Fault indicators and unique mode-dependent state equations from a fixed-causality diagnostic bond graph of linear models with ideal switches

2018 ◽  
Vol 232 (6) ◽  
pp. 695-708 ◽  
Author(s):  
Wolfgang Borutzky
Keyword(s):  
Linear Time ◽  
Bond Graph ◽  
Differential Algebraic Equations ◽  
Fault Detection And Isolation ◽  
Mode Switching ◽  
State Transitions ◽  
Algebraic Equations ◽  
State Equations ◽  
Analytical Redundancy ◽  
Junction Structure

Analytical redundancy relations are fundamental in model-based fault detection and isolation. Their numerical evaluation yields a residual that may serve as a fault indicator. Considering switching linear time-invariant system models that use ideal switches, it is shown that analytical redundancy relations can be systematically deduced from a diagnostic bond graph with fixed causalities that hold for all modes of operation. Moreover, as to a faultless system, the presented bond graph–based approach enables to deduce a unique implicit state equation with coefficients that are functions of the discrete switch states. Devices or phenomena with fast state transitions, for example, electronic diodes and transistors, clutches, or hard mechanical stops are often represented by ideal switches which give rise to variable causalities. However, in the presented approach, fixed causalities are assigned only once to a diagnostic bond graph. That is, causal strokes at switch ports in the diagnostic bond graph reflect only the switch-state configuration in a specific system mode. The actual discrete switch states are implicitly taken into account by the discrete values of the switch moduli. The presented approach starts from a diagnostic bond graph with fixed causalities and from a partitioning of the bond graph junction structure and systematically deduces a set of equations that determines the wanted residuals. Elimination steps result in analytical redundancy relations in which the states of the storage elements and the outputs of the ideal switches are unknowns. For the later two unknowns, the approach produces an implicit differential algebraic equations system. For illustration of the general matrix-based approach, an electromechanical system and two small electronic circuits are considered. Their equations are directly derived from a diagnostic bond graph by following causal paths and are reformulated so that they conform with the matrix equations obtained by the formal approach based on a partitioning of the bond graph junction structure. For one of the three mode-switching examples, a fault scenario has been simulated.

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

scholarly journals Sensitivity Analysis for Hybrid Systems and Systems With Memory

2019 ◽  
Vol 14 (9) ◽  
Author(s):  
Radu Serban ◽  
Antonio Recuero
Keyword(s):  
Hybrid Systems ◽  
Exponential Model ◽  
Differential Algebraic Equations ◽  
Mode Switching ◽  
Continuous Systems ◽  
Algebraic Equations ◽  
Adjoint Sensitivity ◽  
Adjoint Systems ◽  
Systems With Memory ◽  
With Memory

We present an adjoint sensitivity method for hybrid discrete—continuous systems, extending previously published forward sensitivity methods (FSA). We treat ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) of index up to two (Hessenberg) and provide sufficient solvability conditions for consistent initialization and state transfer at mode switching points, for both the sensitivity and adjoint systems. Furthermore, we extend the analysis to so-called hybrid systems with memory where the dynamics of any given mode depend explicitly on the states at the last mode transition point. We present and discuss several numerical examples, including a computational mechanics problem based on the so-called exponential model (EM) constitutive material law for steel reinforcement under cyclic loading.

scholarly journals On the Stability Analysis of Delay Differential-Algebraic Equations

2018 ◽  
Vol 34 (2) ◽  
Author(s):  
Phi Ha
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Spectral Condition ◽  
Algebraic Equations ◽  
Linear Time Invariant ◽  
Stability Of Dynamical Systems ◽  
The Stability ◽  
Delay Differential

The stability analysis of linear time invariant delay differentialalgebraic equations (DDAEs) is analyzed. Examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical systems is not valid for an arbitrarily high index system, and hence, a new concept of weakly exponential stability (w.e.s) is proposed. Then, we characterize the w.e.s in term of a spectral condition for some special classes of DDAEs.

scholarly journals On generalized inverses of singular matrix pencils

2011 ◽  
Vol 21 (1) ◽  
pp. 161-172 ◽  
Author(s):  
Klaus Röbenack ◽  
Kurt Reinschke
Keyword(s):  
Linear Time ◽  
Matrix Pencil ◽  
Differential Algebraic Equations ◽  
Generalized Inverses ◽  
Drazin Inverse ◽  
Algebraic Equations ◽  
Singular Matrix ◽  
Linear Time Invariant ◽  
Matrix Pencils ◽  
Linear Differential

On generalized inverses of singular matrix pencilsLinear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the multiplicity of poles at zero of the Moore-Penrose inverse and the Drazin inverse of the rational matrix are investigated. We present example networks whose circuit equations yield singular matrix pencils.

scholarly journals Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs

2017 ◽  
Vol 231 (1) ◽  
pp. 14-28
Author(s):  
Roger F Ngwompo ◽  
René Galindo
Keyword(s):  
Control Systems ◽  
Internal Energy ◽  
Linear Time ◽  
Bond Graph ◽  
Energy Sources ◽  
Initial State ◽  
Graph Models ◽  
Linear Time Invariant ◽  
Alternative Representation ◽  
Junction Structure

Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of such systems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo-junction structure is proposed as an alternative representation for linear time-invariant (LTI) bond graph models with internal modulated sources. The pseudo-junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realizing the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems.

Uncertain fault estimation using bicausal bond graph: Application to intelligent autonomous vehicle

2019 ◽  
Vol 234 (10) ◽  
pp. 1150-1171 ◽  
Author(s):  
Yacine Lounici ◽  
Youcef Touati ◽  
Smail Adjerid
Keyword(s):  
Uncertain Systems ◽  
Autonomous Vehicle ◽  
Graph Model ◽  
Estimation Procedure ◽  
Bond Graph ◽  
Fault Isolation ◽  
Fault Detection And Isolation ◽  
Fault Estimation ◽  
Analytical Redundancy ◽  
Traction System

This article addresses the fault detection and isolation problem of uncertain systems using the bond graph model–based approach. The latter provides through its causal and structural properties an automatic analytical redundancy relations generation. The numerical evaluation of analytical redundancy relations yields residuals, which are used to verify the coherence between the real system and reference behaviors describing the nominal operation. In fact, the residual is compared to its thresholds to detect the fault. In addition, the comparison between all fault signatures allows making a decision on fault isolation. Moreover, to isolate the faults that activate the same set of residuals, an additional residual must be calculated for each fault. This additional residual is the comparison between two estimations of the considered fault obtained using the sensitivity relations. However, due to the presence of uncertainties, errors can occur in the fault estimation allowing false decisions on fault isolation. The novelties and innovative interests in the present work are (1) to improve the fault estimation procedure based on the uncertainties modeling and bicausality notion, in order to overcome the problem related to errors in the estimated fault and (2) to suitably generate the isolation thresholds in a systematic way using the uncertain fault estimation procedure proposed in this article so that fault can be isolated successfully. The proposed methodology is studied under various scenarios via simulations over an electromechanical traction system corresponding to a quarter of intelligent autonomous vehicle, named RobuCar.

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