scholarly journals Differential Algebraic Equations of MOS Circuits and Jump Behavior

2012 ◽  
Vol 10 ◽  
pp. 327-332
Author(s):  
P. Sarangapani ◽  
T. Thiessen ◽  
W. Mathis
Keyword(s):  
State Space ◽  
Current Model ◽  
Equivalent Circuit Model ◽  
Geometric Approach ◽  
Differential Algebraic Equations ◽  
The State ◽  
Switching Behavior ◽  
Algebraic Equations ◽  
Flip Flop ◽  
Mos Circuits

Abstract. Many nonlinear electronic circuits showing fast switching behavior exhibit jump effects which occurs when the state space of the electronic system contains a fold. This leads to difficulties during the simulation of these systems with standard circuit simulators. A method to overcome these problems is by regularization, where parasitic inductors and capacitors are added at the suitable locations. However, the transient solution will not be reliable if this regularization is not done in accordance with Tikhonov's Theorem. A geometric approach is taken to overcome these problems by explicitly computing the state space and jump points of the circuit. Until now, work has been done in analyzing example circuits exhibiting this behavior for BJT transistors. In this work we apply these methods to MOS circuits (Schmitt trigger, flip flop and multivibrator) and present the numerical results. To analyze the circuits we use the EKV drain current model as equivalent circuit model for the MOS transistors.

State-Space Based Implicit Integration of the Differential-Algebraic Equations of Multibody Dynamics

1999 ◽  
Author(s):  
Dan Negrut ◽  
Edward J. Haug
Keyword(s):  
State Space ◽  
Mechanical System ◽  
Multibody Dynamics ◽  
Reference Frames ◽  
Differential Algebraic Equations ◽  
The State ◽  
Algebraic Equations ◽  
Implicit Integration ◽  
Euler Parameters ◽  
Generalized Coordinates

Abstract Three methods for the state-space based implicit integration of differential-algebraic equations of multibody dynamics are summarized and numerically compared. In the state-space approach, the time evolution of a mechanical system is characterized using a number of generalized coordinates equal with the number of degrees of freedom of the system. In this paper these independent generalized coordinates are a subset of the Cartesian position coordinates and orientation Euler parameters of body centroidal reference frames. Depending on the method, the independent generalized coordinates are implicitly integrated and dependent quantities (including Lagrange multipliers) are determined to satisfy constraint equations at position, velocity, and acceleration levels. Five computational algorithms based on the proposed methods are used to simulate the motion of a stiff 14-body vehicle model. Results show that the proposed methods deal effectively with challenges posed by stiff mechanical system simulation. A comparison with a state-space based explicit algorithm for the simulation of the same model indicates a speed-up of approximately two orders of magnitude.

scholarly journals A Generalized State-Space Aeroservoelastic Model Based on Tangential Interpolation

Aerospace ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 9 ◽  
Author(s):  
David Quero ◽  
Pierre Vuillemin ◽  
Charles Poussot-Vassal
Keyword(s):  
State Space ◽  
Reference Model ◽  
Differential Algebraic Equations ◽  
Summation Method ◽  
Algebraic Equations ◽  
Minimal Order ◽  
New Approach ◽  
Model Based ◽  
Generalized State Space ◽  
Generalized State

In this work, a new approach for the generation of a generalized state-space aeroservoelastic model based on tangential interpolation is presented. The resulting system of differential algebraic equations (DAE) is reduced to a set of ordinary differential equations (ODE) by residualization of the non-proper part of the transfer function matrix. The generalized state-space is of minimal order and allows for the application of the force summation method (FSM) for the aircraft loads recovery. Compared to the classical rational function approximation (RFA) approach, the presented method provides a minimal order realization with exact interpolation of the unsteady aerodynamic forces in tangential directions, avoiding any selection of poles (lag states). The new approach is applied first for the generation of an aerodynamic model for the bidimensional unsteady incompressible flow in the time domain. Next, an application on the generation of an aeroservoelastic model for loads evaluation of the flutter reduced order assessment (FERMAT) model under atmospheric disturbances is done, showing an excellent agreement with the reference model in the frequency domain. The proposed aeroservoelastic model of minimal order is suited for loads analysis and multivariable control design, and an application to a gust loads alleviation (GLA) strategy is shown.

Globally Independent Coordinates for Real-Time Vehicle Simulation

1998 ◽  
Vol 122 (4) ◽  
pp. 575-582 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
State Space ◽  
Real Time ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Generalized Coordinates ◽  
Dynamics Of Multibody Systems ◽  
Improved Performance ◽  
Control Forces

Models of the dynamics of multibody systems generally result in a set of differential-algebraic equations (DAE). State-space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. Therefore, these additional coordinates, together with Cartesian coordinates describing the position and orientation of the chassis, form a set of globally independent coordinates. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization in a state-space formulation, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples with realistic vehicle handling models demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation, yielding real-time for vehicle simulation. [S1050-0472(00)00404-9]

scholarly journals On the estimation of robust stability regions for nonlinear systems with saturation

2004 ◽  
Vol 15 (3) ◽  
pp. 269-278 ◽  
Author(s):  
Daniel F. Coutinho ◽  
Daniel J. Pagano ◽  
Alexandre Trofino
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Actuator Saturation ◽  
Quadratic Function ◽  
Differential Algebraic Equations ◽  
The State ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Algebraic Equations ◽  
Stability Regions

This paper addresses the problem of determining robust stability regions for a class of nonlinear systems with time-invariant uncertainties subject to actuator saturation. The unforced nonlinear system is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters, and the saturation nonlinearity is modelled by a sector bound condition. For this class of systems, local stability conditions in terms of linear matrix inequalities are derived based on polynomial Lyapunov functions in which the Lyapunov matrix is a quadratic function of the state and uncertain parameters. To estimate a robust stability region is considered the largest level surface of the Lyapunov function belonging to a given polytopic region of state. A numerical example is used to demonstrate the approach.

Modeling, Realization, and Simulation of Thermo-Fluid Coupled Systems Using Singularly Perturbed Sliding Manifolds

2000 ◽  
Author(s):  
Brandon W. Gordon ◽  
Harry Asada
Keyword(s):  
State Space ◽  
Time Scale ◽  
Differential Algebraic Equations ◽  
Coupled Systems ◽  
Control Methods ◽  
Algebraic Equations ◽  
Singular Perturbation Method ◽  
New Approach ◽  
Sliding Control ◽  
Fluid Systems

Abstract A new approach based on sliding control is presented for modeling and simulation of thermo-fluid systems described by differential-algebraic equations (DAEs). The dynamics of thermo-fluid systems are often complicated by momentum interactions that occur on a time scale that is orders of magnitude faster than the time scale of interest. To address this problem the momentum equation is often modeled using algebraic steady state approximations. This will, in general, result in a model described by nonlinear DAEs for which few control methods are currently applicable. In this paper, the modeling problem is addressed using an approach that systematically constructs an explicit state space approximation of the DAEs. The state space model can in turn be used with existing control methods. This procedure, known as realization, is achieved by solving an associated nonlinear control problem by combining boundary layer sliding control with the singular perturbation method. The necessary criteria for key properties such as convergence are established. Further, the new approach is illustrated using a vapor compression cycle example. This demonstrates significant advantages over directly modeling momentum interactions.

Modeling, Realization, and Simulation of Thermo-Fluid Systems Using Singularly Perturbed Sliding Manifolds

2000 ◽  
Vol 122 (4) ◽  
pp. 699-707 ◽  
Author(s):  
Brandon W. Gordon ◽  
Harry Asada
Keyword(s):  
State Space ◽  
Time Scale ◽  
State Space Model ◽  
Differential Algebraic Equations ◽  
Control Methods ◽  
Algebraic Equations ◽  
Singular Perturbation Method ◽  
New Approach ◽  
Sliding Control ◽  
Fluid Systems

A new approach based on sliding control is presented for modeling and simulation of thermo-fluid systems described by differential-algebraic equations (DAEs). The dynamics of thermo-fluid systems are often complicated by momentum interactions that occur on a time scale that is orders of magnitude faster than the time scale of interest. To address this problem the momentum equation is often modeled using algebraic steady state approximations. This will, in general, result in a model described by nonlinear DAEs for which few control methods are currently applicable. In this paper, the modeling problem is addressed using an approach that systematically constructs an explicit state space approximation of the DAEs. The state space model can in turn be used with existing control methods. This procedure, known as realization, is achieved by solving an associated nonlinear control problem by combining boundary layer sliding control with the singular perturbation method. The necessary criteria for key properties such as convergence, stability, and controllability are established. Further, the new approach is illustrated using a vapor compression cycle example. This demonstrates significant advantages over directly modeling momentum interactions. [S0022-0434(00)00904-7]

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

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