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Robust Parameter Region or Attraction Region Calculation for Control System...
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Robust Parameter Region or Attraction Region Calculation for Control System Design

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 10193

Special Issue Editors

Prof. Dr. Mingwei Sun

E-Mail Website
Guest Editor
College of Artificial Intelligence, Nankai University, Tianjin 300350, China
Interests: flight guidance and control; model predictive control; active disturbance rejection control; nonlinear optimization
Special Issues, Collections and Topics in MDPI journals
Assoc. Prof. Dr. Jia Song

E-Mail Website
Guest Editor
School of Astronautics, Beihang University, Beijing 100191, China
Interests: autonomous fault diagnosis based on hybrid intelligence; disturbance rejection and fault-tolerant guidance control for unmanned aerial vehicle; cooperative control of multi-agent based on hybrid intelligence
Special Issues, Collections and Topics in MDPI journals
Dr. Jin Tao

E-Mail Website
Guest Editor
1. Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland
2. Senior AI Scientist at Silo AI, 00100 Helsinki , Finland
Interests: complex system dynamics; intelligent control; reinforcement learning; deep learning; robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In practice, the available operating region for an existing control design is quite essential for system evaluation. Two kinds of operating regions are appealing for practitioners. The first one is the uncertain region of the characteristic parameters of the plant that can be robustly stabilized by a specific controller. In the classical control theory, the stability margin is such a physically insightful criterion; while in robust control, the μ singular value also has a similar meaning. On the other hand, the attraction region is the set confining the state to be reliably operated, which amounts to the feasible working space without stability violation. For the standard linear systems, there are mature tools for this evaluation. Especially, an explicitly graphical description of these regions is necessary and welcome. However, there were few such reports on the nonconventional linear systems, such as time-delay systems, switch systems, sector systems, and piecewise systems. The related analysis for these systems is difficult but urgently needed in many application problems. This is a crucial difference between theoretical analysis and practical consideration. In theory, nominal stability is the main concern; while in practice, the description of the feasible region is more crucial. In this Special Issue, we are pleased to collect the recent results on the calculation of feasible regions for the challenging nonconventional physical plants.

Prof. Dr. Mingwei Sun
Dr. Jia Song
Dr. Jin Tao
Guest Editors

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Keywords

  • robustness
  • stability margin
  • attraction region
  • numerical method
  • closed-loop stability
  • characteristic parameters

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Published Papers (5 papers)

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Research

17 pages, 6471 KiB  
Article
Improved Fractional-Order Extended State Observer-Based Hypersonic Vehicle Active Disturbance Rejection Control
by Mingfei Zhao, Yunlong Hu and Jia Song
Mathematics 2022, 10(23), 4414; https://doi.org/10.3390/math10234414 - 23 Nov 2022
Cited by 8 | Viewed by 1367
Abstract
In this work, a novel fractional-order extended state observer (FOESO)-based linear active disturbance rejection control (LADRC) method is firstly proposed for a hypersonic vehicle (HV) to address the measurement noise problem. The uncertainty and external disturbance of an HV was discussed and addressed [...] Read more.
In this work, a novel fractional-order extended state observer (FOESO)-based linear active disturbance rejection control (LADRC) method is firstly proposed for a hypersonic vehicle (HV) to address the measurement noise problem. The uncertainty and external disturbance of an HV was discussed and addressed by the active disturbance rejection control and many different control methods in recent decades. However, the research of an HV with measurement noise is insufficient. For the LADRC, the anti-noise ability is highly dependent on the bandwidth of the extended state observer (ESO). Meanwhile, the control performance of the LADRC is relevant to the bandwidth. The FOESO is presented, aiming to address the tradeoff of the control performance or noise suppression. The FOESO-based LADRC (FOESO-LADRC) introduces fractional calculus. It can enhance the anti-noise ability with little influence on the control performance. The simulation results show that the FOESO-LADRC has a significant improvement in the noise suppression. In addition, compared with the LADRC, it obtains a better solution to address the tradeoff between the bandwidth and noise impact. Full article
(This article belongs to the Special Issue Robust Parameter Region or Attraction Region Calculation for Control System Design)
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13 pages, 7655 KiB  
Article
Kinematic Modes Identification and Its Intelligent Control of Micro-Nano Particle Manipulated by Acoustic Signal
by Xiaodong Jiao, Jin Tao, Hao Sun and Qinglin Sun
Mathematics 2022, 10(21), 4156; https://doi.org/10.3390/math10214156 - 7 Nov 2022
Cited by 2 | Viewed by 1685
Abstract
In this paper, the dynamics of a micro-nano particle on the micro-thin plate driven by an acoustic signal was investigated, including the particle kinematics mode, kinematics equation, and trajectory control. According to Newton’s kinematic theorem, analyzing the forces acting on the particle, the [...] Read more.
In this paper, the dynamics of a micro-nano particle on the micro-thin plate driven by an acoustic signal was investigated, including the particle kinematics mode, kinematics equation, and trajectory control. According to Newton’s kinematic theorem, analyzing the forces acting on the particle, the kinematic modes of the driven particle are distinguished with specific mathematical conditions, which are classified as slide, bounce, and stable modes strictly planned on a thin plate area. Based on the theory of kinematic modal analysis, the simulation results reveal the distribution rules of particle motion modes against the driving signal or plate geometry. The particle kinematics equation governing the sliding movement on the thin plate was then derived in light of the interaction between the particle and driving signal, based on which, the particle trajectory was drawn and analyzed in detail. For the purpose of controlling the particle trajectory, the control problem was designed in accordance with a linear active disturbance rejection controller (LADRC). Further, a guidance law was proposed, and the corresponding controller was designed to realize the linear trajectory following. Full article
(This article belongs to the Special Issue Robust Parameter Region or Attraction Region Calculation for Control System Design)
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14 pages, 476 KiB  
Article
A Super-Twisting Extended State Observer for Nonlinear Systems
by Yi Li, Panlong Tan, Junjie Liu and Zengqiang Chen
Mathematics 2022, 10(19), 3584; https://doi.org/10.3390/math10193584 - 1 Oct 2022
Cited by 9 | Viewed by 2641
Abstract
Disturbances and uncertainties are the main concerns in control systems. To obtain this information in real time, the extended state observer is proposed as the core of the active disturbance rejection control. However, the estimation errors of extended state observer cannot converge to [...] Read more.
Disturbances and uncertainties are the main concerns in control systems. To obtain this information in real time, the extended state observer is proposed as the core of the active disturbance rejection control. However, the estimation errors of extended state observer cannot converge to zero in the presents of unknown but bounded disturbances, which will bring unexpected tracking errors to the closed-loop system. By taking advantage of the linear extended state observer and the super-twisting algorithm, the super-twisting extended state observer is proposed to deal with the non-diminishing second-order derivable disturbances in this paper. The asymptotic convergence of the super-twisting extended state observer and the controller are proved by the Lyapunov method. Moreover, the effectiveness and robustness of the super-twisting extended state observer are verified by simulation analysis. Simulation results show that the proposed super-twisting extended state observer maintains the minimized estimation error with less settling time compared the with linear extended state observer. The tracking performance of the controller with the proposed observer is greatly improved. Full article
(This article belongs to the Special Issue Robust Parameter Region or Attraction Region Calculation for Control System Design)
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19 pages, 2073 KiB  
Article
The Convergence of Data-Driven Optimal Iterative Learning Control for Linear Multi-Phase Batch Processes
by Yan Geng, Shouqin Wang and Xiaoe Ruan
Mathematics 2022, 10(13), 2304; https://doi.org/10.3390/math10132304 - 1 Jul 2022
Cited by 1 | Viewed by 1665
Abstract
For multi-phase batch processes with different dimensions whose dynamics can be described as a linear discrete-time-invariant system in each phase, a data-driven optimal ILC was explored using multi-operation input and output data that subordinate a tracking performance criterion. An iterative learning identification was [...] Read more.
For multi-phase batch processes with different dimensions whose dynamics can be described as a linear discrete-time-invariant system in each phase, a data-driven optimal ILC was explored using multi-operation input and output data that subordinate a tracking performance criterion. An iterative learning identification was constructed to estimate the system Markov parameters by minimizing the evaluation criterion that consists of the residual of the real outputs from the predicted outputs and two adjacent identifications. Meanwhile, the estimated Markov parameters matrix was embedded into the learning control process in the form of an interaction. By virtue of inner product theory, the monotonic descent of the estimation error was derived, which does not restrict the weighting factor at all. Furthermore, algebraic derivation demonstrates that the tracking is strictly monotonically convergent if the estimation error falls within an appropriate domain. Numerical simulations were carried out to illustrate the validity and the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Robust Parameter Region or Attraction Region Calculation for Control System Design)
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20 pages, 4046 KiB  
Article
Event-Triggered Attitude-Orbit Coupled Fault-Tolerant Control for Multi-Spacecraft Formation
by Tao Wang, Yingchun Zhang and Hongchen Jiao
Mathematics 2022, 10(12), 1984; https://doi.org/10.3390/math10121984 - 8 Jun 2022
Viewed by 1749
Abstract
In this paper, the attitude-orbit coupled control problem for multi-spacecraft formation with limited communication capability and actuator failure is investigated. For the purpose of solving this problem, an event-triggered attitude-orbit coupled fault-tolerant control strategy is proposed. First, an integrated nonlinear dynamic model including [...] Read more.
In this paper, the attitude-orbit coupled control problem for multi-spacecraft formation with limited communication capability and actuator failure is investigated. For the purpose of solving this problem, an event-triggered attitude-orbit coupled fault-tolerant control strategy is proposed. First, an integrated nonlinear dynamic model including the coupling characteristics of the attitude and orbit is established based on the Kane equation. Second, the nonlinear dynamic model is linearized at the reference state to facilitate the controller design. Third, a dynamic event-triggered mechanism is designed and an event-triggered fault-tolerant control law is developed. The stability of closed-loop control systems can be ensured under the designed control law and a sufficient condition that Zeno’s behavior can be avoided is presented. Finally, simulation results are given to show the effectiveness of the proposed control method. Full article
(This article belongs to the Special Issue Robust Parameter Region or Attraction Region Calculation for Control System Design)
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