Abstract
This thesis addresses two topics that play a significant role in modern control theory: design of experiments (DoE) and parameter estimation methods for continuoustime (CT) models. In this context, DoE focuses on the impact of experimental design regarding the accuracy of a subsequent estimation of unknown model parameters and applying the theory to realworld applications and its detailed analysis. We introduce the Fisherinformation matrix (FIM), consisting of the parameter sensitivities and the resulting highly nonlinear optimization task. By a firstorder system, we demonstrate the computation of the information content, its visualization, and an illustration of the effects of higher Fisher information on parameter estimation quality. After that, the topic optimal input design (OID), a subarea of DoE, will be thoroughly explored on the practicerelevant linear and nonlinear model of a 1Dposition servo system. Comparison with standard excitation signals shows that the OID signals generally provide higher information content and lead to more accurate parameter estimates using leastsquares methods. Besides, this approach allows taking into account constraints on input, output, and state variables.
In the second major topic of this thesis, we treat parameter estimation methods for CT systems, which provide several advantages to identify discretetime (DT) systems, e.g., allows physical insight into model parameters. We focus on modulating function method (MFM) or Poisson moment functionals (PMF) and leastsquares to estimate unknown model parameters. In the case of noisy measurement data, the problem of biased parameter estimation arises immediately. That is why we discuss the computation and compensation of the socalled estimation bias in detail. Besides the detailed elaboration of a bias compensating estimation method, this work’s main contribution is, based on PMF and least squares for linear systems, the extension to at least slightly nonlinear systems. The derived biascompensated ordinary leastsquares (BCOLS) approach for obtaining asymptotically unbiased parameter estimates is tested on a nonlinear 1Dservo model in the simulation and measurement. A comparison with other methods for bias compensation or avoidance, e.g., total leastsquares (TLS), is performed. Additionally, the BCOLS method is applied to the more general MFM. Furthermore, a practical issue of parameter estimation is discussed, which occurs when the system behavior leaves and reenters the space covered by the identification equation. Using the 1Dservo system, one can show that disabling and reenabling the PMF filters with appropriate initialization can solve this problem.
In the second major topic of this thesis, we treat parameter estimation methods for CT systems, which provide several advantages to identify discretetime (DT) systems, e.g., allows physical insight into model parameters. We focus on modulating function method (MFM) or Poisson moment functionals (PMF) and leastsquares to estimate unknown model parameters. In the case of noisy measurement data, the problem of biased parameter estimation arises immediately. That is why we discuss the computation and compensation of the socalled estimation bias in detail. Besides the detailed elaboration of a bias compensating estimation method, this work’s main contribution is, based on PMF and least squares for linear systems, the extension to at least slightly nonlinear systems. The derived biascompensated ordinary leastsquares (BCOLS) approach for obtaining asymptotically unbiased parameter estimates is tested on a nonlinear 1Dservo model in the simulation and measurement. A comparison with other methods for bias compensation or avoidance, e.g., total leastsquares (TLS), is performed. Additionally, the BCOLS method is applied to the more general MFM. Furthermore, a practical issue of parameter estimation is discussed, which occurs when the system behavior leaves and reenters the space covered by the identification equation. Using the 1Dservo system, one can show that disabling and reenabling the PMF filters with appropriate initialization can solve this problem.
Original language  English 

Qualification  Dr. techn. 
Awarding Institution 

Supervisors/Advisors 

Award date  1 Jun 2022 
Place of Publication  Ilmenau 
DOIs  
Publication status  Published  5 Jul 2022 
Keywords
 Zeitkontinuierliches Signal
 Versuchsplanung
 Methode der kleinsten Quadrate
 Parameteridentifikation