scholarly journals New Tuning Approach of Fuzzy Logic System Using Proportional Integral Observer for Tracking a Nonlinear System

2021 ◽  
Author(s):  
Mustefa Jibril
Keyword(s):  
Fuzzy Logic ◽  
Nonlinear System ◽  
The State ◽  
State Variables ◽  
Hydraulic Actuator ◽  
Nonlinear Controller ◽  
Nonlinear Method ◽  
Proportional Integral ◽  
Road Disturbance ◽  
System Output

Proportional integral observer (PIO) for tracking a nonlinear method has a lower sentiency to cipher the state and output variables. So a more nonlinear controller has to be else to control to activity. In this paper, a fuzzy logic (FLC) controller has been added to the PIO to meliorate the calculation transmute. A fuzzy proportional integral observer (FPIO) for following a nonlinear system has been premeditated to decimate the susceptibleness to cipher the tell and turnout variables with the existent posit and product variables. The FPIO controller has been tested for improving the estimation control using a nonlinear quarter vehicle active suspension system with a nonlinear hydraulic actuator. A comparison simulation of the proposed nonlinear system for estimating the state variables and tracking the output (suspension deflection) with a set point bump road disturbance using FPIO and PIO. The comparison simulation result shows that the estimated state variables and system output match the actual ones perfectly using a fuzzy PIO controller.

Robust attitude control of the three-dimensional unknown chaotic satellite system

2021 ◽  
pp. 014233122110561
Author(s):  
Muhammad Shafiq ◽  
Israr Ahmad ◽  
O Abdullah Almatroud ◽  
M Mossa Al-Sawalha
Keyword(s):  
Attitude Control ◽  
Closed Loop ◽  
Three Dimensional ◽  
Adaptive Controller ◽  
The State ◽  
Feedback Gain ◽  
State Variables ◽  
Nonlinear Controller ◽  
Model Uncertainties ◽  
Control Effort

This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear terms. These controller attributes flourish the robust performance of the closed-loop and establish smooth state vector convergence to zero. The proposed controller consists of three parts: (1) a linear controller establishes the stability of the closed-loop at the origin, (2) a nonlinear controller component that autonomously adjusts the feedback gain, and (3) a nonlinear adaptive controller compensates for the model uncertainties and external disturbances using the online estimates of bounds and model uncertainties. The output of this part remains within a given upper and lower bound. The feedback controller gain is large when the state variables are away from the origin and become small in the origin’s vicinity. This feature is novel and contributes to the synthesis of smooth control effort that establishes robust fast and oscillation-free convergence of the state variables to zero. The Lyapunov direct stability analysis assures the global asymptotic robust stability of the closed-loop. Computer simulations and comparative analysis are included to verify the theoretical findings.

Estimation of State Variables in the Ćuk Converter Mathematical Model with Partially Unknown Parameters

2021 ◽  
Vol 22 (9) ◽  
pp. 451-458
Author(s):  
A. A. Bobtsov ◽  
R. Ortega ◽  
N. A. Nikolaev ◽  
O. V. Slita ◽  
O. A. Kozachek ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Finite Time ◽  
Control Algorithm ◽  
Power Converter ◽  
The State ◽  
Model Parameters ◽  
State Variables ◽  
Unknown Parameters ◽  
Proportional Integral ◽  
The Mathematical Model

In this paper the solution was proposed for the state variables estimation problem in the mathematical model of the DC switch-mode power converter built according to the Ćuk scheme. Pulse converters are one of the main components of most modern electrical devices and the circuit proposed by Slobodan Ćuk in the 70s of the 20th century is still relevant and demanded. Traditionally, PI (proportional-integral) controllers or proportional-integral adaptive control algorithm (PI-PBC), based on passification methods and superior to standard PI controllers in accuracy, are used as the control algorithm for power converters. However, you need to know the entire vector of the state variables of the converter to build a PI-PBC controller, and moreover, all its parameters must be accurately known. Unfortunately, in practice, such assumptions are not fulfilled, since parametric drifting is possible, and measurements of the converter’s state require additional sensors, which in some cases does not justify itself. Thus, there is a need to develop additional observers or estimators that allow obtaining data on all variables of the converter, as well as its parameters. The solution is based on the GPEBO method (generalized parameter estimation-based observers). The problem was solved under assumption that only the output signal (the output voltage of the converter) is measurable and some of the mathematical model parameters are unknown. An important aspect of the observer design is the development of an algorithm for unknown parameters and the state vector of a mathematical model estimation that ensures convergence in a finite time. Finite-time convergence is extremely important when designing observers since transients in pulse converters occur very quickly.

scholarly journals Dynamic Control Applied to a Laboratory Antilock Braking System

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Cuauhtémoc Acosta Lúa ◽  
Bernardino Castillo Toledo ◽  
Stefano Di Gennaro ◽  
Marcela Martinez-Gardea
Keyword(s):  
Dynamic Control ◽  
Difficult Problem ◽  
The State ◽  
Nonlinear Observer ◽  
State Variables ◽  
Nonlinear Controller ◽  
Braking System ◽  
Laboratory Setup ◽  
Antilock Braking System ◽  
Antilock Braking

The control of an antilock braking system is a difficult problem due to the existence of nonlinear dynamics and uncertainties of its characteristics. To overcome these issues, in this work, a dynamic nonlinear controller is proposed, based on a nonlinear observer. To evaluate its performance, this controller has been implemented on an ABS Laboratory setup, representing a quarter car model. The nonlinear observer reconstructs some of the state variables of the setup, assumed not measurable, to establish a fair benchmark for an ABS system of a real automobile. The dynamic controller ensures exponential convergence of the state estimation, as well as robustness with respect to parameter variations.

scholarly journals Estimation of the State Variables of a Nonlinear System with Non-Gaussian Noises

1972 ◽  
Vol 38 (305) ◽  
pp. 116-121
Author(s):  
Takashi SOEDA ◽  
Toshio YOSHIMURA ◽  
Tsutomu FUZIOKA ◽  
Seiji FUKUl
Keyword(s):  
Nonlinear System ◽  
The State ◽  
State Variables ◽  
Non Gaussian

Application of the System Nesting Technology for Studying the Invariance of a Complex Electric System Output in Terms of State Variables

2019 ◽  
Vol 2 (2) ◽  
pp. 26-32
Author(s):  
Kakhraman R. ALLAYEV ◽  
◽  
Akram M. MIRZABAYEV ◽  
Takhir F. MAKHMUDOV ◽  
Temur A. MAKHKAMOV ◽  
...  
Keyword(s):  
State Variables ◽  
Electric System ◽  
System Output

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

Internal Variable Theory Formulated by One Extended Potential Function

2020 ◽  
Vol 45 (3) ◽  
pp. 311-318
Author(s):  
Qiang Yang ◽  
Zhuofu Tao ◽  
Yaoru Liu
Keyword(s):  
Potential Function ◽  
Internal Variable ◽  
The State ◽  
Internal Variables ◽  
State Variables ◽  
Kinetic Rate ◽  
Variable Theory ◽  
Rate Laws ◽  
Flow Potential ◽  
Internal Variable Theory

AbstractIn the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

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