P. van der Kloet

Two algorithms for parameter estimation in groundwater flow problems

Abstract Groundwater movement is often described by equations based on Darcys law and the equation of continuity. These equations contain a number of lumped parameters, representing the properties of the soil. These parameters are not known and have to be estimated from field measurements (e.g., pumping tests) or from calculations. In this paper the situation is considered that groundwater movement can be described by one lumped parameter. Two algorithms are developed to estimate that parameter. Both are based upon an optimal-state estimation with a standard Kalman filter algorithm. The two algorithms are applied to an example with generated data. The estimation methods may be extended to cases with more than one parameter.

Modal factorization of time-varying models for nonlinear circuits by the Riccati transform

In this paper, general linear time-varying systems are addressed. They are considered as small-signal models of nonlinear circuit solutions. The transition matrix is constructed by repeated Riccati transforms. It is shown that each transform factors out a single mode. Key concepts of time-invariant theory are generalized to the time-varying context. They provide a unified mathematical framework, suitable for assessing the local behavior of nonlinear dynamic circuits.

Diagonalization algorithms for linear time-varying dynamic systems

On the basis of a mode-vector representation, we show that its time-varying amplitudes and frequencies can be obtained by diagonalizing the system matrix. Next, we reformulate an explicit diagonalizing algorithm that was earlier proposed by Wu. Then, the missing convergence proof is given. Moreover, we present a new and implicit iteration scheme that is closely related to that given by Wu. In both algorithms, the time-varying system matrix is gradually diagonalized by successive algebraic similarity transformations. It is proved that the convergence conditions are essentially the same. Although the class of systems for which the algorithms are applicable is still not fully known, the results of this paper may be of theoretical and practical interest.

A complementary view on time-varying systems

This contribution is complementary to a previous approach by the authors in that it takes a time-varying mode-vector solution as an a priori assumption. The associated dynamic eigenvalue problem is solved by triangularizing the system equations, again accomplished by successive Riccati transforms. It is explicitly shown that equal eigenvalues do not give rise to the Jordan form. Although the mode-vectors are not uniquely determined, it is demonstrated by example that different representations yield identical transition matrices, as it should.

Dynamic behavior of dynamic translinear circuits: the linear time-varying approximation

Dynamic translinear circuits explore the exponential relation of transistors as a primitive for the synthesis of electronic circuits. In this letter, the linear time-varying approximation is applied to describe the dynamic behavior of a second-order dynamic-translinear oscillator. The Floquet exponents are calculated by the dynamic eigenvalues introduced earlier.

The linear time-varying approach applied to the design of a negative-feedback class-B output amplifier

The increasing number of battery-operated devices asks for more low-power electronic circuits. A major cause of current consumption are the bias currents. Thus designing circuits having no bias currents may lead to considerable reductions in the power consumption. This inherently implies that we have to deal with the nonlinear behavior of devices. Here the design of a low-voltage low-power negative-feedback amplifiers with a class-B output stage is described. The key issue in the design is the description of the dynamics of the amplifier by the linear time-varying approach. This uses a time-varying small-signal model of nonlinear circuits and enables a generalization of the traditional pole-zero concept. The designed amplifier is capable of driving 1 mA through a piezoelectric load (14 nF). The stand-by current varies from 40 /spl mu/A to 100 /spl mu/A.

The Cauchy-Floquet factorization by successive Riccati transformations

Scalar linear time-varying systems are addressed. In particular, a new factorization method for the associated scalar polynomial system differential operator is presented. It differs from the classical results due to Cauchy and Floquet, in that it is based upon successive Riccati transformations of the Frobenius companion system matrix. As a consequence, the factorization is obtained in terms of the earlier introduced dynamic eigenvalues.

The linear time-varying approach applied to a first-order dynamic translinear filter

Dynamic translinear (DTL) circuits use the exponential input-output relation of the transistor as a primitive for the synthesis of electronic circuits. As a consequence the analysis of the dynamic behaviour of this type of circuit in the presence of parasitics results in analyzing dynamic nonlinear circuits. There are three different approaches that can be applied: the linear time-invariant (LTI) approach, the quasi-static (QS) approach and the linear time-varying (LTV) approach. The LTI approach is limited to circuits in which the bias points are fixed. The QS approach can be applied to circuits with time-varying bias points, but these time-variations must be relatively slow. The LTV approach has none of these restrictions and opens the way to a general and structured design method for dynamic nonlinear circuits. We apply the linear time-varying approach to a first-order dynamic translinear filter. Its dynamic eigenvalue is calculated and stability is determined by means of the corresponding Floquet exponent. We also apply the quasi-static approach to the same DTL filter. Comparisons between the linear time-varying approach and the quasi-static approach show the limitations of the quasi-static approach and the usefulness of the linear time-varying approach in the design of DTL circuits.

The Reduction of the Effects on Flora Caused by Drainage Water Quality by a Proposed Reservoir as an Element of a Feedbacksystem

In the southern part of the Netherlands the river Beerse flows through a nature reserve area. The discharge regime of the Beerse is such that in the reserve area inundations occur regularly. As due to upstream use of fertilizers the water quality of the Beerse is poor, the inundations harm the unique vegetation in the reserve area.