scholarly journals A new family of real-time redictor-corrector integration algorithms

SIMULATION ◽  
1991 ◽  
Vol 57 (3) ◽  
pp. 177-186 ◽  
Author(s):  
R.M. Howe
Keyword(s):  
Real Time ◽  
New Family ◽  
Integration Algorithms

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

SIMULATIONS BY TIME-BOUNDED COUNTER MACHINES

2011 ◽  
Vol 22 (02) ◽  
pp. 395-409 ◽  
Author(s):  
HOLGER PETERSEN
Keyword(s):  
Lower Bound ◽  
Real Time ◽  
Polynomial Time ◽  
Time Complexity ◽  
Linear Time ◽  
Fixed Number ◽  
Exponential Time ◽  
New Family ◽  
Counter Machines ◽  
Time Bounds

We investigate the efficiency of simulations of storages by several counters. A simulation of a pushdown store is described which is optimal in the sense that reducing the number of counters of a simulator leads to an increase in time complexity. The lower bound also establishes a tight counter hierarchy in exponential time. Then we turn to simulations of a set of counters by a different number of counters. We improve and generalize a known simulation in polynomial time. Greibach has shown that adding s + 1 counters increases the power of machines working in time ns. Using a new family of languages we show here a tight hierarchy result for machines with the same polynomial time-bound. We also prove hierarchies for machines with a fixed number of counters and with growing polynomial time-bounds. For machines with one counter and an additional "store zero" instruction we establish the equivalence of real-time and linear time. If at least two counters are available, the classes of languages accepted in real-time and linear time can be separated.

Comparison of explicit integration algorithms for real-time hybrid simulation

2015 ◽  
Vol 14 (1) ◽  
pp. 89-114 ◽  
Author(s):  
Fei Zhu ◽  
Jin-Ting Wang ◽  
Feng Jin ◽  
Yao Gui
Keyword(s):  
Real Time ◽  
Hybrid Simulation ◽  
Explicit Integration ◽  
Integration Algorithms

A New Family of Higher-Order Time Integration Algorithms for the Analysis of Structural Dynamics

2017 ◽  
Vol 84 (7) ◽  
Author(s):  
Wooram Kim ◽  
J. N. Reddy
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Higher Order ◽  
Weighted Residual Method ◽  
New Family ◽  
Equal Degree ◽  
Fundamental Limitations ◽  
Mixed Formulations ◽  
Dependent Variables ◽  
Integration Algorithms

For the development of a new family of implicit higher-order time integration algorithms, mixed formulations that include three time-dependent variables (i.e., the displacement, velocity, and acceleration vectors) are developed. Equal degree Lagrange type interpolation functions in time are used to approximate the dependent variables in the mixed formulations, and the time finite element method and the modified weighted-residual method are applied to the velocity–displacement and velocity–acceleration relations of the mixed formulations. Weight parameters are introduced and optimized to achieve preferable attributes of the time integration algorithms. Specific problems of structural dynamics are used in the numerical examples to discuss some fundamental limitations of the well-known second-order accurate algorithms as well as to demonstrate advantages of using the developed higher-order algorithms.

A Comparison of Runge Kutta and Novel L-Stable Methods for Real-Time Integration Methods for Dynamic Substructuring

2006 ◽  
Author(s):  
Alicia Gonzalez-Buelga ◽  
David Wagg ◽  
Simon Neild ◽  
Oreste S. Bursi
Keyword(s):  
Real Time ◽  
Experimental Testing ◽  
Time Integration ◽  
Delay Compensation ◽  
Real Time Control ◽  
Time Dynamic ◽  
Time Control ◽  
Dynamic Substructuring ◽  
Integration Algorithms ◽  
Runge Kutta

In this paper we compare the performance of Runge-Kutta and novel L-stable real-time (LSRT) integration algorithms for real-time dynamic substructuring testing. Substructuring is a hybrid numerical-experimental testing method which can be used to test critical components in a system experimentally while the remainder of the system is numerically modelled. The physical substructure and the numerical model must interact in real time in order to replicate the behavior of the whole (or emulated) system. The systems chosen for our study are mass-spring-dampers, which have well known dynamics and therefore we can benchmark the performance of the hybrid testing techniques and in particular the numerical integration part of the algorithm. The coupling between the numerical part and experimental part is provided by an electrically driven actuator and a load cell. The real-time control algorithm provides bi-directional coupling and delay compensation which couples together the two parts of the overall system. In this paper we consider the behavior of novel L-stable real-time (LSRT) integration algorithms, which are based on Rosenbrock's method. The new algorithms have considerable advantages over 4th order Runge-Kutta in that they are unconditionally stable, real-time compatible and less computationally intensive. They also offer the possibility of damping out unwanted high frequencies and integrating stiff problems. The paper presents comparisons between 4th order Runge-Kutta and the LSRT integration algorithms using three experimental configurations which demonstrate these properties.

Sign in / Sign up

Export Citation Format

Share Document