scholarly journals Design of a Disturbance Rejection Controller for a Class of Nonholonomic Systems with Uncertainties

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Dianguo Cao ◽  
Jiaqian Chen
Keyword(s):  
Disturbance Rejection ◽  
Control Algorithm ◽  
External Disturbance ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Control Law ◽  
Closed Loop System ◽  
External Disturbances ◽  
Disturbance Term ◽  
System States

This study investigates the global output feedback stabilization problem for one type of the nonholonomic system with nonvanishing external disturbances. An extended state observer (ESO) is constructed in order to estimate the external disturbance and unmeasurable system states, in which the external disturbance term is seen as a general state. Thus, a new generalized error dynamic system is obtained. Accordingly, a disturbance rejection controller is designed by making use of the backstepping technique. A control law is given to ensure that all the signals in the closed-loop system are globally bounded, while the system states converge to an equilibrium point. The simulation example is proposed to verify that the control algorithm is effective.

Output tracking and disturbance rejection for 1-D anti-stable wave equation

2019 ◽  
Vol 25 ◽  
pp. 69 ◽  
Author(s):  
Hua-Cheng Zhou
Keyword(s):  
Wave Equation ◽  
Disturbance Rejection ◽  
External Disturbance ◽  
Reference Signal ◽  
Original System ◽  
Delay Systems ◽  
Transport Systems ◽  
Control Law ◽  
Proportional Control ◽  
Output Tracking

In this paper, we solve the output tracking and disturbance rejection problem for a system described by a one-dimensional anti-stable wave equation, with reference and disturbance signals that belong to W1,∞[0, ∞) and L∞[0, ∞), respectively. Generally, these signals cannot be generated from an exosystem. We explore an approach based on proportional control. It is shown that a proportional gain controller can achieve exponentially the output tracking while rejecting disturbance. Our method consists of three steps: first, we convert the original system without disturbance into two transport equations with an ordinary differential equation by using Riemann variables, then we propose a proportional control law by making use of the properties of transport systems and time delay systems. Second, based on our recent result on disturbance estimator, we apply the estimation/cancellion strategy to cancel to the external disturbance and to track the reference asymptotically. Third, we design a controller using a state observer. Since disturbance does not appear in the observer explicitly (the disturbance is exactly compensated), the controlled output signal is exponentially tracking the reference signal. As a byproduct, we obtain a new output feedback stabilizing control law by which the resulting closed-loop system is exponentially stable using only two displacement output signals.

Research on Single Channel Rolling Control for Fixed Canard Rudder

2013 ◽  
Vol 433-435 ◽  
pp. 1150-1153 ◽  
Author(s):  
Ye Bing Cui ◽  
Xiong Chen ◽  
Jing Xu
Keyword(s):  
Disturbance Rejection ◽  
Control Algorithm ◽  
Single Channel ◽  
Switching Time ◽  
External Disturbance ◽  
Nonlinear Friction ◽  
Active Disturbance Rejection ◽  
Working Principle ◽  
Switching Control Strategy ◽  
The Mathematical Model

According to the rotate speed switching problems of rapidity and stability during single channel rolling control for fixed canard rudder, the control algorithm based on active disturbance rejection controller (ADRC) was presented to control the rudders rotate speed switching. The working principle of fixed canard rudder was analyzed, and the mathematical model of the rudder was established, and the ADRC cascade controller for the rudder was designed. The simulation results indicates that not only the proposed rotate speed switching control strategy for the rudder is feasible, but also the proposed ADRC algorithm improves the rapidity of speed switching process, with switching time of 30ms, no overshoot, and very good robustness under inner perturbation and external disturbance with nonlinear friction considered.

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

scholarly journals Adaptive Output Feedback Stabilization of Nonholonomic Systems with Nonlinear Parameterization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanling Shang ◽  
Ye Yuan ◽  
Fushun Yuan
Keyword(s):  
Output Feedback ◽  
Design Procedure ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Nonlinear Parameterization ◽  
Output Feedback Stabilization ◽  
Backstepping Approach ◽  
Nonlinearly Parameterized ◽  
System States ◽  
Parameter Separation

This paper investigates the problem of adaptive output feedback stabilization for a class of nonholonomic systems with nonlinear parameterization and strong nonlinear drifts. A parameter separation technique is introduced to transform nonlinearly parameterized system into a linear-like parameterized system. Then, by using the integrator backstepping approach based on observer and parameter estimator, a constructive design procedure for output feedback adaptive control is given. And a switching strategy is developed to eliminate the phenomenon of uncontrollability. It is shown that, under some conditions, the proposed controller can guarantee that all the system states globally converge to the origin, while other signals remain bounded. An illustrative example is also provided to demonstrate the effectiveness of the proposed scheme.

scholarly journals Global Finite-Time Output Feedback Stabilization for a Class of Uncertain Nonholonomic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Baojian Du ◽  
Fangzheng Gao ◽  
Fushun Yuan
Keyword(s):  
Output Feedback ◽  
Finite Time ◽  
Closed Loop ◽  
Output Feedback Control ◽  
Design Procedure ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Closed Loop System ◽  
Output Feedback Stabilization ◽  
Switching Control Strategy

This paper investigates the problem of global finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. By using backstepping recursive technique and the homogeneous domination approach, a constructive design procedure for output feedback control is given. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Stabilization Control of Nonholonomic Wheeled Mobile Service Robots

2009 ◽  
Vol 419-420 ◽  
pp. 593-596 ◽  
Author(s):  
Jiang Chang ◽  
Qing Xin Meng
Keyword(s):  
Closed Loop ◽  
Feedback Stabilization ◽  
Loop System ◽  
Polar Coordinates ◽  
Service Robots ◽  
Control Law ◽  
Mobile Service ◽  
Closed Loop System ◽  
Stabilization Control ◽  
Mobile Service Robots

Nonholonomic wheeled mobile service robot’s posture error model denoted by polar coordinates in global coordinates is established .Based on the inherent discontinuousness of the closed-loop system model, a novel nonlinear state feedback stabilization control law is proposed，which causes closed-loop system state space equation of robot to have isolated equilibrium state at origin. By Lyapunov candidate function method，this paper concludes that the closed-loop system is global uniformly asymptotically stable at origin. Simulation results indicate that the proposed control law is effective.

Output Feedback Stabilization of Uncertain Nonholonomic Chained Systems

2013 ◽  
Vol 655-657 ◽  
pp. 1354-1360
Author(s):  
Zhu Ping Wang ◽  
Zhan Ping Yuan ◽  
Qi Jun Chen
Keyword(s):  
Output Feedback ◽  
Control Strategies ◽  
Nonholonomic Systems ◽  
Feedback Stabilization ◽  
Stabilization Problem ◽  
Control Laws ◽  
Output Feedback Stabilization ◽  
System States ◽  
Chained Systems ◽  
Control Coefficients

In this paper, output feedback stabilization problem of a class of nonholonomic systems in chained form with drift nonlinearity and unknown virtual control coefficients is considered. Observer-based output feedback design is developed when only partial system states are measurable. The control laws are developed using state scaling and backstepping techniques. The proposed control strategies can steer the system globally converge to the origin.

Stabilization of a class of switched uncertain systems by active disturbance rejection control

2018 ◽  
Vol 40 (16) ◽  
pp. 4421-4431 ◽  
Author(s):  
Chen Liu ◽  
Chaoyang Dong ◽  
Qing Wang ◽  
Maopeng Ran
Keyword(s):  
Disturbance Rejection ◽  
External Disturbance ◽  
Average Dwell Time ◽  
Feedback System ◽  
Active Disturbance Rejection Control ◽  
Extended State ◽  
Active Disturbance Rejection ◽  
Disturbance Rejection Control ◽  
System States ◽  
Estimate System

The problem of stabilization for a class of switched uncertain non-linear systems is studied by active disturbance rejection control (ADRC). Coordinate transformation is applied to transform the system into a strict feedback system in normal form. The unknown non-linearity, parameter uncertainty and external disturbance are treated as an extended state of each subsystem, and a corresponding switched extended state observer (ESO) is designed. Based on the output of the switched ESO, a switching ADRC law is proposed. Rigorous proof is given to show that the switched ESO can estimate system states and the unknown non-linearity of each subsystem effectively. Furthermore, the proposed controller guarantees the closed-loop system be semi-globally uniformly ultimately bounded for a class of switching with average dwell time. A numerical example illustrates the effectiveness of the proposed method.

Time-varying formation control for unmanned aerial vehicles with external disturbances

2019 ◽  
Vol 41 (13) ◽  
pp. 3777-3786 ◽  
Author(s):  
Yu’ang Liu ◽  
Qing Wang ◽  
Chaoyang Dong ◽  
Maopeng Ran
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Control Strategy ◽  
Disturbance Rejection ◽  
Formation Control ◽  
Time Varying ◽  
Closed Loop System ◽  
External Disturbances ◽  
Active Disturbance Rejection ◽  
Aerial Vehicles ◽  
Disturbance Rejection Control

Time-varying formation control for unmanned aerial vehicles (UAVs) swarm systems with external disturbances is investigated via active disturbance rejection control (ADRC). The external disturbances are estimated by a designed extended state observer (ESO). Then, a distributed formation control protocol is designed according to the output of ESO, under which the predefined time-varying formation can be achieved. The closed-loop system under the proposed control strategy is analyzed. In addition, the expression of formation center function of the disturbed formation control is also depicted. Finally, numerical instances are simulated in order to demonstrate the validity and superiority of the proposed control strategy.

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