state feedback
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Jia Song ◽  
Jiangcheng Su ◽  
Yunlong Hu ◽  
Mingfei Zhao ◽  
Ke Gao

This paper investigates the stability and performance of the linear active disturbance rejection control (LADRC)–based system with uncertainties and external disturbance via transfer functions and a frequency-domain view. The performance of LADRC is compared with the state-observer-based state feedback control (SOSFC) and state feedback control (SFC). First, the transfer functions and the error transfer functions for LADRC, SOSFC, and SFC are studied using the state-space method. It is proven that the LADRC-, SOSFC-, and SFC-based closed-loop systems have the same transfer function from the reference input to the output and achieve the same control effects for the nominal system. Then, it is proven for the first time that the LADRC has a better anti-interference ability than the SOSFC and SFC. Besides, the asymptotic stability condition of LADRC-based closed-loop system considering large parameter perturbations is given first. Moreover, the sensitivity analysis of the closed-loop system is carried out. The results show that the LADRC has stronger robustness under parameter perturbations. According to the results, we conclude that the LADRC is of great disturbance rejection ability and strong robustness.

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 157
Mingjun Liu ◽  
Aihua Zhang ◽  
Bing Xiao

A velocity-free state feedback fault-tolerant control approach is proposed for the rigid satellite attitude stabilization problem subject to velocity-free measurements and actuator and sensor faults. First, multiplicative faults and additive faults are considered in the actuator and the sensor. The faults and system states are extended into a new augmented vector. Then, an improved sliding mode observer based on the augmented vector is presented to estimate unknown system states and actuator and sensor faults simultaneously. Next, a velocity-free state feedback attitude controller is designed based on the information from the observer. The controller compensates for the effects of actuator and sensor faults and asymptotically stabilizes the attitude. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 227
Mohsen Dlala ◽  
Abdallah Benabdallah

This paper deals with the stabilization of a class of uncertain nonlinear ordinary differential equations (ODEs) with a dynamic controller governed by a linear 1−d heat partial differential equation (PDE). The control operates at one boundary of the domain of the heat controller, while at the other end of the boundary, a Neumann term is injected into the ODE plant. We achieve the desired global exponential stabilization goal by using a recent infinite-dimensional backstepping design for coupled PDE-ODE systems combined with a high-gain state feedback and domination approach. The stabilization result of the coupled system is established under two main restrictions: the first restriction concerns the particular classical form of our ODE, which contains, in addition to a controllable linear part, a second uncertain nonlinear part verifying a lower triangular linear growth condition. The second restriction concerns the length of the domain of the PDE which is restricted.

2022 ◽  
Jiling Ding ◽  
Weihai Zhang

Abstract This paper considers the prescribed performance tracking control for high-order uncertain nonlinear systems. For any initial system condition, a state feedback control is designed, which guarantees the prescribed tracking performance and the boundedness of closed-loop signals. The proposed controller can be implemented without using any approximation techniques for estimating unknown nonlinearities. In this respect, a significant advantage of this article is that the explosion of complexity is avoided, which is raised by backstepping-like approaches that are typically employed to the control of uncertain nonlinear systems, and a low-complexity controller is achieved. Moreover, contrary to the existing results in existing literature, the restrictions on powers of high-order nonlinear systems are relaxed to make the considered problem having stronger theoretical and practical values. The effectiveness of the proposed scheme is verified by some simulation results.

M. Zazi ◽  
Y. Hajji ◽  
N. Khaldi ◽  
N. Elalami

In this paper, we introduce the development methodology of a reliable centralized control applied to a synchronous permanent magnet machine. The proposed system is nonlinear, we linearize around a point of application. The resulting model will then be used to reproduce the dynamic behavior of the machine for a reliable control. The controller is based on the standard h infinite to increase performance, reduce measurement noise, and to tolerate the outage of certain sensors. To illustrate the results, we made a comparison between a standard state feedback control and reliable h infinite robust control. The simulation results shows, that the system in case of technical placements poles loses classic performance in the presence of an outage, that the reliable centralized robust control remain satisfactory performance even in the presence of outage.

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