scholarly journals Practical Computational Approach for the Stability Analysis of Fuzzy Model-Based Predictive Control of Substrate and Biomass in Activated Sludge Processes

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 531
Author(s):  
Pedro M. Vallejo LLamas ◽  
Pastora Vega
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Activated Sludge ◽  
Predictive Control ◽  
Closed Loop ◽  
Complex Dynamics ◽  
Linear Time ◽  
Fuzzy Model ◽  
The Stability ◽  
The Mathematical Model

This paper presents a procedure for the closed-loop stability analysis of a certain variant of the strategy called Fuzzy Model-Based Predictive Control (FMBPC), with a model of the Takagi-Sugeno type, applied to the wastewater treatment process known as the Activated Sludge Process (ASP), with the aim of simultaneously controlling the substrate concentration in the effluent (one of the main variables that should be limited according to environmental legislations) and the biomass concentration in the reactor. This case study was chosen both for its environmental relevance and for special process characteristics that are of great interest in the field of nonlinear control, such as strong nonlinearity, multivariable nature, and its complex dynamics, a consequence of its biological nature. The stability analysis, both of fuzzy systems (FS) and the very diverse existing strategies of nonlinear predictive control (NLMPC), is in general a mathematically laborious task and difficult to generalize, especially for processes with complex dynamics. To try to minimize these difficulties, in this article, the focus was placed on the mathematical simplification of the problem, both with regard to the mathematical model of the process and the stability analysis procedures. Regarding the mathematical model, a state-space model of discrete linear time-varying (DLTV), equivalent to the starting fuzzy model (previously identified), was chosen as the base model. Furthermore, in a later step, the DLTV model was approximated to a local model of type discrete linear time-invariant (DLTI). As regards the stability analysis itself, a computational method was developed that greatly simplified this difficult task (in a local environment of an operating point), compared to other existing methods in the literature. The use of the proposed method provides useful conclusions for the closed-loop stability analysis of the considered FMBPC strategy, applied to an ASP process; at the same time, the possibility that the method may be useful in a more general way, for similar fuzzy and predictive strategies, and for other complex processes, was observed.

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

Modeling and Stability Analysis of Hydraulic System for Wave Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 1934-1939
Author(s):  
Jian Jun Peng ◽  
Yan Jun Liu ◽  
Yu Li ◽  
Ji Bin Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Mathematical Models ◽  
Hydraulic System ◽  
Simulation System ◽  
Displacement Sensor ◽  
Schematic Diagram ◽  
Wave Simulation ◽  
The Stability ◽  
The Mathematical Model

This thesis put forward a hydraulic wave simulation system based on valve-controlled cylinder hydraulic system, which simulated wave movement on the land. The mathematical model of valve-controlled symmetric cylinder was deduced and the mathematical models of servo valve, displacement sensor and servo amplifier were established according to the schematic diagram of the hydraulic system designed, on the basis of which the mathematical model of hydraulic wave simulation system was obtained. Then the stability of the system was analyzed. The results indicated that the system was reliable.

Formation control of longitudinal vehicular platoons under generic network topology with heterogeneous time delays

2018 ◽  
Vol 25 (3) ◽  
pp. 655-665 ◽  
Author(s):  
Hossein Chehardoli ◽  
Ali Ghasemi
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Formation Control ◽  
Vehicular Networks ◽  
Closed Loop ◽  
Linear Time ◽  
Characteristic Root ◽  
Multiple Delays ◽  
Loop Dynamics ◽  
The Stability

The problem of third-order consensus of homogeneous vehicular platoons in the presence of communication and parasitic delays is investigated. The communication topology of vehicular networks is assumed to be directed and generic. Therefore, a number of eigenvalues of the network’s matrix are complex, entangling the stability analysis of the closed-loop dynamics. By considering both communication and parasitic delays, a new linear centralized consensus protocol is designed for each vehicle. It will be shown that the closed-loop dynamics of vehicular networks with generic topology is in the form of linear systems with multiple delays. By presenting a new approach, the resultant linear time delay system is decoupled to individual third- and sixth-order dynamical equations. By performing the stability analysis of the new equations, it will be proven that the control parameters are independent of the network’s topology. Therefore, the control design and stability analysis will be significantly simplified compared with previous studies. To find the stable regions of time delay, the cluster treatment characteristic root method is employed. Simulation results are provided to show the effectiveness of the proposed approach.

scholarly journals Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10019
Author(s):  
OPhir Nave ◽  
Israel Hartuv ◽  
Uziel Shemesh
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear Differential Equations ◽  
Equilibrium Points ◽  
Asymptotic Methods ◽  
Fast Subsystem ◽  
The Stability ◽  
System Variables ◽  
The Mathematical Model ◽  
Slow Decomposition

In general, a mathematical model that contains many linear/nonlinear differential equations, describing a phenomenon, does not have an explicit hierarchy of system variables. That is, the identification of the fast variables and the slow variables of the system is not explicitly clear. The decomposition of a system into fast and slow subsystems is usually based on intuitive ideas and knowledge of the mathematical model being investigated. In this study, we apply the singular perturbed vector field (SPVF) method to the COVID-19 mathematical model of to expose the hierarchy of the model. This decomposition enables us to rewrite the model in new coordinates in the form of fast and slow subsystems and, hence, to investigate only the fast subsystem with different asymptotic methods. In addition, this decomposition enables us to investigate the stability analysis of the model, which is important in case of COVID-19. We found the stable equilibrium points of the mathematical model and compared the results of the model with those reported by the Chinese authorities and found a fit of approximately 96 percent.

scholarly journals Design and Stability Analysis of Uncertain Networked Predictive Control Systems with Multiple Forward Channels

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongbo Song
Keyword(s):  
Stability Analysis ◽  
Control Systems ◽  
Predictive Control ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Control Performance ◽  
Selection Scheme ◽  
Signal Selection ◽  
Networked Predictive Control ◽  
The Stability

This paper is concerned with the design and stability of networked predictive control for uncertain systems with multiple forward channels. The delays and packet dropouts are distributed such that the classic networked predictive control (NPC) needs modifications to be implemented. An improved control signal selection scheme with distributed prediction length is proposed to increase the prediction accuracy and hence achieve better control performance. Moreover, stability analysis results are obtained for both constant and random cases. Interestingly, it is shown that the stability of the closed-loop NPC system is not related to the distributed delays when they are constant and the system model is accurate. Finally, a two-axis milling machine example is given to illustrate the effectiveness of the proposed method.

scholarly journals Modeling and Stability Analysis of Wedge Clutch System

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jian Yao ◽  
Li Chen ◽  
Chengliang Yin
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Piecewise Linear ◽  
Wedge Angle ◽  
Stable Condition ◽  
System A ◽  
Actuation System ◽  
Linearized System ◽  
The Stability ◽  
The Mathematical Model

A wedge clutch with unique features of self-reinforcement and small actuation force was designed. Its self-reinforcement feature, associated with different factors such as the wedge angle and friction coefficient, brings different dynamics and unstable problem with improper parameters. To analyze this system, a complete mathematical model of the actuation system is built, which includes the DC motor, the wedge mechanism, and the actuated clutch pack. By considering several nonlinear factors, such as the slip-stick friction and the contact or not of the clutch plates, the system is piecewise linear. Through the stability analysis of the linearized system in clutch slipping phase, the stable condition of the designed parameters is obtained asα>arctan⁡(μc). The mathematical model of the actuation system is validated by prototype testing. And with the validated model, the system dynamics in both stable and unstable conditions is investigated and discussed in engineering side.

scholarly journals Stability Analysis of the Corruption Free Equilibrium of the Mathematical Model of Corruption in Nigeria

2020 ◽  
Vol 8 (2) ◽  
pp. 61-68
Author(s):  
Victor Akinsola ◽  
ADEYEMI BINUYO
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Operator Technique ◽  
Eigen Values ◽  
The Stability ◽  
The Mathematical Model

In this paper, a mathematical model of the transmission dynamics of corruption among populace is analyzed. The corruption free equilibrium state, characteristic equation and Eigen values of the corruption model were obtained. The basic reproductive number of the corruption model was also determined using the next generation operator technique at the corruption free equilibrium points. The condition for the stability of the corruption free equilibrium state was determined. The local stability analysis of the mathematical model of corruption was done and the results were presented and discussed accordingly. Recommendations were made from the results on measures to reduce the rate of corrupt practices among the populace.   

The Control of Vibration Transmissibility Using an Electrodynamic Actuator –Close-Loop Solution

2013 ◽  
Vol 436 ◽  
pp. 166-173
Author(s):  
A. Mihaela Mîţiu ◽  
Daniel Constantin Comeagă ◽  
Octavian G. Donţu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mechanical System ◽  
Closed Loop ◽  
Mechanical Systems ◽  
Vibration Transmissibility ◽  
Technical Solutions ◽  
The Mathematical Model

In this paper are presented some aspects of transmissibility control of mechanical systems with 1 DOF so that the effects of vibration on their action to be minimized. Some technical solutions that can be used for this purpose is analyzed. Starting from the mathematical model of an electro-mechanical system with 1 DOF, are identified the parameters which influence the effectiveness of the transmissibility control system using an electrodynamic actuator who work in "closed loop".

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

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