scholarly journals Discrete-Time Exponentially Stabilizing Fuzzy Sliding Mode Control via Lyapunov’s Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Radiša Ž. Jovanović ◽  
Zoran M. Bučevac
Keyword(s):  
Discrete Time ◽  
Control Algorithm ◽  
Fuzzy Controller ◽  
Sliding Mode ◽  
Linear Time ◽  
Variable Structure ◽  
State Feedback Control ◽  
Initial State ◽  
Variable Structure System ◽  
Lyapunov’S Second Method

The exponentially stabilizing state feedback control algorithm is developed by Lyapunov’s second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspaceS, in finite time and with prescribed velocity estimate. Inside the sliding subspaceS, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given.

scholarly journals Tracking Control of Variable Structure System Using Variable Boundary Layer

2001 ◽  
Vol 5 (6) ◽  
pp. 338-345
Author(s):  
Heejin Lee ◽  
Keyword(s):  
Boundary Layer ◽  
Tracking Control ◽  
Linear Time ◽  
Variable Structure ◽  
Second Order ◽  
Initial State ◽  
Variable Boundary ◽  
Variable Structure Systems ◽  
Variable Structure System ◽  
Arbitrary Initial State

In this paper, a new scheme is presented for the accurate tracking control of the second-order variable structure systems using the variable boundary layer. Up to now, variable structure controller(VSC) applying the variable boundary layer did not remove chattering from an arbitrary initial state of the system trajectory because VSC has used the fixed sliding surface. But, by using the linear time-varying sliding surfaces, the scheme has the robustness against chattering from all states. The suggested method can be applied to the second-order nonlinear systems with parameter uncertainty and extraneous disturbances, and have better tracking performance than the conventional method.To demonstrate the advantages of the proposed algorithm, it is applied to a two-link manipulator.

A Novel Fuzzy Sliding Mode Control Scheme for Nonlinear Systems with Bounded Inputs

2002 ◽  
Vol 8 (7) ◽  
pp. 945-965 ◽  
Author(s):  
Juhng-Perng Su ◽  
Chi-Ying Liang
Keyword(s):  
Sliding Mode Control ◽  
Fuzzy Controller ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Variable Structure ◽  
Single Frequency ◽  
Bench Mark ◽  
Mode Control ◽  
Variable Structure System ◽  
Control Scheme

In this paper, we investigated the design of robust controllers for a class of nonlinear uncertain systems with bounded inputs, which have not yet been thoroughly discussed. Based on the variable structure system theory, we developed a novel stable sliding mode control scheme for this class of systems. A key feature of this control scheme is the introduction of a new generalized error as a complement to the conventional generalized error to form a meaningful error measure so that a new sliding mode controller incorporated with a two-input one-output fuzzy controller can be constructed to improve the reaching behavior of the system during the reaching phase as well as the tracking precision while in the boundary layer. The nonlinear bench mark problem, TORA, was used as an example to demonstrate the effectiveness of the design. Simulation results showed that, as compared with various available controllers in literature, much better responses to any initial conditions and to single-frequency sinusoidal disturbances can be obtained.

Model-Free Trajectory Control of a Two-Link Flexible-Joint Robot: Theory and Experiment

2005 ◽  
Author(s):  
Withit Chatlatanagulchai ◽  
Peter H. Meckl
Keyword(s):  
Control Algorithm ◽  
Variable Structure ◽  
State Feedback Control ◽  
External Disturbances ◽  
Control Laws ◽  
Flexible Joint ◽  
Model Free ◽  
The Neural Network ◽  
Lyapunov’S Second Method ◽  
The Mathematical Model

We present a state-feedback control of a two-link flexible-joint robot. First, we obtain desired control laws from Lyapunov’s second method. Then, we use three-layer neural networks to learn the unknown parts of the desired control laws. In this way, the control algorithm does not require the mathematical model representing the robot. We use a smooth variable structure controller to handle uncertainties from the neural network approximation and external disturbances. To show the effectiveness and practicality of this control algorithm, we performed an experiment on one of the robots in our laboratory.

scholarly journals Discrete–Time Integral Sliding Mode Control with Disturbances Compensation and Reduced Chattering for Pv Grid–Connected Inverter

2015 ◽  
Vol 66 (2) ◽  
pp. 61-69 ◽  
Author(s):  
Santolo Meo ◽  
Vincenzo Sorrentino
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Control Algorithm ◽  
Sliding Mode ◽  
Integral Sliding Mode Control ◽  
Integral Sliding Mode ◽  
Mode Control ◽  
Time Integral ◽  
Grid Connected Inverter ◽  
Disturbances Compensation

Abstract In the paper a new discrete-time integral sliding mode control (DISMC) with disturbances compensation and reduced chattering for grid-connected inverter is proposed for active and reactive power regulation. Differently by many SMC proposed in literature that have a time-continuous formulation in spite have been implemented with digital processor, the proposed DISMC is fully formulated in discrete-time, taking into account the effects introduced by a microprocessor-based implementation. As will be demonstrated such approach consents to reduce the chattering about the sliding manifold within a boundary layer of O(T2) thickness instead of O(T) (being T the sampling period of the control algorithm). Moreover it introduces a correction of the control vector which eliminates the influence of modeling error and external disturbances improving stability and robustness of the controlled system. Constant converter switching frequency is achieved by using space vector modulation, which eases the design of the ac harmonic filter. In the paper, after a detailed formalization of the proposed control algorithm, several numerical and experimental results on a three-phase grid-connected inverter prototype are shown, proving the effectiveness of the control strategy.

Slip parameter estimation of a single wheel using a non-linear observer

Robotica ◽  
2008 ◽  
Vol 27 (6) ◽  
pp. 801-811 ◽  
Author(s):  
Z. B. Song ◽  
L. D. Seneviratne ◽  
K. Althoefer ◽  
X. J. Song ◽  
Y. H. Zweiri
Keyword(s):  
Sliding Mode ◽  
Kinematic Model ◽  
Variable Structure ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Observer ◽  
Slip Angle ◽  
Wheel Slip ◽  
Variable Structure System ◽  
Non Linear ◽  
Linear Observer

SUMMARYSliding mode observer is a variable structure system where the dynamics of a nonlinear system is altered via application of a high-frequency switching control. This paper presents a non-linear sliding mode observer for wheel linear slip and slip angle estimation of a single wheel based on its kinematic model and velocity measurements with added noise to simulate actual on-board sensor measurements. Lyapunov stability theory is used to establish the stability conditions for the observer. It is shown that the observer will converge in a finite time, provided the observer gains satisfy constraints based on a stability analysis. To validate the observer, linear and two-dimensional (2D) test rigs are specially designed. The sliding mode observer is tested under a variety of conditions and it is shown that the sliding mode observer can estimate wheel slip and slip angle to a high accuracy. It is also shown that the sliding mode observer can accurately predict wheel slip and slip angle in the presence of noise, by testing the performance of the sliding mode observer after adding white noise to the measurements. An extended Kalman filter is also developed for comparison purposes. The sliding mode observer is better in terms of prediction accuracy.

Sign in / Sign up

Export Citation Format

Share Document