scholarly journals Minimax state estimation for linear discrete-time differential-algebraic equations

Automatica ◽  
2010 ◽  
Vol 46 (11) ◽  
pp. 1785-1789 ◽  
Author(s):  
Sergiy M. Zhuk
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Time Differential

Discrete-Time Inverse Dynamics Control of Flexible Joint Robots

1992 ◽  
Vol 114 (2) ◽  
pp. 229-233 ◽  
Author(s):  
K. P. Jankowski ◽  
H. Van Brussel
Keyword(s):  
Discrete Time ◽  
Control Algorithm ◽  
Inverse Dynamics ◽  
Differential Algebraic Equations ◽  
Control Methods ◽  
Algebraic Equations ◽  
Computationally Efficient ◽  
Electromechanical Actuators ◽  
Flexible Joint Robots ◽  
Inverse Dynamics Control

This paper focuses on the problem of the application of inverse dynamics control methods to robots with flexible joints and electromechanical actuators. Due to drawbacks of the continuous-time inverse dynamics, discussed in the paper, a new control strategy in discrete-time is presented. The proposed control algorithm is based on numerical methods conceived for the solution of index-three systems of differential-algebraic equations. The method is computationally efficient and admits low sampling frequencies. The results of numerical experiments confirm the advantages of the designed control algorithm.

scholarly journals On parameter and state estimation for linear differential–algebraic equations

Automatica ◽  
2007 ◽  
Vol 43 (3) ◽  
pp. 416-425 ◽  
Author(s):  
Markus Gerdin ◽  
Thomas B. Schön ◽  
Torkel Glad ◽  
Fredrik Gustafsson ◽  
Lennart Ljung
Keyword(s):  
State Estimation ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Differential

Multi-Splitting Waveform Relaxation Methods for Solving the Initial Value Problem of Linear Integral-Differential-Algebraic Equations

2011 ◽  
Vol 403-408 ◽  
pp. 1763-1766
Author(s):  
Xiao Lin Lin ◽  
Yuan Sang ◽  
Hong Wei ◽  
Li Ming Liu ◽  
Yu Mei Wang ◽  
...  
Keyword(s):  
Spectral Radius ◽  
Discrete Time ◽  
Initial Value Problem ◽  
Differential Algebraic Equations ◽  
Waveform Relaxation ◽  
Algebraic Equations ◽  
Initial Value ◽  
Relaxation Methods ◽  
Discrete Time Case ◽  
Linear Integral

We present the multi-splitting waveform relaxation (MSWR) methods for solving the initial value problem of linear integral-differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, a convergent condition is proposed for the MSWR method. Finally we discussed the convergent condition of discrete-time case of MSWR.

scholarly journals Co-Simulation of Algebraically Coupled Dynamic Subsystems

2001 ◽  
Author(s):  
Bei Gu ◽  
H. Harry Asada
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Discrete Time ◽  
Sliding Mode ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Step Size ◽  
Sliding Manifold ◽  
Sliding Manifolds ◽  
Algebraic Constraints

Abstract This paper analyzes the problem of Co-Simulation. The term Co-Simulation is used to describe a large dynamic system that is simulated by running a group of independently coded subsystem simulators. Very commonly, the Co-Simulation of subsystems faces incompatible boundary conditions, i.e., causal conflicts. These causal conflicts cannot be directly resolved, due to the nonlinearity and/or difficulties in modification of coded subsystem simulators. Causal conflicts result in algebraic constraints. Boundary Condition Coordinators (BCCs) are designed to calculate boundary conditions based on subsystem models and their algebraic constraints. The Co-Simulation, which is modeled as Differential Algebraic Equations, then relies on BCC to provide compatible boundary conditions for subsystem simulators. The high index constraint is reduced to index one by defining a sliding manifold. Different ways of enforcing the sliding manifold are discussed: A new Discrete-Time Sliding Mode (DTSM) controller is devised to serve as a BCC, enforcing sliding manifolds and providing boundary conditions. The multi-rate scheme can guarantee Co-Simulation stability at any given step size of all subsystem simulators, provided the subsystem simulators are tested stable at that step size. An example is given to demonstrate the DTSM method. Advantages and possible future improvements are discussed.

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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