Variable Structure Systems Theory Research Articles

Discrete Action Dependant Heuristic Dynamic Programming in Control of a Wheeled Mobile Robot

In presented paper we propose a discrete tracking control algorithm for a two-wheeled mobile robot. The control algorithm consists of discrete Adaptive Critic Design (ACD) in Action Dependant Heuristic Dynamic Programming (ADHDP) configuration, PD controller and a supervisory term, derived from the Lyapunov stability theorem and based on the variable structure systems theory. Adaptive Critic Designs are a group of algorithms that use two independent structures for estimation of optimal value function from Bellman equation and estimation of optimal control law. ADHDP algorithm consists of Actor (ASE - Associate Search Element) that estimates the optimal control law and Critic (ACE - Adaptive Critic Element) that evaluates quality of control by estimation of the optimal value function from Bellman equation. Both structures are realized in a form of Neural Networks (NN). ADHDP algorithm does not require a plant model (the wheeled mobile robot (WMR) model) for ACE or ASE neural network weights update procedure (in contrast with other ACD configurations e.g. Heuristic Dynamic Programming or Dual Heuristic Programming that use the plant model). In presented control algorithm Actor-Critic structure is supported by PD controller and the supervisory term, that guarantee stable implementation of tracking in an initial adaptive critic neural networks learning phase, and robustness in a face of disturbances. Verification of proposed control algorithm was realized on the two-wheeled mobile robot Pioneer-2DX.

Neuro-adaptive Approach for Controlling a Quad-rotor Helicopter Using Sliding Mode Learning Algorithm

The interest into the autonomous aerial vehicles has largely increased recently. With the advancement of the technology in the area it has become possible to test efficiently and cost-effectively different autonomous flight control concepts and design variations using small-scale aircrafts. The paper presents a new neuro-adaptive approach for controlling the altitude and yaw angle of a miniature rotorcraft having four rotors. The adaptive structures in the proposed control schemes are comprised of radial basis functions neural networks using a new stable on-line learning algorithm. The latter is based on the variable structure systems theory and establishes a sliding motion in term of the network parameters, leading the learning error toward zero. The pitch and roll movements of the rotorcraft are controlled by an algorithm that employs the principles of the well known nested saturation control strategy. The results obtained from flight simulations with an accurate dynamic model of the DraganFlyer V Ti miniature quad-rotor helicopter demonstrate that the proposed neuro-adaptive control approach can deal successfully with the existing uncertainties and variations in the model parameters and/or changes in the environmental conditions.

Blend of independent joint control and variable structure systems for uni-drive modular robots

SUMMARYIn this paper, a control design methodology for a new class of modular robots, so-called “uni-drive modular robots” is introduced. Uni-drive modular robots have a substantial advantage over regular modular robots in terms of the mass of each module since then employ only a single drive for powering all the joints. The drive is mounted at the robot base and all joints tap power from this single drive using clutches. By controlling the engagement time of the clutches, the position and velocity of the joints are regulated. After reviewing the structure of the uni-drive modular robot, a self-expansion formula to generate the dynamics of the robot is introduced. The control of uni-drive n-module robots is realized by blending independent joint control and theory of variable structure systems via a pulse width modulation technique. A uni-drive modular robot is used to conduct simulations and validate the control design technique.

Smooth sliding-mode observers for specific growth rate and substrate from biomass measurement

This paper addresses the estimation of specific growth rate and substrate concentration from biomass measurements in fermentation processes. Specifically, sliding-mode observers are proposed, for which finite-time global convergence is demonstrated using Lyapunov stability theory and concepts of variable structure systems. Two observers are developed for specific growth rate estimation, one producing a discontinuous estimation which is used afterwards for substrate estimation, and the other one – based on high-gain observers – that generates a smooth estimation with first-order dynamics and finite-time bounded convergence error. In the case of substrate estimation, an observer that increases the convergence rate to a vicinity of the real substrate concentration while achieving asymptotic convergence despite kinetic model uncertainties in properly excited processes is designed. This observer also exhibits first-order dynamics.

Output feedback stabilization of uncertain fuzzy systems using variable structure system approach

Based on the variable structure system theory, an output feedback fuzzy control design method is developed for a class of uncertain nonlinear systems that can be represented by a T–S (Takagi–Sugeno) fuzzy model. The uncertain fuzzy systems under consideration may have mismatched uncertainties in the state matrix. As the local controller a compensator-based sliding mode output feedback controller with a nonlinear discontinuous term is used. In terms of linear matrix inequalities (LMIs), a sufficient condition is derived for the existence of the fuzzy controller guaranteeing a stable sliding motion. It is shown that the compensator gain and the switching surface parameter matrix can be characterized in terms of the solution of the LMI existence condition. Finally, an LMI-based design algorithm and numerical design examples are given.

A New Speed Observer Based on Fuzzy Sliding Mode Sensorless Control Scheme for a High- Performance Induction Motor Drive

The subject of the paper is the implementation of fuzzy sliding mode control conception for robust accurate tracking of induction motor drive operating in a high-performance drives environment. The introducing of fuzzy sliding mode in the control system helps to achieve a good dynamic response, disturbance rejection and low to plant parameter variations of the A.C drive. The fuzzy sliding mode controller combines the advantages of both fuzzy controllers and sliding mode controllers. By combining variable structure systems theory and fuzzy logic concept, a new algorithm is developed. The proposed control scheme can drive the dynamics of controlled system into a designed sliding surface in finite time and guarantee the property of asymptotical stability. The synthesis of sliding mode control and the control laws for the controls of speed are described. In order to verify the performances of the proposed observers and control algorithms and to test behaviour of the controlled system, numerical and real experiments are achieved.

Robust Stabilization of Uncertain Fuzzy Systems Using Variable Structure System Approach

Based on the variable structure system (VSS) theory, we develop a fuzzy control system design method for a class of uncertain nonlinear multivariable systems that can be represented by a Takagi-Sugeno fuzzy model. We make the first attempt to relax the restrictive assumption that each nominal local system model shares the same input channel, which is required in the traditional VSS-based fuzzy control design methods. As the local controller we use a sliding mode controller with a switching feedback control term. In terms of linear matrix inequalities (LMIs), we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing asymptotic stability of the reduced-order equivalent sliding mode dynamics. We present an LMI characterization of such sliding surfaces. We also give an LMI-based algorithm to design the switching feedback control term so that a stable sliding motion is induced in finite time. Finally, we give a numerical design example.

Sliding Mode Algorithm for On-line Learning in Fuzzy Rule-based Neural Networks

A new, variable structure systems theory based, algorithm has been developed for on-line training of fuzzy-neural networks. Such computationally intelligent structures are widely used for modeling, identification and control of nonlinear dynamic systems. The algorithm is applicable to fuzzy rule-based neural nets of Takagi-Sugeno-Kang type with a scalar output. Its convergence is established and the conditions are given. Differently from other similar approaches which are limited to the adaptation of the parameters of the network defuzzification part only, the proposed algorithm tunes also the parameters of the implemented membership functions. The zero level set of the learning error variable is considered as a sliding surface in the space of network learning parameters. The effectiveness of the proposed algorithm is shown when applied to on-line learning of nonlinear functions approximation.

LMI-Based Nonlinear Fuzzy Observer-Controller Design for Uncertain MIMO Nonlinear Systems

Based on the variable structure system theory, we develop a nonlinear fuzzy observer-controller design method for a class of uncertain nonlinear systems that can be represented by a Takagi-Sugeno fuzzy model. We use a sliding mode observer and a sliding mode controller as the local state observer and the local controller. In terms of linear matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the fuzzy controller. We also derive LMI conditions for the existence of the fuzzy observer and the fuzzy controller guaranteeing the alpha-stability or generalized H2/Hinfin performance constraints. We show that the observer and the controller can be independently designed, i.e., the separation property holds. Finally, we give simple LMI-based design algorithms, together with an example.

Theory of variable-structure control systems: Inception and initial development

The article presents a retrospective view of the inception and development of the theory of variable-structure systems. Ideas and approaches that have played a formative role in the theory of variable-structure systems and its applications are identified. The leading role of Russian scientists in this process is highlighted.

Sliding Mode Control

Sliding Mode Control

Neuro‐adaptive sliding‐mode tracking control of robot manipulators

AbstractIn this work, a new dynamical on‐line learning algorithm for robust model‐free neuro‐adaptive control of a class of nonlinear systems with uncertain dynamics is proposed and experimentally tested in order to evaluate its performance and practical feasibility in industrial settings. The control application studied is the trajectory tracking control task for the first three joints of an open architecture articulated robot manipulator. The control scheme makes use of variable structure systems theory and the feedback‐error‐learning concept. An inner sliding motion is established in terms of the neurocontroller parameters, aiming to lead the error in its control signal towards zero. The outer sliding motion bears on the system under control, the state tracking error vector of which is simultaneously driven towards the origin of the phase space. The existing relation between the two sliding motions is shown. Experimental results illustrate that the proposed neural‐network‐based controller possesses a remarkable learning capability to control complex dynamical systems, virtually without requiring a priori knowledge of the plant dynamics and laborious start‐up procedures. Copyright © 2007 John Wiley & Sons, Ltd.

Adaptive variable structure control of a class of non-linear systems

The problem of tuning the parameters of a controller operating in the presence of noise, time-varying parameters, non-linearities, and uncertainties in practice requires the process of continuous adjustment of the parameters influencing the performance. When the diversity of the challenges in the domain of real-time applications is taken into consideration, it becomes apparent that the adopted controller structure must be sufficiently flexible, and its operating principles must be well explained, particularly in accounting for the stability issues. In this paper, a method is proposed for tuning the parameters of controllers whose outputs are linear in the adjustable parameters, utilizing variable structure systems theory. The method discussed constructs the best error measure at the controller output, and uses this quantity with a suitably designed tuning law, which drives the system under control to a predefined sliding regime and maintains the sliding mode. It is shown analytically that the parametric evolution takes place in a finite volume space, indicating that the controller parameters evolve bounded. In the simulation studies, the approach presented has been tested on the control of a double pendulum system and the superior performance of the strategy has been shown under the existence of noisy observations and large non-zero initial errors.

On-line neural training algorithm with sliding mode control and adaptive learning rate

This paper presents a new algorithm for on-line artificial neural networks (ANN) training. The network topology is a standard multilayer perceptron (MLP) and the training algorithm is based on the theory of variable structure systems (VSS) and sliding mode control (SMC). The main feature of this novel procedure is the adaptability of the gain (learning rate), which is obtained from sliding mode surface so that system stability is guaranteed.

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

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.

Controle Adaptativo Por Posicionamento De Pólos E Estrutura Variável Aplicado Ao Controle De Velocidade De Um Motor De Indução Trifásico

Existem dois métodos principais para a construção de controladores adaptativos. Um deles é o Controle Adaptativo por Modelo de Referência (MRAC) e o outro é o Controle Adaptativo por Posicionamento de Pólos (APPC). No MRAC, um modelo de referência é escolhido para gerar a trajetória desejada que o sinal de saída da planta deve seguir, e este modelo pode requerer o cancelamento de zeros da planta. Devido a sua flexibilidade em escolher a metodologia de projeto do controlador (realimentação de estado, projeto de compensador, linear quadrático, etc.) e a lei adaptativa (mínimos quadrados, método do gradiente, etc.), o APPC é o tipo mais geral de controle adaptativo. Tradicionalmente, vem sendo desenvolvido em uma abordagem indireta e, como uma vantagem, pode ser aplicado a plantas de fase não-mínima, já que não envolve cancelamentos de zeros e pólos. A integração aos sistemas com estrutura variável permite agregar rapidez no transitório e robustez às variações paramétricas e perturbações. Neste artigo, um Controlador Adaptativo por Posicionamento de Pólos e Estrutura Variável (VSAPPC) é aplicado ao controle de velocidade de um motor de indução trifásico. São mostrados resultados de simulação e experimentais.

Unidrive Modular Robot: Dynamics, Control, and Experiments

In this paper, a control design methodology for the new class of modular robots so-called “unidrive modular robots” is introduced. Unidrive modular robots because of employing only a single drive for operating all the joints have a substantial advantage over regular modular robots in terms of the mass of each module. The drive is mounted at the robot base and all joints tap power from the single drive using clutches. By controlling the engagement time of the clutches, the position and velocity of the joints are regulated. In this work, a general state space model of the robot is first developed and then based on the theory of variable structure systems and sliding mode control a design methodology for local controllers is introduced. The control design technique is validated by experimental results.

A Study on Effect of VSS Control of Generation Excitation System using Single Machine Infinite Bus System Simulator

It is very effective to enhance the robustness of control over the faults occurred in power system in order to realize stable and reliable power supply. The sliding mode control based on the Variable Structure System (VSS) theory is paid attentions as one of the promising robust control scheme. In the sliding mode control, the structure of the control system is changed across the hyper plane (switching plane) in state space so that the state variables of the system are kept on the hyper plane.This paper proposes a novel control method of generator's excitation system in which the concept of sliding mode control is employed. More specifically, the proposed method switches the reference voltage used in AVR according to the sign of switching function. This paper also discusses the systematic design procedure of the optimal hyper plane. Performance and effectiveness of the proposed control method are investigated through both numerical studies and experimental tests using the single-machine infinite-bus system simulator. Both results show that the proposed control method can damp the transient swing caused by a fault effectively.

Sliding Mode Conditioning for Constrained Processes

A reference conditioning algorithm based on variable structure systems theory is developed to cope with actuator saturation. This sliding mode conditioning presents some distinctive features. In fa...

Second-Order Sliding-Mode Control of DC Drives

One of the most recent topics in variable-structure systems theory is represented by the second-order sliding-mode control (2-SMC) methodology. This approach guarantees the same robustness and dynamic performance of traditional first-order SMC algorithms, and, at the same time, attenuates the chattering phenomenon, which is the main drawback in the actual implementation of this technique. In the present paper, a recently-proposed 2-SMC algorithm is used to synthesize a robust dc-drive control system which does not require current feedback and demands only rough information about the actual motor parameters. Stability and performance are analyzed, and an experimental comparison with a proportional-integral-based control scheme is reported.