Identification Of Linear Systems Research Articles

Linear Motor System Identification and Simulation Experiments Based on LabVIEW

Linear Motor System Identification and Simulation Experiments Based on LabVIEW

Linear Motor System Identification and Simulation Experiments Based on LabVIEW

Linear Motor System Identification and Simulation Experiments Based on LabVIEW

Closed-loop identification of stabilized models using dual input–output parameterization

This paper introduces a dual input–output parameterization (dual IOP) for the identification of linear time-invariant systems from closed-loop data. It draws inspiration from the recent input–output parameterization developed to synthesize a stabilizing controller. The controller is parameterized in terms of closed-loop transfer functions, from the external disturbances to the input and output of the system, constrained to lie in a given subspace. Analogously, the dual IOP method parameterizes the unknown plant with analogous closed-loop transfer functions, also referred to as dual parameters. In this case, these closed-loop transfer functions are constrained to lie in an affine subspace guaranteeing that the identified plant is stabilized by the known controller. Compared with existing closed-loop identification techniques guaranteeing closed-loop stability, such as the dual Youla parameterization, the dual IOP neither requires a doubly-coprime factorization of the controller nor a nominal plant that is stabilized by the controller. The dual IOP does not depend on the order and the state-space realization of the controller either, as in the dual system-level parameterization. Simulation shows that the dual IOP outperforms the existing benchmark methods.

Adaptive identification of linear infinite-dimensional systems

We propose an adaptive algorithm for identifying the unknown parameter (possibly vector-valued) in a linear stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an adaptive update law (a differential equation in time) driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown linearly-varying (in space) coefficient.

Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systems

Strong Consistency and Rate of Convergence of Switched Least Squares System Identification for Autonomous Markov Jump Linear Systems

Identification of Linear Systems Using Binary Sensors with Random Thresholds

Identification of Linear Systems Using Binary Sensors with Random Thresholds

Likelihood-based generalization of Markov parameter estimation and multiple shooting objectives in system identification

This paper considers system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We analyze an optimization objective derived from Bayesian inference for the dynamics of hidden Markov models. We then relate this objective to that used in several state-of-the-art approaches for both linear and nonlinear system ID. In the former, we analyze least squares approaches for Markov parameter estimation, and in the latter, we analyze the multiple shooting approach. We demonstrate the limitations of the optimization problems posed by these existing methods by showing that they can be seen as special cases of the proposed optimization objective under certain simplifying assumptions: conditional independence of data and zero model error. Furthermore, we observe that the proposed approach has improved smoothness and inherent regularization that make it well-suited for system ID and provide mathematical explanations for these characteristics’ origins. Finally, numerical simulations demonstrate a mean squared error over 8.7 times lower compared to multiple shooting when data are noisy and/or sparse. Moreover, the proposed approach identifies accurate and generalizable models even when there are more parameters than data or when the system exhibits chaotic behavior.

Wiener Filter Using the Conjugate Gradient Method and a Third-Order Tensor Decomposition

In linear system identification problems, the Wiener filter represents a popular tool and stands as an important benchmark. Nevertheless, it faces significant challenges when identifying long-length impulse responses. In order to address the related shortcomings, the solution presented in this paper is based on a third-order tensor decomposition technique, while the resulting sets of Wiener–Hopf equations are solved with the conjugate gradient (CG) method. Due to the decomposition-based approach, the number of coefficients (i.e., the parameter space of the filter) is greatly reduced, which results in operating with smaller data structures within the algorithm. As a result, improved robustness and accuracy can be achieved, especially in harsh scenarios (e.g., limited/incomplete sets of data and/or noisy conditions). Besides, the CG-based solution avoids matrix inversion operations, together with the related numerical and complexity issues. The simulation results are obtained in a network echo cancellation scenario and support the performance gain. In this context, the proposed iterative Wiener filter outperforms the conventional benchmark and also some previously developed counterparts that use matrix inversion or second-order tensor decompositions.

Stable Linear System Identification With Prior Knowledge by Riemannian Sequential Quadratic Optimization

Stable Linear System Identification With Prior Knowledge by Riemannian Sequential Quadratic Optimization

Attitude modelling and real-time robust control of a 3-DoF quadcopter UAV test bench

Abstract In this work, a three degrees-of-freedom (3-DoF) static quadcopter unmanned aerial vehicle (UAV) test-rig of a pendulum-type configuration is custom-designed, developed, instrumented, and interfaced with a PC. The rig serves as a test bed to develop high-fidelity mathematical models as well as to investigate autopilot designs and real-time closed-loop controllers’ performances. The Simulink Desktop Real-Time software is employed for the quadcopter’s attitude signals acquisition and real-time implementation of closed-loop controllers on a target microcontroller hardware. The mathematical models for pitch, roll, and yaw axes are derived via the first principle and validated with the experimental linear system identification (SI) techniques. Subsequently, employing the multi-parameter root contour technique, the classical proportional integral derivative (PID) controllers are designed and implemented in real-time on the quadcopter UAV test rig. This served as a benchmark controller for comparing it with an integral-based linear quadratic regulator (LQR) controller. Further, to improve the transient response of the LQR controller, a novel robust integral-based LQR controller with a feedforward term (LQR-FF) is implemented, which shows much superior performance than the benchmark and basic LQR controller. This work thus will act as a precursor for a more complex 3-DoF autopilot design of an untethered quadcopter.

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

Inverse WKB recursive solution method for dynamic load identification of linear time-varying structural systems

Parameter Identification of Discrete-time Linear Time-invariant Systems Using State and Input Data

Parameter Identification of Discrete-time Linear Time-invariant Systems Using State and Input Data

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-Time System Identification

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-Time System Identification

DsPIC Implementation and Performances Evaluation of Adaptive Filters for System Identification

This paper aims to implement and evaluate performances of adaptive filters applied to linear systems identification on a dsPIC platform. To do so, we considered two different applications: the identification of DC motor transfer function and the acoustic echo cancellation. For the DC motor case, real-time identification is not necessarily required. However, for the acoustic echo cancellation case, real-time identification is crucial, making execution time a key parameter in this scenario. We have implemented three adaptive algorithms: LMS, NLMS, and RLS. The first two are known for their computational simplicity, while RLS is recognized for its convergence speed. Performances evaluation is primarily based on accuracy and computation speed. A comparison is carried out in both cases to determine which algorithm is more suitable for each application. The results obtained showed that RLS is better suited for the DC motor case, while NLMS is more suitable for acoustic echo cancellation, particularly when the impulse response of the echo path is long.

Identification of Linear Dynamic Systems in State Sate

System identification has been growing in an engineering community over the last 60 years, and an intensive research has been published in this field. This study presents an identification method of a linear time-invariant continuous dynamic system directly from time series data. The considered system is represented in a state space form. All states are assumed to be measured. The proposed identification algorithm is demonstrated and investigated, with noise-free data and noisy data, on a MATLAB simulation environment. The results confirm that the simple procedures of the proposed algorithm give an effective and successful estimation of the system parameter matrices.

Linear and non-linear thermal system identification based on the integral of non-integer order — Application to solve inverse heat conduction linear and non-linear problems

The identification of thermal systems is an approach particularly well suited to solve inverse heat conduction problems (IHCP) in the case of complex systems where many parameters are unknown and where even the sensors must be modeled in order to obtain accurate results. In this paper, we propose significant advances in the formulation of the mathematical model structure by basing it exclusively on the non-integer order integration operator. We show that this approach is consistent with the heat diffusion process and that it allows to get rid of the step of pre-filtering the experimental signals to the sensors which was necessary when using the derivation operator. Demonstrations are made on the simulated configurations through simple analytical solutions and also a complex real configuration. I generalize the use of the non-integer integration operator in the treatment of non-linear heat conduction problems based on the Volterra series decomposition. We show in particular that the use of a generalized non-integer transfer function gives encouraging and generalizable results for a large class of related problems.

Combined invariant subspace & frequency-domain subspace method for identification of discrete-time MIMO linear systems

Combined invariant subspace & frequency-domain subspace method for identification of discrete-time MIMO linear systems

Kernel-based linear system identification: When does the representer theorem hold?

It holds for any physical (bounded) input if and only if the kernel is stable.

Online System Identification and Control for Linear Systems With Multiagent Controllers Over Wireless Interference Channels

Online System Identification and Control for Linear Systems With Multiagent Controllers Over Wireless Interference Channels

A Novel Computationally Efficient Approach for Exploring Neural Entrainment to Continuous Speech Stimuli Incorporating Cross-Correlation

A linear system identification technique has been widely used to track neural entrainment in response to continuous speech stimuli. Although the approach of the standard regularization method using ridge regression provides a straightforward solution to estimate and interpret neural responses to continuous speech stimuli, inconsistent results and costly computational processes can arise due to the need for parameter tuning. We developed a novel approach to the system identification method called the detrended cross-correlation function, which aims to map stimulus features to neural responses using the reverse correlation and derivative of convolution. This non-parametric (i.e., no need for parametric tuning) approach can maintain consistent results. Moreover, it provides a computationally efficient training process compared to the conventional method of ridge regression. The detrended cross-correlation function correctly captures the temporal response function to speech envelope and the spectral–temporal receptive field to speech spectrogram in univariate and multivariate forward models, respectively. The suggested model also provides more efficient computation compared to the ridge regression to process electroencephalography (EEG) signals. In conclusion, we suggest that the detrended cross-correlation function can be comparably used to investigate continuous speech- (or sound-) evoked EEG signals.