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Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen

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.

2022 ◽  
Judson T. Babcock ◽  
Ryan K. Osteroos ◽  
Mark B. Tischler

2021 ◽  
Vol 33 (12) ◽  
pp. 4211
Shunsuke Shigaki ◽  
Natsuki Minakawa ◽  
Mayu Yamada ◽  
Hirono Ohashi ◽  
Daisuke Kurabayashi ◽  

2021 ◽  
Kun Zhang ◽  
Junhui ZHANG ◽  
Minyao Gan ◽  
Huaizhi Zong ◽  
Ximeng Wang ◽  

Abstract As a kind of hydraulic rotary actuator, helical hydraulic rotary actuator has the excellent characteristics of large angle, high torque and compact structure, which has been widely used in various fields. However, the core technology is in the hands of several companies and has not been disclosed, and the relevant reports are mostly limited to the component level. From the perspective of designing the driving system, the dynamic characteristics of the output when the helical rotary actuator is applied to the closed-loop system are explored. There are two main problems to be studied: one is to establish a reliable mathematical model, and the other is to consider the influence of system parameter perturbation on the output in practice. In this paper, firstly, the dynamic model of valve-controlled helical rotary actuator angle closed-loop system is derived in detail, which has never been reported in the existing literature. Then, the sensitivity analysis of 23 main parameters in the model with perturbation of 10% is carried out under nine working conditions. Finally, the system dynamics model and the sensitivity analysis results are verified by the prototype experiment and co-simulation, which shows the reliability of the theoretical results in this paper.

2021 ◽  
Vol 2 ◽  
Saeed Salavati ◽  
Karolos Grigoriadis ◽  
Matthew Franchek

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints and matched input disturbances. A gain-scheduled dynamic output feedback controller, coupled with a disturbance observer to cancel out input disturbance effects, was augmented with an anti-windup compensator to locally stabilize the input-delay LPV system under saturation, model uncertainty, and exogenous disturbances. Sufficient delay-dependent conditions to asymptotically stabilize the closed-loop system were derived using Lyapunov-Krasovskii functionals and a modified generalized sector condition to address the input saturation nonlinearity. The level of disturbance rejection was characterized via the closed-loop induced L2-norm of the closed-loop system in the form of linear matrix inequality (LMI) constraints. The results are examined in the context of the mean arterial pressure (MAP) control in the clinical resuscitation of critical hypotensive patients. The MAP variation response to the injection of vasopressor drugs was modeled as an LPV system with a varying input delay and was susceptible to model uncertainty and input/output disturbances. A Bayesian filtering method known as the cubature Kalman filter (CKF) was used to estimate the instantaneous values of the parameters. The varying delay was estimated via a multiple-model approach. The proposed input-delay LPV control was validated in closed-loop simulations to demonstrate its merits and capabilities in the presence of drug administration constraints.

Huaizhen Wang ◽  
Lijin Fang ◽  
Junyi Wang ◽  
Tangzhong Song ◽  
Hesong Shen

Robust and precise control of robot systems are still challenging problems due to the existence of uncertainties and backlash hysteresis. To deal with the problems, an adaptive neural sliding mode control with prescribed performance is proposed for robotic manipulators. A finite-time nonsingular terminal sliding mode control combined with a new prescribed performance function (PPF) is developed to guarantee the transient and steady-state performance of the closed-loop system. Based on the sliding mode variable, an adaptive law is presented to effectively estimate the bound of system uncertainties where the prior knowledge of uncertainties is not needed. To approximate nonlinear function and unknown dynamics, the Gaussian radial basis function neural networks(RBFNNs) is introduced to compensate the lumped nonlinearities. All signals of the closed-loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov analysis. Finally, comparative simulations are conducted to illustrate superiority and reliability of the proposed control strategy.

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