scholarly journals Backstepping Control Using Barrier Lyapunov Function for Dynamic Positioning Control System with Passive Observer

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Guoqing Xia ◽  
Jingjing Xue ◽  
Chuang Sun ◽  
Bo Zhao
Keyword(s):  
Lyapunov Function ◽  
Closed Loop ◽  
Control Law ◽  
Dynamic Positioning ◽  
Backstepping Technique ◽  
Closed Loop System ◽  
Positioning Control ◽  
Barrier Lyapunov Function ◽  
Backstepping Controller ◽  
Simulation Results

This paper presents a backstepping controller using barrier Lyapunov function (BLF) for dynamic positioning (DP) system. For safety reasons, the position and heading of DP ship are to be maintained in certain range. Thus, in this paper, a control law based on BLF and backstepping technique is proposed to limit the position and heading. The closed-loop system is proved stable in the sense of Lyapunov stability theories. In addition, since the velocities of ship are not measurable and the wave frequency (WF) motion is unavailable, a passive observer is adopted to estimate the velocities and the effect of WF motion. The simulation results show that the proposed controller can limit the position and heading of the vessel in a predefined range and verify the performance of the proposed controller and the passive observer.

Stable Nonlinear Control Allocation for Aircraft with Multiple Control Effectors

2011 ◽  
Vol 138-139 ◽  
pp. 404-409 ◽  
Author(s):  
Heng Li ◽  
Jin Yong Yu ◽  
You An Zhang
Keyword(s):  
Closed Loop ◽  
Dynamic Control ◽  
Lyapunov Stability Theory ◽  
Invariant Set ◽  
Control Law ◽  
Control Allocation ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Multiple Control ◽  
Simulation Results

With respect to aircraft with redundant multiple control effectors, a nonlinear controller, which is composed of a virtual control law and a dynamic control allocation with position constraints of each effector, is designed. Based on Lyapunov stability theory and LaSalle invariant set theorem, asymptotic stabilities of upper control subsystem, dynamic control allocation subsystem and overall closed-loop system are proved respectively. Simulation results show the effectiveness of the proposed method.

Control Design for the System of Manipulator Handling a Flexible Payload With Input Constraints

2018 ◽  
Author(s):  
Shuyang Liu ◽  
Reza Langari ◽  
Yuanchun Li
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Closed Loop ◽  
Semigroup Theory ◽  
Control Design ◽  
Hyperbolic Function ◽  
Control Law ◽  
Input Constraints ◽  
Closed Loop System ◽  
Simulation Results

In this paper, we consider the control design for manipulator handling a flexible payload in the presence of input constraints. The dynamics of the system is described by coupled ordinary differential equation and a partial differential equation. Considering actuators saturation, the proposed control law applies a smooth hyperbolic function to handle the effect of the input constraints. The asymptotic stability of the closed-loop system is proved by using semigroup theory and extended LaSalle’s Invariance Principle. Simulation results show that the proposed controller is effective.

Adaptive Boundary Control for a Flexible Manipulator With State Constraints Using a Barrier Lyapunov Function

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Tingting Jiang ◽  
Jinkun Liu ◽  
Wei He
Keyword(s):  
Lyapunov Function ◽  
Boundary Control ◽  
Closed Loop ◽  
State Constraints ◽  
Lyapunov Stability Theory ◽  
Loop System ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Control Laws ◽  
Barrier Lyapunov Function

In this paper, the problem of state constraints control is investigated for a class of output constrained flexible manipulator system with varying payload. The dynamic behavior of the flexible manipulator is represented by partial differential equations. To prevent states of the flexible manipulator system from violating the constraints, a barrier Lyapunov function which grows to infinity whenever its arguments approach to some limits is employed. Then, based on the barrier Lyapunov function, boundary control laws are given. To solve the problem of varying payload, an adaptive boundary controller is developed. Furthermore, based on the theory of barrier Lyapunov function and the adaptive algorithm, state constraints and output control under vibration condition can be achieved. The stability of the closed-loop system is carried out by the Lyapunov stability theory. Numerical simulations are given to illustrate the performance of the closed-loop system.

Nonlinear Control of Semi-Active MacPherson Suspension System

2012 ◽  
Author(s):  
Olugbenga M. Anubi ◽  
Carl D. Crane
Keyword(s):  
Closed Loop ◽  
Control Design ◽  
Mr Damper ◽  
Suspension System ◽  
Time Domain Simulation ◽  
Closed Loop System ◽  
Output Feedback Controller ◽  
Space Frequency ◽  
Simulation Results ◽  
Active Damper

This paper presents the control design and analysis of a non-linear model of a MacPherson suspension system equipped with a magnetorheological (MR) damper. The model suspension considered incorporates the kinematics of the suspension linkages. An output feedback controller is developed using an ℒ2-gain analysis based on the concept of energy dissipation. The controller is effectively a smooth saturated PID. The performance of the closed-loop system is compared with a purely passive MacPherson suspension system and a semi-active damper, whose damping coefficient is tunned by a Skyhook-Acceleration Driven Damping (SH-ADD) method. Simulation results show that the developed controller outperforms the passive case at both the rattle space, tire hop frequencies and the SH-ADD at tire hop frequency while showing a close performance to the SH-ADD at the rattle space frequency. Time domain simulation results confirmed that the control strategy satisfies the dissipative constraint.

ADAPTIVE CONTROL OF UNCERTAIN LORENZ SYSTEM USING DECOUPLED BACKSTEPPING

2004 ◽  
Vol 14 (04) ◽  
pp. 1439-1445 ◽  
Author(s):  
S. S. GE
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Lorenz System ◽  
Physical Property ◽  
Asymptotic Convergence ◽  
Closed Loop System ◽  
Feedback Form ◽  
Controlling Chaos ◽  
Simulation Results ◽  
The Lorenz System

In this letter, we reconsider the problem of controlling chaos in the well-known Lorenz system. Firstly, the difficulty in controlling the Lorenz system is discussed in the general strict-feedback form. Then, singularity-free adaptive control is presented for the Lorenz system with three key parameters unknown by exploiting the physical property of the system using decoupled backstepping design. The proposed controller guarantees the asymptotic convergence of the output and the boundedness of all the signals in the closed-loop system. Simulation results are conducted to show the effectiveness of the approach.

Anti-windup reconfigurable control for dynamic positioning vessel with thruster faults

2020 ◽  
Vol 42 (16) ◽  
pp. 3216-3224
Author(s):  
Mingyang Li ◽  
Wenbo Xie ◽  
Jian Zhang
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Input Saturation ◽  
Control Process ◽  
Dynamic Positioning ◽  
Closed Loop System ◽  
Reconfigurable Control ◽  
Positioning Control ◽  
Dynamic Positioning System ◽  
System A

In this study, an anti-windup reconfigurable control method is developed for dynamic positioning vessel in the presence of thruster faults and input saturation. The designed reconfiguration block acting as a virtual thruster aims at hiding the faults from the nominal controller. Also, it is added into the closed-loop system between the nominal controller and the dynamic positioning system. A thruster saturation-failure fault matrix technique is proposed to regard the thruster saturation as thruster fault, meanwhile an auxiliary system is constructed to achieve extra compensation for the adverse effects induced by input saturation. Furthermore, an integral sliding mode control method is presented to accommodate the nonlinear items in the reconfiguration block. An adaptive technique is also employed to preserve robustness against the unknown uncertainties. Finally, a vessel dynamic positioning control process is adopted to evaluate the effectiveness of the proposed method.

scholarly journals Circular Formation Control of Multiagent Systems with Any Preset Phase Arrangement

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Lina Jin ◽  
Shuanghe Yu ◽  
Dongxu Ren
Keyword(s):  
Control Problem ◽  
Multiagent Systems ◽  
Formation Control ◽  
Closed Loop ◽  
Phase Distribution ◽  
The Other ◽  
Control Law ◽  
Closed Loop System ◽  
The Stability ◽  
Phase Arrangement

This paper deals with the circular formation control problem of multiagent systems for achieving any preset phase distribution. The control problem is decomposed into two parts: the first is to drive all the agents to a circle which either needs a target or not and the other is to arrange them in positions distributed on the circle according to the preset relative phases. The first part is solved by designing a circular motion control law to push the agents to approach a rotating transformed trajectory, and the other is settled using a phase-distributed protocol to decide the agents’ positioning on the circle, where the ring topology is adopted such that each agent can only sense the relative positions of its neighboring two agents that are immediately in front of or behind it. The stability of the closed-loop system is analyzed, and the performance of the proposed controller is verified through simulations.

Model Simplification and Stability Robustness With Elastic Flight Vehicles

1995 ◽  
Vol 117 (3) ◽  
pp. 336-342
Author(s):  
Brett Newman ◽  
David K. Schmidt
Keyword(s):  
Closed Loop ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Control Law ◽  
Model Simplification ◽  
Closed Loop System ◽  
Order Model ◽  
Reduced Order ◽  
Stability Robustness

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced order model will be preserved when controlling the higher order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. A weighted balanced order reduction technique is shown to lead to results that meet the necessary criteria. The procedure is applied to an aeroelastic vehicle model, and the results are used for control law development. Critical robustness properties designed into the lower order closed-loop system are shown to be present in the higher order closed-loop system.

Iterative Learning Impedance Control in Gait Rehabilitation Robot

2014 ◽  
Vol 494-495 ◽  
pp. 1084-1087
Author(s):  
Fu Cheng Cao ◽  
Hai Xin Sun ◽  
Li Rong Wang
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Closed Loop ◽  
Impedance Control ◽  
Iterative Learning ◽  
Gait Rehabilitation ◽  
Control Law ◽  
Rehabilitation Robot ◽  
Simulation Results ◽  
Impedance Parameters

An iterative learning impedance control algorithm is presented to control a gait rehabilitation robot. According to the circumstances of the patient, the appropriate rehabilitation target impedance parameters are set. With the adoption of iterative learning control law, the impedance error in the closed loop is guaranteed to converge to zero and the iterative trajectories follow the desired trajectories over the entire operation interval. The effectiveness of the proposed method is shown through numerical simulation results.

Barrier Lyapunov function-based adaptive output feedback failure compensation for a class of non-linear systems with unknown dead-zone non-linearity

2016 ◽  
Vol 39 (8) ◽  
pp. 1169-1181 ◽  
Author(s):  
Yuefei Wu ◽  
Jianyong Yao
Keyword(s):  
Lyapunov Function ◽  
Output Feedback ◽  
Dead Zone ◽  
Output Feedback Control ◽  
Control Law ◽  
Unknown Input ◽  
Barrier Lyapunov Function ◽  
Non Linear ◽  
Bounded Disturbances ◽  
Non Linear Systems

In this paper, an adaptive robust output feedback control approach is proposed for a class of uncertain non-linear systems with unknown input dead-zone non-linearity, unknown failures and unknown bounded disturbances. By constructing the dead-zone inverse and applying the backstepping recursive design technique, a robust adaptive backstepping controller is proposed, in which adaptive control law is synthesized to handle parametric uncertainties and a novel robust control law to attenuate disturbances. The robust output feedback control law is developed by integrating a switching function σ algorithm at each step of the backstepping design procedure. In addition, K-filters are designed to estimate the unmeasured states and neural networks are employed to approximate the unknown non-linear functions. By ensuring boundedness of the barrier Lyapunov function, the major feature of the proposed controller is that it can theoretically guarantee asymptotic output tracking performance, in spite of the presence of unknown input dead-zone non-linearity, various actuator failures and unknown bounded disturbances via Lyapunov stability analysis. The effectiveness of the proposed approach is illustrated by the simulation examples.

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