scholarly journals Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Raquel S. Rodríguez ◽  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Bond Graph ◽  
Physical Domain ◽  
Graph Models ◽  
Simple Task ◽  
Analysis And Synthesis ◽  
Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

Modeling of Uncertain Nonlinear System With Z-Numbers

2021 ◽  
pp. 290-314
Author(s):  
Raheleh Jafari ◽  
Sina Razvarz ◽  
Alexander Gegov ◽  
Satyam Paul
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Network Approach ◽  
Uncertain Nonlinear System ◽  
Neural Network Approach ◽  
The Neural Network ◽  
Simulation Results ◽  
Fuzzy Equations

In order to model the fuzzy nonlinear systems, fuzzy equations with Z-number coefficients are used in this chapter. The modeling of fuzzy nonlinear systems is to obtain the Z-number coefficients of fuzzy equations. In this work, the neural network approach is used for finding the coefficients of fuzzy equations. Some examples with applications in mechanics are given. The simulation results demonstrate that the proposed neural network is effective for obtaining the Z-number coefficients of fuzzy equations.

Analysis of loading effect of systems in a bond graph approach with application to a synchronous machine

2011 ◽  
Vol 226 (2) ◽  
pp. 243-255
Author(s):  
G Gonzalez
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Bond Graph ◽  
Physical Domain ◽  
Closed Loop System ◽  
Graph Models ◽  
Loading Effect ◽  
Closed Loop Systems ◽  
New Type ◽  
Feedback Connections

A new type of bond designed as an adapted bond is proposed. This bond can be considered in the transition from an active bond to a bond. This approach makes it possible to know the loading effect of the controller–plant and the feedback connections. In order to determine the loading effect of the closed-loop system, the transfer function using causal paths and causal loops of the system in the physical domain is presented. However, this proposed adapted bond should be used in fault cases. Finally, some examples of bond graph models in open- and closed-loop systems are given.

A novel global harmony search method based off-line tuning of RFNN for adaptive control of uncertain nonlinear systems

2015 ◽  
Vol 8 (1) ◽  
pp. 69-98 ◽  
Author(s):  
Fouad Allouani ◽  
Djamel Boukhetala ◽  
Fares Boudjema ◽  
Gao Xiao-Zhi
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Method ◽  
Harmony Search ◽  
Optimization Method ◽  
Uncertain Nonlinear Systems ◽  
Content Type ◽  
Supervisory Controller ◽  
Fuzzy Neural ◽  
Simulation Results

Purpose – The two main purposes of this paper are: first, the development of a new optimization algorithm called GHSACO by incorporating the global-best harmony search (GHS) which is a stochastic optimization algorithm recently developed, with the ant colony optimization (ACO) algorithm. Second, design of a new indirect adaptive recurrent fuzzy-neural controller (IARFNNC) for uncertain nonlinear systems using the developed optimization method (GHSACO) and the concept of the supervisory controller. Design/methodology/approach – The novel optimization method introduces a novel improvization process, which is different from that of the GHS in the following aspects: a modified harmony memory representation and conception. The use of a global random switching mechanism to monitor the choice between the ACO and GHS. An additional memory consideration selection rule using the ACO random proportional transition rule with a pheromone trail update mechanism. The developed optimization method is applied for parametric optimization of all recurrent fuzzy neural networks adaptive controller parameters. In addition, in order to guarantee that the system states are confined to the safe region, a supervisory controller is incorporated into the IARFNNC global structure. Findings – First, to analyze the performance of GHSACO method and shows its effectiveness, some benchmark functions with different dimensions are used. Simulation results demonstrate that it can find significantly better solutions when compared with the Harmony Search (HS), GHS, improved HS (IHS) and conventional ACO algorithm. In addition, simulation results obtained using an example of nonlinear system shows clearly the feasibility and the applicability of the proposed control method and the superiority of the GHSACO method compared to the HS, its variants, particle swarm optimization, and genetic algorithms applied to the same problem. Originality/value – The proposed new GHS algorithm is more efficient than the original HS method and its most known variants IHS and GHS. The proposed control method is applicable to any uncertain nonlinear system belongs in the class of systems treated in this paper.

Energy-based viscoelastic model: a physical approach for material an elastic behavior by the bond graph approach

SIMULATION ◽  
2019 ◽  
Vol 96 (1) ◽  
pp. 111-127
Author(s):  
Amir Zanj ◽  
Fangpo He ◽  
Peter C Breedveld
Keyword(s):  
Dynamic Process ◽  
Viscoelastic Model ◽  
Physical Nature ◽  
Bond Graph ◽  
Elastic Behavior ◽  
Physical Domain ◽  
True Nature ◽  
Physical Systems ◽  
Viscoelastic Behaviors ◽  
Simulation Results

Understanding the true nature of viscoelastic behaviors in multi-physical systems has always been a challenging issue in system dynamic investigations, as each existing physical subdomain of the system may follow a different attenuation pattern during the dynamic process. In this study, to generate a viscoelastic model suitable for multi-physical domain dynamic investigations, a physical combined viscoelastic model is proposed. To this aim, by means of the bond graph approach, an energy-based conventional viscoelastic model is first generated, and its embedded dispersive mechanisms are interpreted physically. By including the interpreted dissipative mechanisms into the relative subdomains of an elastic domain, an energy-based combined viscoelastic model is then proposed. The obtained simulation results indicate that the proposed viscoelastic model is able to capture a variety of viscoelastic behaviors in the system with respect to the true physical nature of the system.

Function Driven Redesign Method for Conceptual Design

2009 ◽  
Vol 628-629 ◽  
pp. 119-124
Author(s):  
Xu Ling Chen ◽  
Pei Huang Lou ◽  
Dun Bing Tang
Keyword(s):  
Conceptual Design ◽  
Design Method ◽  
Bond Graph ◽  
System Dynamic ◽  
Original Design ◽  
Graph Models ◽  
Advantages And Disadvantages ◽  
Dynamic Performances ◽  
Simulation Results

In order to assimilate and redesign the existing product, a conceptual design driven by function is proposed. Firstly, the behaviors, structures and functions of the product are analyzed in detail. Then bond graph models are used to describe the behaviors which indicate the dynamic performances of the existing product. Secondly, the advantages and disadvantages of the product can be revealed through these dynamic performances which are abstracted by simulating the bond graph models. To catch the intention of the original design, the simulation results are analyzed regarding the system dynamic performances. According to the evolutional routes, several redesign results are obtained by grouping some optimized alternatives. Finally, applying the method to a frictional driver redesign, the control and dynamic performances are both improved, which verifies the validity and practicability of the proposed design method.

A Robust Delay Compensator for Uncertain Nonlinear Systems With Unknown Time-Varying Input Delay

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Ashish Kumar Jain ◽  
Shubhendu Bhasin
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Tracking Error ◽  
Input Delay ◽  
Control Law ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Uniformly Ultimately Bounded ◽  
Simulation Results

This paper proposes a robust compensator for a class of uncertain nonlinear systems subjected to unknown time-varying input delay. The proposed control law is based on the integral of past values of control and a novel filtered tracking error. Sufficient gain conditions dependent on the known bound of the delay are derived using a Lyapunov-based stability analysis, where Lyapunov–Krasovskii (LK) functionals are used to achieve a global uniformly ultimately bounded (GUUB) tracking result. Simulation results for a nonlinear system are used to evaluate the performance and robustness of the controller for different values of time-varying input delay.

Observer-Based State Tracking Adaptive Controller for a Class of Non-Affine Nonlinear Systems: An Intelligent Approach

2012 ◽  
Vol 488-489 ◽  
pp. 1798-1802
Author(s):  
R. Ghasemi ◽  
M.B. Menhaj ◽  
B. Abdi
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Nonlinear Observer ◽  
Asymptotic Convergence ◽  
Affine Nonlinear Systems ◽  
State Tracking ◽  
Simulation Results ◽  
Intelligent Approach

This paper proposes a new method for designing both nonlinear observer and adaptive controller for a class of non-affine nonlinear systems with unknown functions of the system. The states of the nonlinear system are assumed to be unavailable for measurement. The merits of this paper is as: asymptotic convergence of the observer and tracking error to zero, boundedness of all signals involved, and robustness. The simulation results illustrate the promising performance of the proposed algorithm.

Bond Graph Models for Fluid Networks Using Modal Approximation

1985 ◽  
Vol 107 (3) ◽  
pp. 169-175 ◽  
Author(s):  
D. L. Margolis ◽  
W. C. Yang
Keyword(s):  
Transmission Lines ◽  
Bond Graph ◽  
Bond Graphs ◽  
Graph Models ◽  
Graph Representations ◽  
Approximation Techniques ◽  
Fluid Networks ◽  
Simulation Results ◽  
Dissipative Model ◽  
Modal Approximation

Modal bond graph representations of the dissipative model of rigid, cylindrical fluid transmission lines with laminar flow are developed. Modal approximation techniques are used for both hydraulic and pneumatic lines. The modeling and simulation procedures for fluid networks coupled with nonlinear and dynamic systems are greatly facilitated using bond graphs. The physical interpretation of the model is preserved in this approach. Simulation results for hydraulic single lines are compared with results derived by the quasi-method of characteristics. The simulation results for fluid networds for various line and termination configurations are illustrated.

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