Bias Compensating Direct Identification of Continuous Time System with Noisy Output Data

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.

A criterion is introduced for determining the optimum sampling interval for the identification of system parameters. It increases the accuracy and stability in identification procedures. This is done by employing a bilinear transformation from the z-plane to the w-plane. Some results of simulations are also included. These reveal the usefulness of the suggested algorithm even in the presence of measurement noise.

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.

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

It is shown how genetic algorithms can be applied for system identification of both continuous and discrete time systems. It is shown that they are effective in both domains and are able to directly identify physical parameters or poles and zeros. This can be useful because changing one physical parameter might affect every parameter of a system transfer function. The estimates of poles and zeros are then used to design a discrete time pole placement adaptive controller. Simulations for minimum and nonminimum phase systems and a system with unmodeled dynamics are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A general framework for modeling of a time-varying continuous-time SISO system from its sampled input and output while retaining the system parameters with their physical interpretation is presented. The theory can be specialized to the Poisson moment functional approach, the integrated sampling approach, the instantaneous sampling approach or the use of state variable filters. In all methods, the initial conditions can be removed by applying an appropriate discrete-time operator. Digital filtering is used to explicitly or implicitly reconstruct the time-derivatives of the sampled continuous-time signals involved. A thorough study of the approximations resulting from converting the continuous-time model to a discrete-time version is presented. It is shown how these errors can be controlled and that system parameter estimates can be obtained with an arbitrary accuracy. The digital filtering approach to integrated sampling and instantaneous sampling exhibit optimal properties among all methods that fit in the general framework. Moreover, using digital filter designs instead of numerical integration allows slower sampling. A maximum likelihood estimator is derived for time-invariant systems in an errors-in-variables stochastic framework. Finally, the theory is verified through simulations.

Identification of continuous-time systems using arbitrary signals

The analysis of discrete-time identification methods for continuous-time system models usually involves the assumption of a piecewise-constant (ZOH) input excitation. However, as has recently been discussed, i e. [1], this assumption is often violated in practice. This paper investigates estimation when the input excitation corresponds to a filtered ZOH signal. An exact discrete-time model representation for the sampled input-output signals is derived, and the effects on estimation investigated through simulation studies. The studies show how the appropriate selection of the various estimation options can yield relatively accurate continuous-time model estimates.

Nonlinear Model Tracking (NMT) has been shown to be a robust method for predicting failure through nondestructive health monitoring. The method has been applied to slender cantilever beams of varying geometry subjected to harmonic nonstationary base excitation around the beams second natural frequency. Working with a nonlinear differential equation model, model parameters are mapped as the system health degrades. Continuous Time System Identification is populated with healthy system stimulus and response data and updated with aging real time response data. While the NMT method indicates with repeatability the onset of plasticity, crack initiation and growth well in advance of system failure, a phenomenon associated with specific geometries known as early onset drift can incorrectly flag system failure. Through numerical methods this phenomenon is explored. Additionally, two investigative numerical techniques are developed to give greater understanding and utility to the NMT method.

Subspace-based identification for continuous-time stochastic systems via distribution-theoretic approach

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.

SET-MEMBERSHIP IDENTIFICATION OF CONTINUOUS-TIME SYSTEMS

Continuous-time system identification has primarily dealt with sampled input and output data for constructing continuous-time models. However, sampled signals can lead to inaccurate models if their intersample behavior is not addressed appropriately. In this paper, this effect is explored in detail with respect to the SRIVC and CLSRIVC estimators, which are some of the most popular methods for open and closed-loop continuous-time system identification respectively. Based on our consistency analysis, we propose an algorithm that alleviates the asymptotic bias of these methods for arbitrary input excitations and provide an alternative procedure to achieve consistent estimates for band-limited signals. Simulation examples show the effectiveness of our approach.

In this paper, we study the Lagrange–Sylvester interpolation of rational matrix functions which are analytic at infinity, and propose a new interpolation algorithm based on the recent subspace‐based identification methods. The proposed algorithm is numerically efficient and delivers a minimal interpolant in state‐space form. The solvability condition for the subspace‐based algorithm is particularly simple and depends only on the total multiplicity of the interpolation nodes. As an application, we consider subspace‐based system identification with interpolation constraints, which arises, for example, in the identification of continuous‐time systems with a given relative degree.

In order to obviate the requirement of drift dynamics in adaptive dynamic programming, integral reinforcement learning (IRL) has been proposed as an alternate formulation of Bellman equation. However control coupling dynamics is still needed to obtain closed-form expression of optimal control effort. In addition to this, initial stabilizing controller and two sets of neural networks (NN) (known as Actor-Critic) are required to implement IRL scheme. In order to remedy these, this paper presents a critic-only IRL controller coupled with an experience replay (ER)-based identifier to solve optimal tracking control problem for an unknown continuous-time systems under actuator constraints. The presented control architecture is shown to yield tighter residual sets for state tracking error and error in NN weights. The simulation results establish the efficacy of the presented control scheme on continuous-time systems.