Design and Simulation of Robust and Adaptive Controls for a Nonlinear String System1

2004 ◽  
Vol 126 (1) ◽  
pp. 54-62
Author(s):  
Weiwei Jin ◽  
Zhihua Qu ◽  
Kuo-Chi Lin
Keyword(s):  
Numerical Simulation ◽  
Vibration Control ◽  
Boundary Control ◽  
Closed Loop ◽  
Direct Method ◽  
Closed Loop System ◽  
Lyapunov Direct Method ◽  
Adaptive Controls ◽  
Control Designs ◽  
Nonlinear String

In this paper, vibration control of a nonlinear string system is considered. The system consists of a nonlinear string, two boundary supporting mechanisms, and a moving transporter at the base. To suppress the vibration, boundary control designs are carried out. A new robust and adaptive boundary controller is designed using the Lyapunov direct method. The proposed control is implemented at the two ends supporting the string to compensate for vibration induced by the base motion. It is shown that the adaptive/robust boundary control can asymptotically stabilize the nonlinear string. Numerical simulation of the closed loop system demonstrates the effectiveness of the proposed control.

Design and Simulation of Robust and Adaptive Controls for a Nonlinear String System

2000 ◽  
Author(s):  
Weiwei Jin ◽  
Zhihua Qu ◽  
Kurt Lin
Keyword(s):  
Numerical Simulation ◽  
Vibration Control ◽  
Boundary Control ◽  
Closed Loop ◽  
Direct Method ◽  
Closed Loop System ◽  
Lyapunov Direct Method ◽  
Adaptive Controls ◽  
Control Designs ◽  
Nonlinear String

Abstract In this paper, vibration control of a nonlinear string system is considered. The system consists of a nonlinear string, two boundary supporting mechanisms, and a moving transporter at the base. To suppress the vibration, boundary control designs are carried out. A new robust and adaptive boundary controller is designed using the Lyapunov direct method. The proposed control is implemented at the two ends supporting the string to compensate for vibration induced by the base motion. It is shown that the adaptive/robust boundary control can asymptotically stabilize the nonlinear string. Numerical simulation of the closed loop system demonstrates the effectiveness of the proposed control.

Vibration Reduction by Active Control of Flexible Marine Riser Angle Subjected to Time-Varying Distributed Force

2016 ◽  
Author(s):  
F. Bakhtiari-Nejad ◽  
A. Azimi
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Direct Method ◽  
Surface Current ◽  
Ocean Surface ◽  
Distributed Parameter ◽  
Time Varying ◽  
Parameter System ◽  
Closed Loop System ◽  
Ocean Surface Current

In this research, boundary control is developed at the upper end of the riser based on the Lyapanuv’s direct method to reduce top angle and transverse vibration of the riser subjected to time-varying disturbance. First, ocean surface current is assumed to be linearly declined to zero from the ocean surface to the ocean floor and then it is assumed to be exponentially declined to zero. The riser is modeled as a distributed parameter system with one partial differential equation (PDE) coupled with boundary conditions (ODE). Since all of the control signals can be measured by sensors or can be calculated by a backwards difference algorithm, so the boundary control is practical and implementable with existing instrumentation. The Lyapunov’s direct method is applied to stability analysis of the closed-loop system. Finally, efficiency of the controller is verified and results of linear and exponential profiles are compared to each other.

PI Control of HSFDs for Active Control of Rotor-Bearing Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 658-667 ◽  
Author(s):  
J. P. Hathout ◽  
A. El-Shafei
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Closed Loop ◽  
Rotating Machinery ◽  
Loop System ◽  
Pi Control ◽  
Closed Loop System ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Bearing

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

A comparative study for collocated and non-collocated sensor/actuator placement in vibration control of a maneuvering flexible satellite

2014 ◽  
Vol 229 (8) ◽  
pp. 1415-1424 ◽  
Author(s):  
Morteza Shahravi ◽  
Milad Azimi
Keyword(s):  
Vibration Control ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Lyapunov Analysis ◽  
Closed Loop System ◽  
Sensors And Actuators ◽  
Sensor Actuator ◽  
Attitude Maneuver ◽  
System Equations ◽  
Actuator Placement

This paper presents a study concerning the vibration control of smart flexible sub-structures of satellite during attitude maneuver. A comparison between the collocated and non-collocated piezoceramic patches acting as sensors and actuators is performed in order to investigate their effectiveness to suppress vibrations in flexible substructures. A rigid hub with two elastic appendages containing surface bounded piezoelectric patches is being considered as satellite model. Finite element method and Lagrangian formulation are used for derivation of system equations of motion. Stability proof of the overall closed-loop system is given via Lyapunov analysis. The numerical simulations verify the results of the study.

Adaptive boundary control and vibration suppression of a flexible satellite system with input saturation

2018 ◽  
Vol 41 (9) ◽  
pp. 2666-2677
Author(s):  
Yun Fu ◽  
Yu Liu ◽  
Daoping Huang
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Input Saturation ◽  
Satellite System ◽  
Closed Loop System ◽  
Adaptive Law ◽  
Control Scheme ◽  
Boundary Disturbance ◽  
Adaptive Boundary Control

In this paper, the vibration suppression problem of a flexible satellite system is addressed. The dynamic model of the flexible satellite system is expressed by a set of non-homogeneous partial differential equations (PDEs). By using the theory of systems with uniform ultimate bounded (UUB) solutions and adaptive techniques, adaptive boundary control is presented to suppress the vibration of the flexible satellite with parametric uncertainties. A disturbance adaptive law is constructed to compensate for the effect of the boundary disturbance, and an auxiliary system is considered to mitigate the effect of input saturation. The well-posedness of the closed-loop system is discussed, and UUB stability can be ensured through a rigorous Lyapunov-like analysis. Numerical simulation results show the effectiveness of the proposed control scheme.

Output feedback boundary control of a flexible marine riser system

2017 ◽  
Vol 24 (16) ◽  
pp. 3617-3630 ◽  
Author(s):  
Yu Liu ◽  
Fang Guo
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
High Gain ◽  
Loop System ◽  
System State ◽  
Marine Riser ◽  
Closed Loop System ◽  
Observer Error ◽  
System States

This paper is concerned with the design of boundary control for globally stabilizing a flexible marine riser system. The dynamics of the riser system are represented in the form of hybrid partial–ordinary differential equations. Firstly, when the system state available for feedback is unmeasurable, an observer backstepping method is employed to reconstruct the system state and then design the boundary control for vibration suppression of the riser system. Subsequently, for the case that the system states in the designed control law cannot be accurately obtained, the high-gain observers are utilized to estimate those unmeasurable system states. With the proposed control, the uniformly ultimately bounded stability of the closed-loop system is demonstrated by the use of Lyapunov’s synthetic method and the state observer error is converged exponentially to zero as time approaches to infinity. In addition, the disturbance observer is introduced to track external environmental disturbance. Finally, the control performance of the closed-loop system is validated by carrying out numerical simulation.

scholarly journals The Effect of Control Strength on Lag Synchronization of Nonlinear Coupled Complex Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Shuguo Wang ◽  
Hongxing Yao
Keyword(s):  
Numerical Simulation ◽  
Complex Networks ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Lyapunov Direct Method ◽  
Lag Synchronization ◽  
Control Strength

This paper mainly investigates the lag synchronization of nonlinear coupled complex networks using methods that are based on pinning control, where the weight configuration matrix is not necessarily symmetric or irreducible. We change the control strength into a parameter concerning timet, by using the Lyapunov direct method, some sufficient conditions of lag synchronization are obtained. To validate the proposed method, numerical simulation examples are provided to verify the correctness and effectiveness of the proposed scheme.

Vibration control of an axially moving accelerated/decelerated belt system with input saturation

2016 ◽  
Vol 40 (2) ◽  
pp. 685-697 ◽  
Author(s):  
Yu Liu ◽  
Zhijia Zhao ◽  
Fang Guo ◽  
Yun Fu
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Direct Method ◽  
Input Saturation ◽  
Unknown Boundary ◽  
Disturbance Adaptation ◽  
Axially Moving ◽  
Adaptation Law ◽  
Belt System

This article describes an investigation of a boundary control for vibration suppression of an axially moving accelerated or decelerated belt system with input saturation. Firstly, after considering the effects of the high acceleration or deceleration and unknown distributed disturbance, an infinite-dimensional model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations. Secondly, by synthesizing boundary control techniques and Lyapunov’s direct method, a boundary control is developed to suppress the belt’s vibration and to stabilize the belt system at its equilibrium position globally; an auxiliary system is proposed to compensate for the nonlinear input saturation characteristic; a disturbance adaptation law is employed to mitigate the effects of unknown boundary disturbance; and the S-curve acceleration/deceleration method is adopted to plan the belt’s axial speed. Thirdly, with the proposed boundary control, the wellposedness of the closed-loop belt system is mathematically demonstrated and uniformly bounded stability of the closed-loop system is achieved without any discretization of the system dynamic model. Finally, simulation results are presented to verify the validity and effectiveness of the proposed control scheme.

scholarly journals PI Control of HSFDs for Active Control of Rotor-Bearing Systems

1996 ◽  
Author(s):  
J. P. Hathout ◽  
A. El-Shafei
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Closed Loop ◽  
Rotating Machinery ◽  
Loop System ◽  
Pi Control ◽  
Closed Loop System ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Run Up

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDs) for active control of vibrations of rotors. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient run-up through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated to the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

STABILITY ANALYSIS AND VIBRATION CONTROL OF A CLASS OF NEGATIVE IMAGINARY SYSTEMS

2015 ◽  
Vol 77 (17) ◽  
Author(s):  
Auwalu M. Abdullahi ◽  
Z. Mohamed ◽  
M. S. Zainal Abidin ◽  
R. Akmeliawati ◽  
Amiru A. Bature
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Vibration Control ◽  
Horizontal Plane ◽  
Closed Loop ◽  
Flexible Manipulator ◽  
The Finite Element Method ◽  
Closed Loop System ◽  
Resonance Modes ◽  
Resonant Controller

This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB.

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