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.

An adaptive PID-like controller for vibration suppression of piezo-actuated flexible beams

2017 ◽  
Vol 24 (12) ◽  
pp. 2656-2670 ◽  
Author(s):  
Teerawat Sangpet ◽  
Suwat Kuntanapreeda ◽  
Rüdiger Schmidt
Keyword(s):  
Vibration Suppression ◽  
Flexible Structures ◽  
Flexible Beam ◽  
Flexible Beams ◽  
Present Scheme ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
Control Scheme ◽  
The Stability

Flexible structures have been increasingly utilized in many applications because of their light-weight and low production cost. However, being flexible leads to vibration problems. Vibration suppression of flexible structures is a challenging control problem because the structures are actually infinite-dimensional systems. In this paper, an adaptive control scheme is proposed for the vibration suppression of a piezo-actuated flexible beam. The controller makes use of the configuration of the prominent proportional-integral-derivative controller and is derived using an infinite-dimensional Lyapunov method. In contrast to existing schemes, the present scheme does not require any approximated finite-dimensional model of the beam. Thus, the stability of the closed loop system is guaranteed for all vibration modes. Experimental results have illustrated the feasibility of the proposed control scheme.

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.

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.

scholarly journals Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Xiaohui Xu ◽  
Xiaofeng Yin ◽  
Jiye Zhang ◽  
Peng Wang
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Stochastic Disturbances ◽  
Infinite Dimensional ◽  
Disturbance Propagation ◽  
Vector Lyapunov Function ◽  
Look Ahead ◽  
The Stability

Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness of the obtained results.

Design of an adaptive control law using trigonometric functions for robot manipulators

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 93-99 ◽  
Author(s):  
Recep Burkan
Keyword(s):  
Adaptive Control ◽  
Robot Manipulators ◽  
Tracking Error ◽  
Uncertain System ◽  
Control Law ◽  
Trigonometric Functions ◽  
Feed Forward ◽  
Inertia Parameters ◽  
The Stability ◽  
Adaptive Control Law

In this study, a new approach of adaptive control law for controlling robot manipulators using the Lyapunov based theory is derived, thus the stability of an uncertain system is guaranteed. The control law includes a PD feed forward part and a full dynamics feed forward compensation part with the unknown manipulator and payload parameters. The novelty of the obtained result is that an adaptive control algorithm is developed using trigonometric functions depending on manipulator kinematics, inertia parameters and tracking error, and both system parameters and adaptation gain matrix are updated in time.

Active Fault Tolerant Control Based on Fault Estimation

2014 ◽  
Vol 635-637 ◽  
pp. 1199-1202 ◽  
Author(s):  
Zheng Gao Hu ◽  
Guo Rong Zhao ◽  
Da Wang Zhou
Keyword(s):  
Active Fault ◽  
Fault Tolerant ◽  
Sliding Mode ◽  
Fault Tolerant Control ◽  
Sliding Mode Observer ◽  
Fault Estimation ◽  
Control Law ◽  
Active Fault Tolerant Control ◽  
The Stability ◽  
Twisting Algorithm

For the chattering problem in the traditional sliding mode observer-based fault estimation, a second order sliding mode observer based on the Super-twisting algorithm was proposed. In order to avoid the cumbersome process of proving the stability of the Super-twisting algorithm, a Lyapunov function was adopted. An active fault tolerant control law was designed based on the fault estimation. Finally, simulation show the effectiveness of the proposed approach.

scholarly journals Design and Comparative Study of Advanced Adaptive Control Schemes for Position Control of Electronic Throttle Valve

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 65 ◽  
Author(s):  
Amjad Humaidi ◽  
Akram Hameed
Keyword(s):  
Adaptive Control ◽  
Position Control ◽  
Sliding Mode ◽  
Angular Position ◽  
Estimation Errors ◽  
Electronic Throttle ◽  
Control Schemes ◽  
Backstepping Controller ◽  
Matlab Package ◽  
The Stability

This paper investigates the performance of two different adaptive control schemes for controlling the angular position of an electronic throttle (ET) plate. The adaptive backstepping controller and adaptive sliding mode backstepping controller are the controllers under consideration. The control design based on these adaptive controllers is firstly addressed and the stability analysis of each controller has been presented and the convergence of both position and estimation errors for both controllers have been proved. A comparison study of the performance of both controllers has been conducted in terms of system transient characteristics and the behavior of their associated adaptive gain. The simulation has been implemented within the environment of the MATLAB package.

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