The Venture Capital Solution to the Problem of Close Corporation Shareholder Fiduciary Duties

Abstract

In this report we study estimation of time-delays in linear dynamical systems with additive noise. Estimating time-delays is a common engineering problem, e.g. in automatic control, system identification and signal processing. The purpose with this work is to test and evaluate a certain class of methods for time-delay estimation, especially with automatic control applications in mind. The principle of the methods in the class is to estimate several discrete-time models of a certain model structure with different explicit time-delays. The estimated time-delay is the time-delay whose model has the lowest mean square difference between the true and estimated output signal. The methods are evaluated experimentally with the aid of simulations and plots of RMS error and confidence intervals for different cases.The results are: The output error (OE) model structure has the lowest RMS error but is very slow. Low model orders give the best result. The ARX model structure has a higher RMS error but is very fast. High model orders give the best result. An ARX model structure with prefiltered input and output signals was also tested. It has an RMS error that is nearly as good as for the OE model structure and is fast but not as fast as the unfiltered ARX. The best model orders are high for the denominator polynomial and low for the numerator polynomial