The SRIVC algorithm for continuous-time system identification with arbitrary input excitation in open and closed loop

This dissertation presents a new method for the statistical performance analysis of subspace system identification algorithms. A perturbation expansion of the singular value decomposition is used to approximate the effects of process and measurement noise on the identified system poles. Eigenvalue variance results are obtained that do not depend on asymptotic statistics and are therefore applicable for short data records. These performance measures are conditional upon the specific input and the parameters of the actual system being identified. This method is demonstrated on two variations of the Numerical Subspace State-Space System Identification (N4SID) algorithm. The accuracy of these theoretical performance measures is validated using simulation. Finally, this new method is applied to the first step of three well known subspace identification algorithms to determine the effects of row and column weighting on the variance of identified poles.

System identification deals with the problem of building the mathematical models of dynamical systems according to the input and output data. The open-loop system identification (Observer/Kalman Filter SystemIdentification, OKID) for stable systems without requiring feedback control is introduced first. For identifying marginally stable or unstable system, however, feedback control is required to ensure the overall system stability. The algorithm of closed-loop system identification (CLID) with known feedback dynamics is shown next.

This paper investigates the identification of Continuous-Time models based on binary observations. Currently, no identification algorithm has been proposed in this field. The reason is twofold: first the time-domain differentiation operator of a such model structure prevents the use of existing identification methods based on binary observations, second the simple knowledge of binary observations on the output prevents the use of existing Continuous-Time identification methods. In this paper a two steps identification algorithm is derived. It is based on the combined use of a specific input signal and Support Vector Machines for the reconstruction of a high resolution output signal. This high resolution output signal is then used for the estimation of a Continuous-Time model. An extension for the identification of a MISO system is also proposed. Some simulation results are given in order to illustrate the validity of the proposed method.

A novel nonlinear modelling approach has been developed and implemented on Alstom gasifier using Wiener model. The linear element of the Wiener model was identified by a combined subspace state space method, which integrated MOESP (Multivariable Output-Error State Space) and N4SID (Numerical algorithms for subspace state space system identification) method in the estimation of system matrices. Then a single layer neural network was chosen as the nonlinearity of the model. The proposed model identification method was used to model Alstom gasifier with strong nonlinearity and multivariable couples. The results compared to a combined linear subspace identification method demonstrate that the nonlinear method proposed in this paper behave better approximation.

This paper deals with simultaneous identification of continuous systems with multiple unknown time delays from sampled input–output data. In order to estimate, simultaneously, the parameters and the time delays of the system, an output errors method using a nonlinear programming algorithm based on sensitivity functions is discussed. Nevertheless, the initial values of the adjustable parameters should be determined from physical insight or guessed by previous methods. The convergence of the proposed method has been analyzed with theorems and proofs. The simulation example indicates that the proposed algorithm can generate highly accurate parameter estimates.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

This paper presents a novel deterministic approach for the identification of linear continuous-time systems. The approach is based on the projection of measured signals onto the finite dimensional signal subspace whose basis is determined by the parameter structure of the target system model. In this paper, we describe the basic concept and implementation of the proposed identification framework, and develop the methodology to deal with multi-variable input and/or output case. In addition, the initial state estimation technique, which enables us to use the truncated I/O data for identification, is introduced. The important features of the proposed approach are (i) the ability to handle both open and closed loop systems in a unified way and (ii) the robustness against the measurement noise. These features are demonstrated through a numerical example.

The instrumental variable (IV) method is one of the most renowned methods for parameter estimation. Its bigger advantage is that it is applicable for open-loop as well as for closed-loop systems. The main difficulty in closed-loop identification is due to the correlation between the disturbances and the control signal induced by the loop. In order to overcome this problem, additional excitation signal is introduced. Non-recursive modifications of the instrumental variable method for closed-loop system identification on the base of a generalized IV method have been developed (Atanasov and Ichtev, 2009; Gilson and Van den Hof, 2001; Gilson and Van den Hof, 2003). In this paper, recursive algorithms for theses modifications are proposed and investigated. A simulation is carried out in order to illustrate the obtained results.

This paper studies a continuous-time system identification method based on system transformation using generalized orthonormal basis functions, especially the Laguerre basis. It is known that the expansion of observation signals with Laguerre basis functions is useful for analyzing linear dynamical systems. This processing however, involves the calculation with infinite integral, hence, the problem with truncation occurs at the stage of implementation. The proposed method of signal transformation using finitely-supported filter kernels avoids this problem, still preserves the exact system transformation. It turns out that the instrumental variable subspace identification method successfully works with the transformed signals and achieve consistent estimates for systems disturbed with possibly colored noise. The proposed method is applicable to recursive identification. Some numerical examples are presented to demonstrate the results.

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

System identification is a well known technique for developing mathematical models based on plant input and output data sequences. Models that describe the systems may be in various forms and one of the possibilities is a state space model formulation. The state space mathematical modelling involves vectors and matrices in a unique geometrical framework. It offers the key advantages on providing low parameter sensitivity with respect to perturbation for high order systems and also has shown its ability to present multi-input and multi-output systems with minimal state dimensions. We use a time domain subspace approach in conjunction with Laguerre filters and instrumental variables to develop a mathematical formulation of the state space model for identification of a continuous time system. The method aims at searching for accurate matrices of the state space model to ensure that the constructed model closely mimics the actual system as well as provide information for the purpose of control system design. The subspace identification algorithm provides state space models with better conditioning, improved quality and easily maintainable parametrisation. The algorithm is validated with identification of two systems: a simulated plant, and a magnetic bearing system. For both systems, the computer simulation results demonstrate that the obtained model describes the system closely.

In this paper we study the problem of identifying single input-multiple output (SIMO) linear systems that are common in digital communication and control systems. We present an adaptive algorithm for the identification of SIMO linear system. The algorithm is based on a mild co-prime condition and can be implemented as a recursive least square algorithm that has shown quick convergence in simulations. This system identification method can find important applications in digital communications, wideband antenna array processing, and noise control systems. >

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a full analytical model and a simple system identification (SI) method of a piezoelectric actuator, which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, is described extensively. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results. Some of the most well-known forms of system identification are shown briefly, while a new and simple algorithm is described systematically and verified by the model. The main advantage of this work is to provide a solid background and domain knowledge of modelling and system identification methods for further investigations in the field of piezoelectric actuators. Due to their simplicity, both the model and the system identification method can be easily modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in applying a simple system identification algorithm while using the system-level approach for piezoelectric actuators. Lastly, this review work is concluded and some recommendations for researchers working in this area are presented.

This paper deals with a nonparametric identification of continuous-time nonlinear systems using multiple local Gaussian process (GP) models. Multiple sets of training input and output data are collected to train the local GP prior models. Each local GP prior model is trained by minimizing the negative log marginal likelihood of each set of the training data. The final nonlinear function with confidence measure is estimated by weighted mean of the local estimated nonlinear functions using the predictive variances of local GP posterior distributions. Compared to the standard GP-based identification method, the proposed method can reduce the computational cost and improve the accuracy of identification. Simulation results are shown to illustrate the effectiveness of the proposed identification method.

Modal parameter identification of a multiple-span post-tensioned concrete bridge using hybrid vibration testing data