CS) Boost Inverter, considering that the conventional CS boost inverter has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the known non-minimum-phase effects. In this context, a special design with low boost inductance and a multi-loop control is developed in order to assure stable and very fast dynamics. Furthermore, the proposed inverter presents output voltage with very low total harmonic distortion (THD), reduced components and high power density. Therefore, this paper presents the inverter operation, the proposed control technique, the main simulation results and a prototype in order to demonstrate the feasibility of the proposal. © 2011 IEEE.

BONA FIDE, STRONG-VARIABLE GALACTIC LUMINOUS BLUE VARIABLE STARS ARE FAST ROTATORS: DETECTION OF A HIGH ROTATIONAL VELOCITY IN HR CARINAE

We report optical observations of the luminous blue variable (LBV) HR Carinae which show that the star has reached a visual minimum phase in 2009. More importantly, we detected absorptions due to Si lambda lambda 4088-4116. To match their observed line profiles from 2009 May, a high rotational velocity of nu(rot) similar or equal to 150 +/- 20 km s(-1) is needed (assuming an inclination angle of 30 degrees), implying that HR Car rotates at similar or equal to 0.88 +/- 0.2 of its critical velocity for breakup (nu(crit)). Our results suggest that fast rotation is typical in all strong-variable, bona fide galactic LBVs, which present S-Dor-type variability. Strong-variable LBVs are located in a well-defined region of the HR diagram during visual minimum (the ""LBV minimum instability strip""). We suggest this region corresponds to where nu(crit) is reached. To the left of this strip, a forbidden zone with nu(rot)/nu(crit) > 1 is present, explaining why no LBVs are detected in this zone. Since dormant/ex LBVs like P Cygni and HD 168625 have low nu(rot), we propose that LBVs can be separated into two groups: fast-rotating, strong-variable stars showing S-Dor cycles (such as AG Car and HR Car) and slow-rotating stars with much less variability (such as P Cygni and HD 168625). We speculate that supernova (SN) progenitors which had S-Dor cycles before exploding (such as in SN 2001ig, SN 2003bg, and SN 2005gj) could have been fast rotators. We suggest that the potential difficulty of fast-rotating Galactic LBVs to lose angular momentum is additional evidence that such stars could explode during the LBV phase.

Simplified parameter adaptive control

A simple parameter adaptive controller design methodology is introduced in which steady-state servo tracking properties provide the major control objective. This is achieved without cancellation of process zeros and hence the underlying design can be applied to non-minimum phase systems. As with other self-tuning algorithms, the design (user specified) polynomials of the proposed algorithm define the performance capabilities of the resulting controller. However, with the appropriate definition of these polynomials, the synthesis technique can be shown to admit different adaptive control strategies, e.g. self-tuning PID and self-tuning pole-placement controllers. The algorithm can therefore be thought of as an embodiment of other self-tuning design techniques. The performances of some of the resulting controllers are illustrated using simulation examples and the on-line application to an experimental apparatus.

Robust blind deconvolution algorithm: variance approximation and series decoupling

An alternative blind deconvolution algorithm for white-noise driven minimum phase systems is presented and verified by computer simulation. This algorithm uses a cost function based on a novel idea: variance approximation and series decoupling (VASD), and suggests that not all autocorrelation function values are necessary to implement blind deconvolution.

Determinação dos parâmetros do controlador preditivo generalizado com função de pesos variante no tempo através de algoritmos genéticos

The predictive control technique has gotten, on the last years, greater number of adepts in reason of the easiness of adjustment of its parameters, of the exceeding of its concepts for multi-input/multi-output (MIMO) systems, of nonlinear models of processes could be linearised around a operating point, so can clearly be used in the controller, and mainly, as being the only methodology that can take into consideration, during the project of the controller, the limitations of the control signals and output of the process. The time varying weighting generalized predictive control (TGPC), studied in this work, is one more an alternative to the several existing predictive controls, characterizing itself as an modification of the generalized predictive control (GPC), where it is used a reference model, calculated in accordance with parameters of project previously established by the designer, and the application of a new function criterion, that when minimized offers the best parameters to the controller. It is used technique of the genetic algorithms to minimize of the function criterion proposed and searches to demonstrate the robustness of the TGPC through the application of performance, stability and robustness criterions. To compare achieves results of the TGPC controller, the GCP and proportional, integral and derivative (PID) controllers are used, where whole the techniques applied to stable, unstable and of non-minimum phase plants. The simulated examples become fulfilled with the use of MATLAB tool. It is verified that, the alterations implemented in TGPC, allow the evidence of the efficiency of this algorithm

Uma proposta de um controlador adaptativo por posicionamento de pólos e estrutura variável

There are two main approaches for using in adaptive controllers. One is the so-called model reference adaptive control (MRAC), and the other is the so-called adaptive pole placement control (APPC). In MRAC, a reference model is chosen to generate the desired trajectory that the plant output has to follow, and it can require cancellation of the plant zeros. Due to its flexibility in choosing the controller design methodology (state feedback, compensator design, linear quadratic, etc.) and the adaptive law (least squares, gradient, etc.), the APPC is the most general type of adaptive control. Traditionally, it has been developed in an indirect approach and, as an advantage, it may be applied to non-minimum phase plants, because do not involve plant zero-pole cancellations. The integration to variable structure systems allows to aggregate fast transient and robustness to parametric uncertainties and disturbances, as well. In this work, a variable structure adaptive pole placement control (VS-APPC) is proposed. Therefore, new switching laws are proposed, instead of using the traditional integral adaptive laws. Additionally, simulation results for an unstable first order system and simulation and practical results for a three-phase induction motor are shown

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.

Síntese de sistemas estritamente reais positivos através do critério de routh-hurwitz

Given a linear time-invariant plant Gol(s) with one input and q outputs, where q > 1, a method based on the Routh-Hurwitz Stability Criterion is proposed to obtain a constant tandem matrix F ∈ ℝq, such that FGOl(s) is a minimumphase system. From this solution, the system FGol(s) is represented in state space by {A, B, FC} and a constant output feedback matrix K0 ∈ ℝ is obtained such that the feedback system {A - BK0C, B, FC} is Strictly Positive Real (SPR). The proposed procedure offers necessary and sufficient conditions for both problems. Initially, the general case, with a generic q, is analyzed. Following, the particular cases q = 2 and q = 3 are studied.

Inversor CS Boost monofásico em aplicações com fontes renováveis

This paper presents a new methodology for the operation and control of a single-phase current-source (CS) Boost Inverter, considering that the conventional current-source inverter (CSI) has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the known non-minimum-phase effects. In this context, a special design with low boost inductance and a multi-loop control is developed in order to assure stable and very fast dynamics. Furthermore, the Inverter presents output voltage with very low total harmonic distortion (THD), reduced components and high power density. Therefore, this paper presents the inverter operation, the proposed control technique, and main simulation and experimental results in order to demonstrate the feasibility of the proposal. © 2010 IEEE.

Active vibration control using delayed resonant feedback

Delayed feedback (DF) control is a well-established technique to suppress single frequency vibration of a non-minimum phase system. Modal control is also a well-established technique to control multiple vibration modes of a minimum phase system. In this paper these techniques are combined to simultaneously suppress multiple vibration modes of a non-minimum phase system involving a small time delay. The control approach is called delayed resonant feedback (DRF) where each modal controller consists of a modal filter to extract the target mode signal from the vibration response, and a phase compensator to account for the phase delay of the mode. The methodology is first discussed using a single mode system. A multi-mode system is then studied and experimental results are presented to demonstrate the efficacy of the control approach for two modes of a beam. It is shown that the system behaves as if each mode under control has a dynamic vibration absorber attached to it, even though the actuator and the sensor are not collocated and there is a time delay in the control system. © 2013 IOP Publishing Ltd.

Uma nova metodologia de projeto e controle para o inversor Boost (CSI) monofásico, para o aproveitamento de fontes alternativas e renováveis de energia elétrica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Fluxo de carga não-iterativo para a análise de sistemas de distribuição de energia elétrica radiais e malhados

Pós-graduação em Engenharia Elétrica - FEIS