Aldayr D. Araujo

Design and stability analysis of an indirect variable structure model reference adaptive control

This paper presents the stability and robustness analysis of an indirect adaptive control based variable structure algorithm for uncertain plants with relative degree one. The indirect approach has been proposed as a way to get an easier design of the switching laws, compared to the direct relationship between the plant transfer function parameters and the physical parameters of the system. Here, a singular perturbation approach is used to establish the robustness of the controller in the presence of unmodelled dynamics and disturbances. It is shown that, for sufficiently small parasitics, the system remains stable with respect to some small residual set.

Variable Structure Aadaptive Backstepping Controller

This paper presents a Variable Structure Adaptive Backstepping Controller (VS-ABC) for plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are used to increase robustness to parametric uncertainties and disturbances, as well as, to improve transient response. Moreover, the controller design is easier when compared with the original adaptive backstepping controller, since the amplitude relays are related to the plant nominal parameters. Additionally, preliminary simulation results for an unstable second order system are shown.

Controlador em modo dual adaptativo robusto para plantas com grau relativo arbitrário

Neste artigo e apresentado o Controlador em Modo Dual Adaptativo Robusto (DMARC). O DMARC e um sistema de controle que combina as estrategias de Controle Adaptativo por Modelo de Referencia (MRAC) com leis integrais de adaptacao e o Controle Adaptativo por Modelo de Referencia e Estrutura Variavel (VS-MRAC) com leis chaveadas de acordo com a teoria de sistemas com estrutura variavel. A ideia basica e incorporar as vantagens de desempenho transitorio de um VS-MRAC, com as propriedades de regime permanente de um MRAC convencional. Desta forma, obtem-se um sistema de controle robusto a incertezas parametricas e perturbacoes externas, com desempenho rapido e pouco oscilatorio durante o transitorio e um sinal de controle suave em regime permanente.

Variable Structure Adaptive Backstepping Controller for plants with arbitrary relative degree based on modular design

This paper presents a Variable Structure Adaptive Backstepping Controller (VS-ABC) for linear plants with arbitrary relative degree, using only input/output measurements. In order to improve the transient response, switching laws are proposed in the adaptive backstepping approach via modular design, instead of the integral adaptive laws. Furthermore, simplified algorithms are presented for the VS-ABC, motivating applications on industrial environments. Simulation results for an unstable system with relative degree three are shown.

Design and stability analysis of a Variable Structure Adaptive Pole Placement Controller for first order systems

This paper shows the design and the stability analysis of a Variable Structure Adaptive Pole Placement Controller (VS-APPC) for first order plants, both for regulation and tracking. The VS-APPC was proposed in previous papers and it provides a fast and non-oscillatory transient. Besides, it suggests robustness to parameter uncertainties and disturbances, by using switching adaptive laws for the plant parameters, instead of the traditional integral ones, as the gradient method. Additionally, simulations results are shown.

Indirect Binary Model Reference Adaptive Control

This paper proposes an Indirect Binary Model Reference Adaptive Controller (IB-MRAC), with the main objective of combining the steady-state features of controllers based in integral parameter adaptation with the fast and non oscillatory transient of variable structure based strategies. The indirect approach offers the possibility to get an easier controller design, either in the selection of the initial estimatives for the plant parameters or in the definition of a suitable region (ball) in which these ones should not escape. These more intuitive selections are due to the direct relationship between the plant parameters and physical system parameters, as inertia moments, resistances, capacitances, etc. The choice of adaptive gains defines how the IB-MRAC behaves between the Indirect MRAC (IMRAC) and the recently proposed Indirect Variable Structure Model Reference Adaptive Control (IVS-MRAC). Simulations to an unstable second order plant and a stability analysis for plants of relative degree one are presented, ensuring the global stability of system, considering a persistently exciting reference signal.

A Modified Design for the VS-MRAC Based on the Indirect Approach: Stability Analysis

Abstract Recently, an alternative to achieve a robust controller that provides a straightforward and intuitive design and tuning of its parameters named Indirect Variable Structure Model Reference Adaptive Controller (IVS-MRAC) was presented for relative degree one LTI plants, suggesting to be globally asymptotically stable with superior transient behavior and disturbance rejection properties. Its novelty is in the procedure to obtain the bounds for the relays amplitudes, used in the switching laws. These bounds are now associated with the plant parameters, instead of the controller parameters. In this paper, a modification is made on the plant high frequency gain switching law, in order to develop a first formal stability analysis, considering the presence of input disturbances and unmodeled dynamics. It is shown that the overall system error is stable with respect to some small residual set.

A VARIABLE STRUCTURE ADAPTIVE POLE PLACEMENT CONTROL APPLIED TO THE SPEED CONTROL OF A THREE-PHASE INDUCTION MOTOR

Abstract Due to its flexibility in choosing the controller design methodology and the adaptive law (least squares, gradient, etc.), the Adaptive Pole Placement Control (APPC) is the most general type of adaptive control. 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 cancellation of plant zeros. The use of the variable structure systems theory has allowed to aggregate fast transient and robustness to parametric uncertainties and disturbances. In this paper, a Variable Structure Adaptive Pole Placement Control (VS-APPC) is applied to the speed control of an induction motor. Simulations and experimental results are shown.

Modular variable structure adaptive backstepping controller: Design and stability analysis☆

Abstract This paper presents the design and stability analysis of a Modular Variable Structure Adaptive Backstepping Controller (MVS-ABC) for plants with arbitrary relative degree, using only input/output measurements. In order to improve the transient response of adaptive backstepping approach via modular design, switching laws are proposed instead of traditional integral adaptive laws. Robustness properties with respect to external disturbances are also demonstrated. Furthermore, simplified algorithms are presented, where the number of relays was significantly reduced (only one is necessary). Simulation results for an unstable system with relative degree three are shown.

Robust Adaptive Control Applied to Chua's Circuit

Abstract Many practical systems (for example: robotic systems, power system and electronic circuits) are multiple-input multiple-output nonlinear systems and some of them have coupled relations between inputs and outputs. Besides all that, these systems can suffer from plant uncertainties and external disturbances. Any control techniques to be applied to these systems are complex. This work proposes a new control structure, based on the union between the variable structure model reference adaptive control and a decouple left-inverse technique, to transform the nonlinear multiple-inputs multiple-outputs system into a number of single-input single-output linear systems. In that case each input affects only one output and with a desired closed-loop performance. The proposed structure uses only input/output measurements, improves the transient performance (reducing the output “chattering”) and it is robust to parametric uncertainties and disturbances. All these features are demonstrated by simulation results of a simple electronic circuit that exhibits chaotic behavior (Chuas circuit). The proposed structure may be used to smooth the control signal, thus reducing the chattering in the output signal.