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Machines
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Nonlinear Control Applications and New Perspectives
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Nonlinear Control Applications and New Perspectives

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Automation and Control Systems".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 10321

Special Issue Editor

Dr. Stefan Palis

E-Mail Website
Guest Editor
Institute of Automation Technology, Otto von Guericke University of Magdeburg, 39106 Magdeburg, Germany
Moscow Power Engineering Institute, National Research University, Moscow 101000, Russia
Interests: nonlinear control - industrial magnetic bearings, anti-sway for slewing cranes and ballon cranes; control and identification of distributed parameter systems - stabilization of nonlinear oscillations in fluidized bed spray granulation and continuous coolin

Special Issue Information

Dear Colleagues,

Nonlinear control theory has been in the focus of research for a long time. It evolved into a well-founded theory and is taught in many graduate curricula in engineering. Successful applications are, however, still challenging and often raise new research problems, due to the increased complexity in analysis and design. 

More recently, the renaissance of artificial intelligence resulted in a renewed and increased interest in learning-based nonlinear control approaches with numerous promising results. Many of these provide new facets to the well-established concepts of adaption and identification and greatly benefit from the strong foundation of nonlinear control and systems theory.

This Special Issue focuses on recent theoretical developments in nonlinear control theory and on applications in various fields of engineering. Suitable topics include:

Data-driven approaches for nonlinear control;

Machine learning for nonlinear control;

Nonlinear control of distributed parameter systems;

Fast algorithms for nonlinear control;

Nonlinear state estimation;

Robust nonlinear control;

Nonlinear control methods in different application areas, e.g.: Manufacturing; Process control; Autonomous vehicles; Robotics; Power systems

Dr. Stefan Palis
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

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Research

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27 pages, 1519 KiB  
Article
Imperative Formal Knowledge Representation for Control Engineering: Examples from Lyapunov Theory
by Carsten Knoll, Julius Fiedler and Stefan Ecklebe
Machines 2024, 12(3), 181; https://0-doi-org.brum.beds.ac.uk/10.3390/machines12030181 - 8 Mar 2024
Viewed by 813
Abstract
In this paper, we introduce a novel method to formally represent elements of control engineering knowledge in a suitable data structure. To this end, we first briefly review existing representation methods (RDF, OWL, Wikidata, ORKG). Based on this, we introduce our own approach: [...] Read more.
In this paper, we introduce a novel method to formally represent elements of control engineering knowledge in a suitable data structure. To this end, we first briefly review existing representation methods (RDF, OWL, Wikidata, ORKG). Based on this, we introduce our own approach: The Python-based imperative representation of knowledge (PyIRK) and its application to formulate the Ontology of Control Systems Engineering (OCSE). One of its main features is the possibility to represent the actual content of definitions and theorems as nodes and edges of a knowledge graph, which is demonstrated by selected theorems from Lyapunov’s theory. While the approach is still experimental, the current result already allows the application of methods of automated quality assurance and a SPARQL-based semantic search mechanism. The feature set of the framework is demonstrated by various examples. The paper concludes with a discussion of the limitations and directions for further development. Full article
(This article belongs to the Special Issue Nonlinear Control Applications and New Perspectives)
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49 pages, 10276 KiB  
Article
Adaptive Sliding Mode Feedback Control Algorithm for a Nonlinear Knee Extension Model
by Saharul Arof, Emilia Noorsal, Saiful Zaimy Yahaya, Zakaria Hussain, Yusnita Mohd Ali, Mohd Hanapiah Abdullah and Muhamad Khuzzairie Safie
Machines 2023, 11(7), 732; https://0-doi-org.brum.beds.ac.uk/10.3390/machines11070732 - 12 Jul 2023
Cited by 2 | Viewed by 1075
Abstract
Functional electrical stimulation (FES) has been widely used to treat spinal cord injury (SCI) patients. Many research studies employ a closed-loop FES system to monitor the stimulated muscle response and provide a precise amount of charge to the muscle. However, most closed-loop FES [...] Read more.
Functional electrical stimulation (FES) has been widely used to treat spinal cord injury (SCI) patients. Many research studies employ a closed-loop FES system to monitor the stimulated muscle response and provide a precise amount of charge to the muscle. However, most closed-loop FES devices perform poorly and sometimes fail when muscle nonlinearity effects such as fatigue, time delay response, stiffness, spasticity, and subject change happen. The poor performance of the closed-loop FES device is mainly due to discrepancies in the feedback control algorithms. Most of the existing feedback control algorithms were not designed to adapt to new changes in patients with different nonlinearity effects, resulting in early muscle fatigue. Therefore, this research proposes an adaptive sliding mode (SM) feedback control algorithm that could adapt and fine-tune internal control settings in real-time according to the current subject’s nonlinear and time-varying muscle response during the rehabilitation (knee extension) exercise. The adaptive SM feedback controller consists mainly of system identification, direct torque control, and tunable feedback control settings. Employing the system identification unit in the feedback control algorithm enables real-time self-tuning and adjusting of the SM internal control settings according to the current patient’s condition. Initially, the patient’s knee trajectory response was identified by extracting meaningful information, which included time delay, rise time, overshoot, and steady-state error. The extracted information was used to fine-tune and update the internal SM control settings. Finally, the performance of the proposed adaptive SM feedback control algorithm in terms of system response time, stability, and rehabilitation time was analysed using a nonlinear knee model. The findings from the simulation results indicate that the adaptive SM feedback controller demonstrated the best control performance in accurately tracking the desired knee angle movement by having faster response times, smaller overshoots, and lower steady-state errors when compared with the conventional SM across four reference angle settings (20°, 30°, 40°, and 76°). The adaptive feedback SM controller was also observed to compensate for muscle nonlinearities, including fatigue, stiffness, spasticity, time delay, and other disturbances. Full article
(This article belongs to the Special Issue Nonlinear Control Applications and New Perspectives)
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21 pages, 868 KiB  
Article
A High-Gain Observer for Embedded Polynomial Dynamical Systems
by Daniel Gerbet and Klaus Röbenack
Machines 2023, 11(2), 190; https://0-doi-org.brum.beds.ac.uk/10.3390/machines11020190 - 1 Feb 2023
Cited by 6 | Viewed by 1814
Abstract
This article deals with the construction of high-gain observers for autonomous polynomial dynamical systems. In contrast to the usual approach, the system’s state is embedded into a higher dimensional Euclidean space. The observer state will be contained in said Euclidean space, which has [...] Read more.
This article deals with the construction of high-gain observers for autonomous polynomial dynamical systems. In contrast to the usual approach, the system’s state is embedded into a higher dimensional Euclidean space. The observer state will be contained in said Euclidean space, which has usually higher dimension than the system’s state space. Due to this embedding it is possible to avoid singularities in the observation matrix. For some systems this even allows constructing global observers in a structured way, which would not be possible in the lower-dimensional case. Finally, the state estimate in the original coordinates can be obtained by a projection. The proposed method is applied on some example systems. Full article
(This article belongs to the Special Issue Nonlinear Control Applications and New Perspectives)
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16 pages, 1779 KiB  
Article
Design of Fuzzy PID Controller Based on Sparse Fuzzy Rule Base for CNC Machine Tools
by Zaiqi Yu, Ning Liu, Kexin Wang, Xianghan Sun and Xianjun Sheng
Machines 2023, 11(1), 81; https://0-doi-org.brum.beds.ac.uk/10.3390/machines11010081 - 9 Jan 2023
Cited by 1 | Viewed by 1979
Abstract
The robustness of the control algorithm plays a crucial role in the precision manufacturing and measurement of the CNC machine tool. This paper proposes a fuzzy PID controller based on a sparse fuzzy rule base (S-FPID), which can effectively control the position of [...] Read more.
The robustness of the control algorithm plays a crucial role in the precision manufacturing and measurement of the CNC machine tool. This paper proposes a fuzzy PID controller based on a sparse fuzzy rule base (S-FPID), which can effectively control the position of a nonlinear CNC machine tool servo system consisting of a rotating motor and ball screw. In order to deal with the influences of both the internal and external uncertainties in the servo system, fuzzy logic is used to adjust the proportion, and integral and differential parameters in real-time to improve the robustness of the system. In the fuzzy inference engine of FPID, a sparse fuzzy rule base is used instead of a full-order fuzzy rule base, which significantly improves the computational efficiency of FPID and saves a lot of RAM storage space. The sensitivity analysis of S-FPID verifies the self-tuning ability of its parameters. Furthermore, the proposed S-FPID has been compared with the PID and FPID via simulation and experiment. The results show that compared with the classical PID controller, the overshoot of the S-FPID controller is reduced by 74.29%, and the anti-interference ability is increased by 62.43%; compared with FPID algorithm, the efficiency of the SPID is improved by 87.25% on the premise of a slight loss in robustness. Full article
(This article belongs to the Special Issue Nonlinear Control Applications and New Perspectives)
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23 pages, 5626 KiB  
Article
Feature-Based MPPI Control with Applications to Maritime Systems
by Hannes Homburger, Stefan Wirtensohn, Moritz Diehl and Johannes Reuter
Machines 2022, 10(10), 900; https://0-doi-org.brum.beds.ac.uk/10.3390/machines10100900 - 6 Oct 2022
Cited by 1 | Viewed by 1793
Abstract
In this paper, a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control is presented. Using the MPPI approach, the optimal feedback control is calculated by solving a stochastic optimal control (OCP) problem online by evaluating the weighted inference of [...] Read more.
In this paper, a novel feature-based sampling strategy for nonlinear Model Predictive Path Integral (MPPI) control is presented. Using the MPPI approach, the optimal feedback control is calculated by solving a stochastic optimal control (OCP) problem online by evaluating the weighted inference of sampled stochastic trajectories. While the MPPI algorithm can be excellently parallelized, the closed-loop performance strongly depends on the information quality of the sampled trajectories. To draw samples, a proposal density is used. The solver’s and thus, the controller’s performance is of high quality if the sampled trajectories drawn from this proposal density are located in low-cost regions of state-space. In classical MPPI control, the explored state-space is strongly constrained by assumptions that refer to the control value’s covariance matrix, which are necessary for transforming the stochastic Hamilton–Jacobi–Bellman (HJB) equation into a linear second-order partial differential equation. To achieve excellent performance even with discontinuous cost functions, in this novel approach, knowledge-based features are introduced to constitute the proposal density and thus the low-cost region of state-space for exploration. This paper addresses the question of how the performance of the MPPI algorithm can be improved using a feature-based mixture of base densities. Furthermore, the developed algorithm is applied to an autonomous vessel that follows a track and concurrently avoids collisions using an emergency braking feature. Therefore, the presented feature-based MPPI algorithm is applied and analyzed in both simulation and full-scale experiments. Full article
(This article belongs to the Special Issue Nonlinear Control Applications and New Perspectives)
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Review

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22 pages, 3183 KiB  
Review
Review and Comparison of Clearance Control Strategies
by Bingwei Gao, Wei Shen, Hao Guan, Wei Zhang and Lintao Zheng
Machines 2022, 10(6), 492; https://0-doi-org.brum.beds.ac.uk/10.3390/machines10060492 - 20 Jun 2022
Cited by 6 | Viewed by 1829
Abstract
The nonlinearity of clearance has a significant influence on the performance of a system while ensuring the reliability of the variable-speed transmission, and hinders the development of the controlled object according to the predetermined trajectory. Aimed at the transmission clearance problem in different [...] Read more.
The nonlinearity of clearance has a significant influence on the performance of a system while ensuring the reliability of the variable-speed transmission, and hinders the development of the controlled object according to the predetermined trajectory. Aimed at the transmission clearance problem in different systems, this study summarizes the existing literature and provides a reference for the research and compensation of clearance characteristics. First, the influence of clearance on system performance is analyzed and summarized, and it is shown that the existence of clearance causes problems, such as system response delay and limited cycle oscillation. Then, the control strategies for studying clearance are introduced, which are mainly divided into the control strategy based on the clearance model and the non-clearance model control strategy, and these are respectively explained. Finally, some opinions are proposed for the perfection and development of future clearance nonlinear control theory. Ideas for realizing the suppression of the adverse effects of clearances have their characteristics, and in practical applications, the difficulty of implementation and cost control should be comprehensively considered. In the future, to cope with complex and changeable environments, the clearance control strategy will continue to be optimized. Full article
(This article belongs to the Special Issue Nonlinear Control Applications and New Perspectives)
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