On Validating Closed-Loop Behaviour from Noisy Frequency-Response Measurements

It is shown how noisy closed-loop frequency-response measurements can be used to obtain pointwise in frequency bounds on the possible difference between the actual closed-loop system and the closed-loop comprising a nominal model of the plant and the stabilising controller. To this end, Vinnicombe's gap metric framework for robustness analysis plays a central role. Indeed, an optimisation problem and corresponding algorithm are proposed for estimating the chordal distance between the frequency responses of the nominal plant model and a plant that is consistent with the closed-loop data and a priori information, when projected onto the Riemann sphere

Optimal Multisine Probing Signal Design for Power System Electromechanical Mode Estimation

This paper proposes a methodology for the design of a probing signal used for power system electromechanical mode estimation. Firstly, it is shown that probing mode estimation accuracy depends solely on the probing signal’s power spectrum and not on a specific time-domain realization. A relationship between the probing power spectrum and the accuracy of the mode estimation is used to determine a multisine probing signal by solving an optimization problem. The objective function is defined as a weighting sum of the probing signal variance and the level of the system disturbance caused by the probing. A desired level of the mode estimation accuracy is set as a constraint. The proposed methodology is demonstrated through simulations using the KTH Nordic 32 power system model

Data Informativity for the Identication of particular Parallel Hammerstein Systems

To obtain a consistent estimate when performing an identication with Prediction Error, it is important that the excitation yields informative data with respect to the chosen model structure. While the characterization of this property seems to be a mature research area in the linear case, the same cannot be said for nonlinear systems. In this work, we study the data informativity for a particular type of Hammerstein systems for two commonly-used excitations: white Gaussian noise and multisine. The real life example of the MEMS gyroscope is considered

Data Informativity for the Open-Loop Identification of MIMO Systems in the Prediction Error Framework

In Prediction Error identification, to obtain a consistent estimate of the true system, it is crucial that the input excitation yields informative data with respect to the chosen model structure. We consider in this paper the data informativity property for the identification of a Multiple-Input Multiple-Output system in open loop and we derive conditions to check whether a given input vector will yield informative data with respect to the chosen model structure. We do that for the classical model structures used in prediction-error identification and for the classical types of input vectors, i.e., input vectors whose elements are either multisines or filtered white noises

Closed-loop Identification of MIMO Systems in the Prediction Error Framework: Data Informativity Analysis

In the Prediction Error Identification framework, it is essential that the experiment yields informative data with respect to the chosen model structure to get a consistent estimate. In this work, we focus on the data informativity property for the identification of Multi-Inputs Multi-Outputs system in closed-loop and we derive conditions to verify if a given external excitation combined with the feedback introduced by the controller yields informative data with respect to the model structure. This study covers the case of the classical model structures used in prediction-error identification and the classical types of external excitation vectors, i.e., vectors whose elements are either multisine or filtered white noises

Data Informativity for the Identication of MISO FIR Systems with Filtered White Noise Excitation

For Prediction Error Identication, there are two main ingredients to get a consistent estimate: one of them is the data informativity with respect to (w.r.t.) the considered model structure. One common criterion used for the informativity is the positive deniteness of the input density spectral power (DSP) matrix at all frequencies. This criterion is not appropriate for multisine excitation but can be used for ltered white noise excitation for many identication problems. However, this criterion is not necessary and its application for some identication problems might not be possible. In this paper, we propose a necessary and sucient condition for the data informativity in the case of multiple-inputs single-output (MISO) nite impulse response (FIR) model structure in open-loop

Informativity: how to get just sufficiently rich for the Identification of MISO FIR Systems with Multisine Excitation?

In Prediction Error Identification, the consistency of the identified parameter vector is only guaranteed if the data are informative enough i.e. if the excitation signal is sufficiently rich. For single-input single-output systems, one can verify whether a given excitation is sufficiently rich for a system based on the number of frequencies at which its power spectrum is nonzero. The extension of this criterion to multivariate systems is not straightforward. In the literature, one has proposed criteria based on the number of frequencies at which the power spectrum matrix of the excitation signal is strictly positive definite. However, this criterion is too restrictive as it does not cover the case of multisine excitations, while it is well known that such excitation signals can lead to consistent estimates. This paper proposes less restrictive conditions for the consistency of the identified parameter vector when FIR multiple-inputs single-output systems have to be identified with multisine signals in the open loop configuration

Least costly identification experiment for the identification of one module in a dynamic network

In this paper we consider the design of the least costly experiment for the identification of one module in a given network of locally controlled systems. The identification experiment will be designed in such a way that we obtain a sufficiently accurate model of the to-be-identified module with the smallest identification cost i.e. with the least perturbation of the network

Robust optimal identification experiment design for multisine excitation

In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal. 1 Introduction We consider in this paper the problem of optimally designing the spectrum Φ u of the excitation signal u of an open-loop identification experiment. By optimal spectrum , we here mean the spectrum yielding the smallest experiment cost while guaranteeing that the accuracy of the identified parameter vector of the plant transfer function is larger than a given threshold. We thus consider the least costly experiment design framework [5], but the approach can easily be adapted to other (dual) frameworks [10,17,13]. The experiment cost J can be defined as a linear combination of the power of the exci-tation signal u and of the power of the part of the output signal induced by u. The experiment cost will therefore be a function of the spectrum Φ u , but also of the unknown true parameter vector θ 0 (we therefore denote the cost as J (θ 0 , Φ u)). Likewise, the accuracy constraint will also depend on θ 0 and on Φ u since the classical accuracy constraints are of the type P −1 (θ 0 , Φ u) ≥ R adm where P (θ 0 , Φ u) is the covariance matrix of the to-be-identified parameter vector (which depends on θ 0 and Φ u) and R adm a matrix reflecting the desired accuracy. The dependency of the optimal spectrum Φ u,opt on the unknown true parameter vector θ 0 is the so-called chicken-and-egg issue encountered in optimal experiment design. This issue is generally circumvented by replacing θ 0 b