Quoc Viet Dang

Design and implementation of a robust fuzzy controller for a rotary inverted pendulum using the Takagi-Sugeno descriptor representation

The rotary inverted pendulum (RIP) is an under-actuated mechanical system. Because of its nonlinear behavior, the RIP is widely used as a benchmark in control theory to illustrate and validate new ideas in nonlinear and linear control. This paper presents a robust Takagi-Sugeno (T-S) fuzzy descriptor approach for designing a stabilizing controller for the RIP with real-time implementation. It is shown in this paper how the modeling of the physical system on descriptor T-S form with a reduced number of rules possible can lead to a simplified controller that is practically implementable. Relaxed linear matrix inequality-based stability conditions for the non quadratic case are given. Experimental results illustrate the effectiveness of the proposed approach.

Real-time control of a force feedback haptic interface via EtherCAT fieldbus

This paper is to present a technological solution for implementing a force feedback haptic interface in the context of virtual reality interaction applications. The real-time haptic algorithms are implemented in TwinCAT runtime environment to control drivers via EtherCAT fieldbus. A 3-dimensional visualization model for the virtual reality interaction is developed through Virtual Reality Toolbox in Matlab/Simulink and interconnected with TwinCAT software through the Automation Device Specification communication protocol. The using of Matlab/Simulink with model-based programming method instead of the C++ programming language allows researchers in haptic domain to focus more on the control engineering issues than programming skills. Some experimental tests and verification of the haptic algorithms with visualization model are presented.

Control of Haptic Systems with Time-Varying Delay: A Novel Approach.

Abstract This paper addresses the stable implementation of high stiffness interactions of objects in the virtual environment. The virtual wall is modeled as a mechanical system including a linear spring characterized by a virtual stiffness and a damper with a virtual damping in parallel. A novel approach for improving the stability of discrete-time haptic systems in the case of time-varying delay is proposed by using an augmented state observer instead of the traditional backward finite differentiator. Based on Lyapunovs stability theory, the delay-dependent asymptotic stability condition expressed in terms of LMI for choosing the virtual-wall parameters is presented. The numerical simulation results in the case of the PHANTOM 1.0 haptic devices are included in order to prove the effectiveness of the proposed method.

Design of stabilizing controller for uncertain nonlinear systems under input saturation

The paper aim is to propose a new framework for the design of robust stabilizing controllers for uncertain nonlinear systems under input saturation. A new method for modeling the saturation effect is presented that allows taking its nonlinearity effects into the problem of controller design. The proposed controller is a modified parallel distributed compensation state feedback. Based on Lyapunov theory, sufficient conditions for assuring the system global stability are formulated in terms of linear matrix inequalities (LMI). The problem of maximizing the domain of attraction is expressed as an optimization problem. A numerical example is presented to illustrate the effectiveness of the proposed method.

Multi-objective synthesis for Takagi-Sugeno model subject to input saturation via dynamic output feedback controller

This paper is to propose a systematic method for the design of a dynamic output feedback controller for nonlinear systems in Takagi-Sugeno form subject to input saturation. The proposed method is based on a new technique for modeling the saturation effect that allows taking its nonlinearity effects into the problem of controller design. Based on Lyapunov theory, sufficient conditions for ensuring the system global stability are formulated in terms of linear matrix inequalities (LMIs) considering the L2 -gain performance specification under amplitude bounded exogenous disturbances. An example is presented to illustrate the effectiveness of the proposed method.

Robust stabilizing controller design for Takagi–Sugeno fuzzy descriptor systems under state constraints and actuator saturation

Abstract The aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by Takagi–Sugeno fuzzy descriptor systems and subject to input and state constraints. For this, a novel structure of modified parallel distributed compensation control laws is proposed. The controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from Lyapunovs stability theory and the choice of an original Lyapunov function. This ensures the stabilization of the closed-loop system and the respect of the state and input constraints regionally. The technique is illustrated through three numerical examples.

Experimental study on the stability of an impedance-type force-feedback architecture based on an augmented-state observer for a haptic system under time delay using a LMI approach

One of the most important performance measures of a haptic interface may be characterized by its behaviour in the implementation of a virtual wall in terms of the biggest value of the virtual stiffness that still leaves the device stable. This value depends on many factors including time delays and the virtual world implementation. In this paper we propose a new architecture for this latter factor based on the use of an augmented-state observer which contributes to improving, without additional costs, the performance of a haptic device with respect to the standard implementation based on the use of the backward finite-difference method. In order to compute the stability boundaries of the device in terms of virtual wall parameters, some conditions expressed in terms of LMI (linear matrix inequality) for the stability of discrete-time haptic systems under constant or variable time delay are given. An implementation of a force-feedback haptic test bench is presented. The obtained experimental results confirm the efficiency of the proposed force-feedback architecture with respect to the traditional backward finite-difference method in enlarging the choice for the parameters of the virtual environment for which the haptic system is stable.

Analyzing stability of haptic interface using linear matrix inequality approach

This paper presents a use of the linear matrix inequality approach to analyze stability of haptic device in the interaction with a virtual wall. The haptic device is modeled as a 1-DoF (Degree of Freedom) linear mechanical system composed of masses, springs and dampers. The virtual wall is modeled as a mechanical system composed of a virtual spring and damper. The paper investigates a discrete-time state-space representation of the haptic system by taken into account the effect of ZOH (Zero Order Holder). The second method of Lyapunov is applied to determine stability boundaries. These boundaries are characterized by the critical virtual stiffness, for several values of delay and virtual damping. The qualitative modification of stable region of the haptic interface under the influence of the flexible mode, the human operator model and the time delay are also presented.

Application of a novel structure with observer for force-feedback haptic system under variable time delay

This paper addresses the implementation of a novel structure with observer for force-feedback haptic system under variable time delay. Theoretical approach for stabilizing haptic interface in interaction with a virtual environment is proposed. The obtained experimental results confirm the efficiency of the proposed force-feedback architecture instead of the traditional backward finite-difference method in improving the stability of haptic system.

Experimental study on stability of a haptic system with variable time delays

Stability of force feedback haptic systems under variable time delays remains a major challenge. This paper presents a theoretical and experimental approach for studying the stability of a haptic interface in interaction with a virtual environment. A novel approach based on Lyapunov theory for assuring the stability of haptic systems under constant and variable time delays is firstly presented through conditions in terms of linear matrix inequalities (LMI). The description of a 1 DOF test bench, the experimental protocol and results are next included in order to highlight significant effects of the time delays on the stability, especially for variable time delay. The effects of backward finite difference method, first-order low-pass filter and buffer technique are also examined through an experimental stability domain.