scholarly journals Discrete-time adaptive control using a sliding mode

1996 ◽  
Vol 2 (2) ◽  
pp. 131-142 ◽  
Author(s):  
Tetsuo Semba ◽  
Katsuhisa Furuta
Keyword(s):  
Adaptive Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Control Law ◽  
Control Input ◽  
Discontinuous Control ◽  
Fast Tracking ◽  
Performance Improvements ◽  
Equivalent Control ◽  
The Stability

Adaptive control using a sliding mode in discrete time systems is proposed as a means of achieving robustness with respect to parameter variations, fast tracking to a desired trajectory, and fast parameter convergence, without increasing the chattering of the control inputs. We first prove the stability of a system in which the control inputs consist of equivalent control driven by the adaptive control law and bounded discontinuous control. The discontinuous control driven by the sliding control law is then obtained so that the output error quickly converges to zero. Finally, the performance improvements obtained by adding the sliding mode control input are shown through computer simulations.

scholarly journals Adaptive Vibration Control of Piezoactuated Euler-Bernoulli Beams Using Infinite-Dimensional Lyapunov Method and High-Order Sliding-Mode Differentiation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Teerawat Sangpet ◽  
Suwat Kuntanapreeda ◽  
Rüdiger Schmidt
Keyword(s):  
Adaptive Control ◽  
Lyapunov Method ◽  
Sliding Mode ◽  
High Order ◽  
Control Law ◽  
Flexible Beams ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Sensor Configuration ◽  
The Stability

This paper presents an adaptive control scheme to suppress vibration of flexible beams using a collocated piezoelectric actuator-sensor configuration. A governing equation of the beams is modelled by a partial differential equation based on Euler-Bernoulli theory. Thus, the beams are infinite-dimensional systems. Whereas conventional control design techniques for infinite-dimensional systems make use of approximated finite-dimensional models, the present adaptive control law is derived based on the infinite-dimensional Lyapunov method, without using any approximated finite-dimension model. Thus, the stability of the control system is guaranteed for all vibration modes. The implementation of the control law requires a derivative of the sensor output for feedback. A high-order sliding mode differentiation technique is used to estimate the derivative. The technique features robust exact differentiation with finite-time convergence. Numerical simulation and experimental results illustrate the effectiveness of the controller.

scholarly journals Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Qudrat Khan ◽  
Aamer Iqbal Bhatti ◽  
Antonella Ferrara
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Integral Manifold ◽  
Control Variable ◽  
Control Design ◽  
Pole Placement ◽  
Control Law ◽  
Control Input ◽  
Discontinuous Control ◽  
Mode Control

An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In conventional sliding mode the control variable suffers from high frequency oscillations due to the discontinuous control component. However, in the present proposal, the designed control law is applied to the actual system after passing through a chain of integrators. As a consequence, the control input actually fed into the system is continuous, which is a positive feature in terms of chattering attenuation. By applying the proposed controller, the system output is regulated to zero even in the presence of the uncertainties. In the paper, the proposed control law is theoretically analyzed and its performances are demonstrated in simulation.

General lemma for the stability analysis of discrete-time adaptive control

1990 ◽  
Vol 51 (2) ◽  
pp. 283-288 ◽  
Author(s):  
FOUAD GIRI ◽  
MOHAMED M'SAAD ◽  
JEAN-MICHEL DION ◽  
LUC DUGARD
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Discrete Time ◽  
General Lemma ◽  
The Stability

DESIGN OF ADAPTIVE FUZZY SLIDING MODE CONTROL FOR NONLINEAR SYSTEMS

1999 ◽  
Vol 07 (05) ◽  
pp. 463-474 ◽  
Author(s):  
JEN-YANG CHEN
Keyword(s):  
Sliding Mode ◽  
Membership Functions ◽  
System Specification ◽  
Pendulum System ◽  
Control Rules ◽  
Inverted Pendulum System ◽  
Equivalent Control ◽  
Fuzzy Sliding Mode ◽  
The Stability ◽  
The Individual

In this paper, a fuzzy sliding mode controller (FSMC), which is synthesized by a collection of linguistic control rules whose membership functions of THEN-part is adapted, is proposed. Both the membership functions of IF-part and THEN-part are arranged symmetrically and distributed equally in the individual universe of discourse. In particular, the membership functions of the THEN-part can be adapted via one parameter adaptation to meet the required system specification. The proposed direct adaptive FSMC can be synthesized through the following stages. First, the control rules are constructed according to the concepts of SMC, and the fuzzy sets whose membership functions are symmetrically covered in state space. Then, the derived adaptive law is used to adjust the membership functions of the THEN-part. The FSMC is employed to approximate the equivalent control of SMC without knowing the mathematical model of the controlled system. Third, a hitting control is developed to guarantee the stability of the control system. Finally, we apply this FSMC to control a nonlinear inverted pendulum system for confirming the validity of the proposed approach.

Three-dimensional adaptive fixed-time guidance law against maneuvering targets with impact angle constraints and control input saturation

2021 ◽  
pp. 014233122110598
Author(s):  
Fei Ma ◽  
Yunjie Wu ◽  
Siqi Wang ◽  
Xiaofei Yang ◽  
Yueyang Hua
Keyword(s):  
Sliding Mode ◽  
Input Saturation ◽  
Three Dimensional ◽  
Fixed Time ◽  
Impact Angle ◽  
Guidance System ◽  
Control Input ◽  
Guidance Law ◽  
The Stability ◽  
And Control

This paper presents an adaptive fixed-time guidance law for the three-dimensional interception guidance problem with impact angle constraints and control input saturation against a maneuvering target. First, a coupled guidance model formulated by the relative motion equation is established. On this basis, a fixed-time disturbance observer is employed to estimate the lumped disturbances. With the help of this estimation technique, the adaptive fixed-time sliding mode guidance law is designed to accomplish accurate interception. The stability of the closed-loop guidance system is proven by the Lyapunov method. Simulation results of different scenarios are executed to validate the effectiveness and superiority of the proposed guidance law.

scholarly journals Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems

2008 ◽  
Vol 3 (1) ◽  
pp. 6 ◽  
Author(s):  
Hafedh Abid ◽  
Mohamed Chtourou ◽  
Ahmed Toumi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Fuzzy Model ◽  
Uncertain System ◽  
Control Technique ◽  
Control Law ◽  
Mode Control ◽  
Equivalent Control ◽  
Fuzzy Sliding Mode ◽  
Discrete Nonlinear Systems

In this work we are interested to discrete robust fuzzy sliding mode control. The discrete SISO nonlinear uncertain system is presented by the Takgi- Sugeno type fuzzy model state. We recall the principle of the sliding mode control theory then we combine the fuzzy systems with the sliding mode control technique to compute at each sampling time the control law. The control law comports two terms: equivalent control law and switching control law which has a high frequency. The uncertainty is replaced by its upper bound. Inverted pendulum and mass spring dumper are used to check performance of the proposed fuzzy robust sliding mode control scheme.

Disturbance Adaptive Discrete-Time Sliding Control With Application to Engine Speed Control

1998 ◽  
Vol 123 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Mooncheol Won ◽  
J. K. Hedrick
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Control Method ◽  
Sliding Mode ◽  
Input Saturation ◽  
Adaptive Sliding Mode Control ◽  
Control Law ◽  
Sliding Surface ◽  
Sliding Control ◽  
Error Dynamics

This paper presents a discrete-time adaptive sliding control method for SISO nonlinear systems with a bounded disturbance or unmodeled dynamics. Control and adaptation laws considering input saturation are obtained from approximately discretized nonlinear systems. The developed disturbance adaptation or estimation law is in a discrete-time form, and differs from that of conventional adaptive sliding mode control. The closed-loop poles of the feedback linearized sliding surface and the adaptation error dynamics can easily be placed. It can be shown that the adaptation error dynamics can be decoupled from sliding surface dynamics using the proposed scheme. The proposed control law is applied to speed tracking control of an automatic engine subject to unknown external loads. Simulation and experimental results verify the advantages of the proposed control law.

Cooperative Tracking Control for Formation Keeping of Fractionated Spacecraft Based on Error Exchanging

2014 ◽  
Vol 1016 ◽  
pp. 649-654
Author(s):  
Ya Feng Niu ◽  
Yong Ming Gao
Keyword(s):  
Tracking Control ◽  
Cooperative Control ◽  
Sliding Mode ◽  
Control Law ◽  
Velocity Information ◽  
The Stability ◽  
Cooperative Tracking ◽  
Fractionated Spacecraft ◽  
High Degree ◽  
Formation Keeping

This paper discusses the cooperative control for formation keeping of fractionated spacecraft, which is a new concept in recent years. For system of second-order differential equations of formation flying dynamics, knowledge of graph and consensus theory is introduced in study. By means of the idea of sliding mode control, we design a tracking control law for time-varying desired signal. Via exchanging error information among modules, the control law can make errors synchronized up to zero to achieve tracking. Relative velocity information between modules is not needed in this control law, which will efficiently reduce the requirements for relative navigation between modules. Then we prove the stability of the control system. Finally numerical simulation results show the effectiveness of the control law. By configuring the control parameters reasonably, we can achieve high degree of control accuracy.

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