scholarly journals Time-Varying Uncertainty in Shock and Vibration Applications Using the Impulse Response

2012 ◽  
Vol 19 (3) ◽  
pp. 433-446 ◽  
Author(s):  
J.B. Weathers ◽  
Rogelio Luck
Keyword(s):  
Linear Time ◽  
Nonlinear Differential Equations ◽  
Uncertainty Propagation ◽  
External Input ◽  
Simulation Software ◽  
Model Parameters ◽  
Time Varying ◽  
Principle Of Superposition ◽  
Dynamic Simulations ◽  
Uncertainty Model

Design of mechanical systems often necessitates the use of dynamic simulations to calculate the displacements (and their derivatives) of the bodies in a system as a function of time in response to dynamic inputs. These types of simulations are especially prevalent in the shock and vibration community where simulations associated with models having complex inputs are routine. If the forcing functions as well as the parameters used in these simulations are subject to uncertainties, then these uncertainties will propagate through the models resulting in uncertainties in the outputs of interest. The uncertainty analysis procedure for these kinds of time-varying problems can be challenging, and in many instances, explicit data reduction equations (DRE's), i.e., analytical formulas, are not available because the outputs of interest are obtained from complex simulation software, e.g. FEA programs. Moreover, uncertainty propagation in systems modeled using nonlinear differential equations can prove to be difficult to analyze. However, if (1) the uncertainties propagate through the models in a linear manner, obeying the principle of superposition, then the complexity of the problem can be significantly simplified. If in addition, (2) the uncertainty in the model parameters do not change during the simulation and the manner in which the outputs of interest respond to small perturbations in the external input forces is not dependent on when the perturbations are applied, then the number of calculations required can be greatly reduced. Conditions (1) and (2) characterize a Linear Time Invariant (LTI) uncertainty model. This paper seeks to explain one possible approach to obtain the uncertainty results based on these assumptions.

Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

2021 ◽  
Vol 22 (8) ◽  
pp. 404-410
Author(s):  
K. B. Dang ◽  
A. A. Pyrkin ◽  
A. A. Bobtsov ◽  
A. A. Vedyakov ◽  
S. I. Nizovtsev
Keyword(s):  
Linear Time ◽  
State Observer ◽  
Observer Design ◽  
Model Parameters ◽  
Time Varying ◽  
State Variables ◽  
Unknown Constant ◽  
Established Method ◽  
Time Varying Parameters ◽  
True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

scholarly journals Model-Matching-Based Control of the Beverton-Holt Equation in Ecology

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
M. De La Sen ◽  
S. Alonso-Quesada
Keyword(s):  
Carrying Capacity ◽  
Linear Time ◽  
External Input ◽  
Reference Sequence ◽  
Time Varying ◽  
Model Matching ◽  
Discrete Dynamic System ◽  
Population Evolution ◽  
Adaptive Law ◽  
Aquaculture Management

This paper discusses the generation of a carrying capacity of the environment so that the famous Beverton-Holt equation of Ecology has a prescribed solution. The way used to achieve the tracking objective is the design of a carrying capacity through a feedback law so that the prescribed reference sequence, which defines the suitable behavior, is achieved. The advantage that the inverse of the Beverton-Holt equation is a linear time-varying discrete dynamic system whose external input is the inverse of the environment carrying capacity is taken in mind. In the case when the intrinsic growth rate is not perfectly known, an adaptive law implying parametrical estimation is incorporated to the scheme so that the tracking property of the reference sequence becomes an asymptotic objective in the absence of additive disturbances. The main advantage of the proposal is that the population evolution might behave as a prescribed one either for all time or asymptotically, which defines the desired population evolution. The technique might be of interest in some industrial exploitation problems like, for instance, in aquaculture management.

Adaptive control of time-varying non-linear plants by speed-gradient algorithms

2019 ◽  
pp. 37-44 ◽  
Author(s):  
O. P. Tomchina ◽  
D. N. Polyakhov ◽  
O. I. Tokareva ◽  
A. L. Fradkov
Keyword(s):  
Adaptive Control ◽  
Adaptive Systems ◽  
Reference Model ◽  
Maximum Deviation ◽  
Model Parameters ◽  
Time Varying ◽  
System Solution ◽  
Non Linear ◽  
Initial Uncertainty ◽  
Speed Gradient

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.

scholarly journals Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Interest Rate ◽  
Algebraic Approach ◽  
Dynamical Symmetry ◽  
Bond Pricing ◽  
Model Parameters ◽  
Time Varying ◽  
Single Factor ◽  
Bond Price ◽  
Interest Rate Models ◽  
Root Model

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

scholarly journals Numerical Evaluation of a HVAC System Based on a High-Performance Heat Transfer Fluid

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3298
Author(s):  
Gianpiero Colangelo ◽  
Brenda Raho ◽  
Marco Milanese ◽  
Arturo de Risi
Keyword(s):  
Heat Transfer ◽  
High Performance ◽  
Cooling System ◽  
Electrical Energy ◽  
Simulation Software ◽  
Heat Transfer Fluid ◽  
Hvac System ◽  
Dynamic Simulations ◽  
Heating And Cooling ◽  
The University

Nanofluids have great potential to improve the heat transfer properties of liquids, as demonstrated by recent studies. This paper presents a novel idea of utilizing nanofluid. It analyzes the performance of a HVAC (Heating Ventilation Air Conditioning) system using a high-performance heat transfer fluid (water-glycol nanofluid with nanoparticles of Al2O3), in the university campus of Lecce, Italy. The work describes the dynamic model of the building and its heating and cooling system, realized through the simulation software TRNSYS 17. The use of heat transfer fluid inseminated by nanoparticles in a real HVAC system is an innovative application that is difficult to find in the scientific literature so far. This work focuses on comparing the efficiency of the system working with a traditional water-glycol mixture with the same system that uses Al2O3-nanofluid. The results obtained by means of the dynamic simulations have confirmed what theoretically assumed, indicating the working conditions of the HVAC system that lead to lower operating costs and higher COP and EER, guaranteeing the optimal conditions of thermo-hygrometric comfort inside the building. Finally, the results showed that the use of a nanofluid based on water-glycol mixture and alumina increases the efficiency about 10% and at the same time reduces the electrical energy consumption of the HVAC system.

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

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