Development of a Robust Observer for Constrained Nonlinear Systems

2007 ◽  
Author(s):  
G. A. Kfoury ◽  
N. G. Chalhoub
Keyword(s):  
Combustion Engine ◽  
General Procedure ◽  
Equations Of Motion ◽  
The State ◽  
Nonlinear Observer ◽  
State Variables ◽  
Connecting Rod ◽  
Algebraic Form ◽  
Highly Nonlinear ◽  
Multi Body

The equations of motion for a constrained multi-body system are usually governed by a set of highly nonlinear differential-algebraic (D-A) equations. For nonlinear complex systems, the substitution method cannot be implemented to eliminate the superfluous coordinates. Thus, the differential-algebraic form of the equations of motion has to be retained. For control purposes, the state variables of the system should be available for the computation of the control signals. The current study presents a general procedure for developing a robust nonlinear observer capable of yielding accurate estimates of the state variables for a complex system whose dynamics are governed by a set of D-A equations. To assess the viability of the proposed approach, the multi-body dynamics of a piston/connecting-rod/crankshaft mechanism for a single cylinder internal combustion engine is considered in this study. The equations of motion account for both the rigid and flexible motions of the crank-slider mechanism. The simulation results demonstrate the capability of the proposed observer in accurately estimating all the state variables of the system including the superfluous ones. They illustrate the robustness of the observer to both structured and unstructured uncertainties. Moreover, they demonstrate that the nominal constraint equations are satisfied by the estimated state variables.

An Efficient Method for Simulation of 3D Multi-Body Dynamic Problems Using Maple and Simulink Packages

2011 ◽  
Author(s):  
Kourosh H. Shirazi ◽  
Behrooz Attaran ◽  
Reza Zaeri
Keyword(s):  
Efficient Method ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
State Variables ◽  
Dynamic Problems ◽  
Algebraic Form ◽  
Graphical Environment ◽  
Time Accuracy ◽  
Multi Body ◽  
Body Dynamic

In this paper, an efficient method is proposed for modelling and simulation of multi-body dynamic problems. The method employs symbolic computational abilities of Maple as well as graphical environment of Matlab-Simulink to obtain and solve the equations of motion of a multi-body system accurately and rapidly. Considering a typical multi-body dynamical system the governing equations of system including second order equations of motion, first order nonholonomic and holonomic algebraic constraint equations are derived in Maple software. The state variables of the system are defined based on the systems degrees of freedom or generalized velocities. Converting the system’s equations to an algebraic form and combining them together by using a few Maple commands, the simplest form of the system’s equations of motion are obtained in the canonical standard state space form. This form is suitable when an explicit numerical method of integration is used. Then using a few toolboxes of Simulink, the equations are solved and can be studied. To procedural illustration of the method a lateral vehicle dynamic problem having thirty equations is considered. Beside the present method, Maple as well as Matlab is used to solve the problem. The results show the distinction of the method from the points of execution CPU time, accuracy and longer simulation. This method is suitable when investigation of long term behavior of multi-body dynamical systems is needed.

Robust active disturbance attenuation control of an uncertain quadrotor

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nigar Ahmed ◽  
Ajeet kumar Bhatia ◽  
Syed Awais Ali Shah
Keyword(s):  
Control Algorithm ◽  
Sliding Mode ◽  
The State ◽  
Disturbance Attenuation ◽  
State Variables ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Content Type ◽  
Highly Nonlinear ◽  
The Stability

PurposeThe aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).Design/methodology/approachFor designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.FindingsThe major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.Practical implicationsIn practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.Originality/valueDesigning control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

Probabilistic Tolerance Allocation for the Dynamics of an Internal Combustion Engine With a Flexible Connecting Rod

1997 ◽  
Author(s):  
F. Zhang ◽  
B. J. Gilmore ◽  
A. Sinha
Keyword(s):  
Internal Combustion Engine ◽  
Combustion Engine ◽  
Equations Of Motion ◽  
Optimization Procedure ◽  
Internal Combustion ◽  
Tolerance Allocation ◽  
Radial Clearance ◽  
Connecting Rod ◽  
Link Length ◽  
Design Variables

Abstract Tolerance allocation standards do not exist for mechanical systems with flexibility and whose response are time varying, subjected to discontinuous forcing functions. Previous approaches based on optimization and numerical integration of the dynamic equations of motion encounter difficulty with determining sensitivities around the force discontinuity. The Alternating Frequency/Time approach is applied here to capture the effect of the discontinuity. The effective link length model is used to model the system and to account for the uncertainties in the link length, radial clearance and pin location. Since the effective link length model is applied, the equations of motion for the nominal system can be applied for the entire analysis. Optimization procedure is applied to the problem where the objective is to minimize the manufacturing costs and satisfy the constraints imposed on mechanical errors and design variables. Examples of tolerance allocation are presented for a single cylinder internal combustion engine with a flexible connecting rod.

scholarly journals Synchronization of oscillations for coupled Van der Pol oscillators by output

2018 ◽  
Vol 32 ◽  
pp. 56-66
Author(s):  
Nadiya Zhogoleva ◽  
Volodymyr Shcherbak
Keyword(s):  
Control Theory ◽  
The State ◽  
Nonlinear Observer ◽  
External Control ◽  
Control Law ◽  
State Variables ◽  
Phase Vector ◽  
Van Der Pol ◽  
Practical Applications ◽  
Synchronization Problem

A number of automatic control tasks, in particular, the synchronization of trajectories, the tracking task, control by a reference system are associated with the synthesis of control algorithms for dynamic cascade systems, which are a set of interconnected active subsystems. In this paper, the oscillation synchronization problem is considered for two Van der Pol coupled oscillators. It is assumed that the driven subsystem depends on the external control action, in addition, the phase vector is not fully known. On the first step the solution of the problem of synchronization in the form of state feedback is written. The aim of the work is to find the synchronizing control in the form of feedback on the state estimation. Such a formulation is relevant, since for many practical applications of control theory, a typical situation is when the complete state vector of the system is unknown and only some of the functions of the state variables - the outputs of the system are accessible to measurement. One can try to use the control law obtained from feedback by replacing the state with its estimate obtained by observer - a special dynamical system whose state eventually approaches (asymptotically or exponentially) to the state of the original system. In this case a question arises whether such control will be solving the synchronization problem. In mathematical control theory, in particular for the stabilization problem of dynamical systems, similar questions constitute the content of the known principle of separation. For the observation problem solving the apparatus of the method of synthesis of auxiliary invariant relations for constructing a nonlinear observer was used. In accordance with this approach a nonlinear observer is constructed for the system under consideration, which ensures the exponential estimates of the phase vector. It is further shown that the use in the control law instead of the state of the system of its evaluation under simultaneously solving the problems of observation and synchronization leads to the local solution of the problem under consideration.

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.

Development of a Robust Nonlinear Observer for a Single-Link Flexible Manipulator

2004 ◽  
Author(s):  
Nabil G. Chalhoub ◽  
Giscard A. Kfoury
Keyword(s):  
Sliding Mode ◽  
Initial Conditions ◽  
The State ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Flexible Manipulator ◽  
State Variables ◽  
State Equations ◽  
On Line ◽  
Simulation Results

Accurate measurements of all the state variables of a given system are often not available due to the high cost of sensors, the lack of space to mount the transducers or the hostile environment in which the sensors must be located. The purpose of this study is to design a robust sliding mode observer that is capable of accurately estimating the state variables of the system in the presence of disturbances and model uncertainties. It should be emphasized that the proposed observer design can handle state equations expressed in the general form. The performance of the nonlinear observer is assessed herein by examining its capability of predicting the rigid and flexible motions of a compliant beam that is connected to a revolute joint. The simulation results demonstrate the ability of the observer in accurately estimating the state variables of the system in the presence of structured uncertainties and under different initial conditions between the observer and the plant. Moreover, they illustrate the deterioration in the performance of the observer when subjected to unstructured uncertainties of the system. Furthermore, the nonlinear observer was successfully implemented to provide on-line estimates of the state variables for two model-based controllers. The simulation results show minimal deterioration in the closed-loop response of the system stemming from the usage of estimated rather than exact state variables in the computation of the control signals.

Asymptotic evaluation of the state and stiffness of the van der Paul oscillator

2019 ◽  
Vol 33 ◽  
pp. 91-99
Author(s):  
Nadiya Zhogoleva ◽  
Volodymyr Shcherbak
Keyword(s):  
Stable Limit Cycle ◽  
Cardiac Activity ◽  
The State ◽  
The Body ◽  
Nonlinear Observer ◽  
Control Problems ◽  
Analytical Mechanics ◽  
Stable Limit ◽  
State Variables ◽  
Model Equations

In many applications of physics, biology, and other sciences, an approach based on the concept of model equations is used as an approximate model of complex nonlinear processes. The basis of this concept is the provision that a small number of characteristic types movements of simple mathematical models inherent in systems gives the key to understanding and exploring a huge number of different phenomena. With this approach it is a priori assumed that the entire physical diverseness can be represented in the form of fairly simple model equations. It is contributes to a qualitative study of complex systems for various physical nature since basic models individually are well studied, their parameters have a physical interpretation. In particular, it is well known that oscillatory motion of various systems with a stable limit cycle can be modeled by a system consisting of one or more coupled van der Pol oscillators. Such systems are widely represented in various technical devices and in the study and modeling of some biological functions of the body, such as cardiac activity, respiration, locomotor activity, etc. It is considered a typical situation for many practical applications of control theory when the complete state vector of the system is unknown and only some of the functions of the state variables -- the outputs of the system are accessible to measurement. Therefore, the problem of determining in real time the state and parameters of such systems based on the results of measuring the output signals are relevant. One of these inverse control problems, namely, the problem of observability and parameter identification of an model oscillatory system is considered in this article. For observation and identification scheme design the method of invariant relations developed in analytical mechanics is used. Its modification in control problems allows us to synthesize additional relationships between known and unknown quantities of a dynamical system that arise during the observed motion. The method does not involve linearization of the original system and is essentially non-linear. The constructed nonlinear observer provides an asymptotic estimation of unknown parameter and velocity of oscillations.

Explicit Poincaré equations of motion for general constrained systems. Part II. Applications to multi-body dynamics and nonlinear control

2007 ◽  
Vol 463 (2082) ◽  
pp. 1435-1446 ◽  
Author(s):  
Firdaus E Udwadia ◽  
Phailaung Phohomsiri
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Control ◽  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Constrained Systems ◽  
The Third ◽  
Highly Nonlinear ◽  
Body Dynamics ◽  
Multi Body

The power of the new equations of motion developed in part I of this paper is illustrated using three examples from multi-body dynamics. The first two examples deal with the problem of accurately controlling the orientation of a rigid body, while the third example deals with the synchronization of two rigid bodies so that their relative orientations are ‘locked’ through prescribed dynamical relationships. The ease, simplicity and accuracy with which control of such highly nonlinear systems is achieved are demonstrated.

scholarly journals Impact Dynamics Analysis of Mobile Mechanical Systems

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1776
Author(s):  
Sorin Dumitru ◽  
Andra Constantin ◽  
Cristian Copilusi ◽  
Nicolae Dumitru
Keyword(s):  
Mechanical System ◽  
Combustion Engine ◽  
Mechanical Systems ◽  
Free Fall ◽  
Radial Clearance ◽  
Connecting Rod ◽  
Element Analysis ◽  
Multi Body ◽  
The Impact ◽  
Two Bodies

The current paper focuses on the impact phenomenon analysis, in the case of multi-body mechanical systems undergoing fast motion, due to the presence of some manufacturing and mounting errors or due to some accident during the transport mechanical systems. Thus, the impact phenomenon was analyzed in two cases, the first one consisting of a two bodies, namely, a free-fall body brought in contact with the other considered fixed in space and the second case, which is a complex one, when the analyzed bodies are components of a multi-body mechanical system. The research main objective is to analyze the impact generated between the two bodies through three methods, i.e., the analytical method, a virtual prototyping method accomplished with MSC Adams software and a method based on finite element analysis with Ansys and Abaqus software. A dynamic model of the impact force was developed, which allows to make a comparison of the numerical results obtained through the abovementioned methods. As a multi-body mechanical system, it was considered a mechanism from an internal combustion engine from which the radial clearance between the piston bolt and connecting rod head of the considered mechanism was analyzed.

Considerations on Parameter and State Estimation with Ensemble Data Assimilation Methods – A Case Study with a Nonlinear Oscillator

2020 ◽  
Author(s):  
Arundhuti Banerjee ◽  
Femke Vossepoel
Keyword(s):  
Data Assimilation ◽  
The State ◽  
State Variables ◽  
Model Framework ◽  
Time Period ◽  
Highly Nonlinear ◽  
Using Data ◽  
Variable Errors ◽  
Parameter Values

<p>This study investigates the effect of erroneous parameter values for state and parameter estimation using data assimilation. The numerical model chosen for this study solves the van der Pol equation, a second-order differential equation that can be used to simulate oscillatory processes, such as earthquakes. In the model, discrepancies in the parameter values can have a significant influence on the forecasted states of the model, which is even more significant if its behaviour is highly nonlinear. When observations of the state variables are assimilated to update the parameters along with the state variables, this improves the quality of the state forecasts. The results suggest that corrections in the model parameter not only recover the actual parameter values but also reduce state-variable errors after a certain time period. However, data assimilation that updates the state variables but not the parameter can lead to erroneous estimates as well as forecasts of the oscillation. Since the study is performed on a simplified nonlinear model framework, the consequences of these results for data assimilation in more realistic models remains to be investigated.</p>

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