602,693 research outputs found
Model reduction and simulation of complex dynamic systems
A novel method for reducing the order of discrete time systems is developed. This model reduction technique based on Continued Fraction approach allows design parameters to be preserved. A reduced order model obtained using this technique is compared with those by other techniques to show its superiority. Furthermore, form a practical point of view, it is shown that this method can be used to design lower order digital controllers for higher order plants. Development of various model reduction techniques for continuous and discrete time systems are discussed in details and computer programs are implemented. A modified algorithm that reduces the computational complexities for model reduction of both continuous and discrete time systems is also developed. This technique is attractive because of its computational simplicity and ability to preserve system characteristics
Model Reduction for Aperiodically Sampled Data Systems
Two approaches to moment matching based model reduction of aperiodically
sampled data systems are given. The term "aperiodic sampling" is used in the
paper to indicate that the time between two consecutive sampling instants can
take its value from a pre-specified finite set of allowed sampling intervals.
Such systems can be represented by discrete-time linear switched (LS) state
space (SS) models. One of the approaches investigated in the paper is to apply
model reduction by moment matching on the linear time-invariant (LTI) plant
model, then compare the responses of the LS SS models acquired from the
original and reduced order LTI plants. The second approach is to apply a moment
matching based model reduction method on the LS SS model acquired from the
original LTI plant, and then compare the responses of the original and reduced
LS SS models. It is proven that for both methods, as long as the original LTI
plant is stable, the resulting reduced order LS SS model of the sampled data
system is quadratically stable. The results from two approaches are compared
with numerical examples
Model Reduction of Linear PDE Systems: A Continuous Time Eigensystem Realization Algorithm
The Eigensystem Realization Algorithm (ERA) is a well known system identification and model reduction algorithm for discrete time systems. Recently, Ma, Ahuja, and Rowley (Theoret. Comput. Fluid Dyn. 25(1) : 233-247, 2011) showed that ERA is theoretically equivalent to the balanced POD algorithm for model reduction of discrete time systems. We propose an ERA for model reduction of continuous time linear partial differential equation systems. The algorithm differs from other existing approaches as it is based on a direct approximation of the Hankel integral operator of the system. We show that the algorithm produces accurate balanced reduced order models for an example PDE system
Balanced truncation for linear switched systems
In this paper, we present a theoretical analysis of the model reduction
algorithm for linear switched systems. This algorithm is a reminiscence of the
balanced truncation method for linear parameter varying systems. Specifically
in this paper, we provide a bound on the approximation error in L2 norm for
continuous-time and l2 norm for discrete-time linear switched systems. We
provide a system theoretic interpretation of grammians and their singular
values. Furthermore, we show that the performance of bal- anced truncation
depends only on the input-output map and not on the choice of the state-space
representation. For a class of stable discrete-time linear switched systems (so
called strongly stable systems), we define nice controllability and nice
observability grammians, which are genuinely related to reachability and
controllability of switched systems. In addition, we show that quadratic
stability and LMI estimates of the L2 and l2 gains depend only on the
input-output map.Comment: We have corrected a number of typos and inconsistencies. In addition,
we added new results in Theorem
Effectiveness of Variable Message Signs Using Empirical Loop Detector Data
The effectiveness of Variable Messages Signs (VMS) on route guidance is assessed by a discrete probit choice model that estimates the proportion of vehicles that diverts to an alternative routes given the characteristics of different messages. A before–and–after study is also conducted to quantitatively evaluate the network wide reduction of travel time and total delay of VMS systems. We find that VMS has no obvious effect on reduction of travel time, but can reduce the total delay.Route Choice, Diversion Behavior, Cost Benefit Analysis
Structure Preserving Model Reduction of Parametric Hamiltonian Systems
While reduced-order models (ROMs) have been popular for efficiently solving
large systems of differential equations, the stability of reduced models over
long-time integration is of present challenges. We present a greedy approach
for ROM generation of parametric Hamiltonian systems that captures the
symplectic structure of Hamiltonian systems to ensure stability of the reduced
model. Through the greedy selection of basis vectors, two new vectors are added
at each iteration to the linear vector space to increase the accuracy of the
reduced basis. We use the error in the Hamiltonian due to model reduction as an
error indicator to search the parameter space and identify the next best basis
vectors. Under natural assumptions on the set of all solutions of the
Hamiltonian system under variation of the parameters, we show that the greedy
algorithm converges with exponential rate. Moreover, we demonstrate that
combining the greedy basis with the discrete empirical interpolation method
also preserves the symplectic structure. This enables the reduction of the
computational cost for nonlinear Hamiltonian systems. The efficiency, accuracy,
and stability of this model reduction technique is illustrated through
simulations of the parametric wave equation and the parametric Schrodinger
equation
Design of PID Controller for Higher Order Discrete Systems Based on Order Reduction Employing ABC Algorithm
This paper proposes a new computational simple scheme for Model Order Reduction to design a discrete PID controller for higher order linear time invariant discrete systems. Artificial Bee Colony (ABC) optimization algorithm is employed for both order reduction and controller design. First a successful reduced order model is obtained for original higher order discrete system using ABC optimization algorithm which is based on the minimization of integral square error between the original and reduced order models pertaining to step input. Then a PID controller is designed for reduced order model, based on the minimization of integral square error between the desired response and actual response, pertaining to a unit step input using ABC algorithm. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specifications. The validity of the proposed method is illustrated through a numerical example. Keywords: Discrete system, Model order reduction, PID controller, Integral square error, Artificial Bee Colony algorithm
What can systems and control theory do for agricultural science?
Abstract: While many professionals with a background in agricultural and bio-resource sciences work with models, only few have been exposed to systems and control theory. The purpose of this paper is to elucidate a selection of methods from systems theory that can be beneficial to quantitative agricultural science. The state space representation of a dynamical system is the corner stone in the mainstream of systems theory. It is not well known in agro-modelling that linearization followed by evaluation of eigenvalues and eigenvectors of the system matrix is useful to obtain dominant time constants and dominant directions in state space, and offers opportunities for science-based model reduction. The continuous state space description is also useful in deriving truly equivalent discrete time models, and clearly shows that parameters obtained with discrete models must be interpreted with care when transferred to another model code environment. Sensitivity analysis of dynamic models reveals that sensitivity is time and input dependent. Identifiability and sensitivity are essential notions in the design of informative experiments, and the idea of persistent excitation, leading to dynamic experiments rather than the usual static experiments can be very beneficial. A special branch of systems theory is control theory. Obviously, control plays an important part in agricultural and bio-systems engineering, but it is argued that also agronomists can profit from notions from the world of control, even if practical control options are restricted to alleviating growth limiting conditions, rather than true crop control. The most important is the idea of reducing uncertainty via feed-back. On the other hand, the systems and control community is challenged to do more to address the problems of real life, such as spatial variability, measurement delays, lacking data, environmental stochasticity, parameter variability, unavoidable model uncertainty, discrete phenomena, variable system structures, the interaction of technical ad living systems, and, indeed, the study of the functioning of life itself
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