Single-input Single-output Linear Time Research Articles

Online adaptive identification of multichannel systems for audio applications.

Impulse responses (IRs) estimation of multi-input acoustic systems is a prerequisite for many audio applications. In this paper, an adaptive identification problem based on the Autostep algorithm is extended to the simultaneous estimation of room IRs for multiple input single output linear time invariant systems without any a priori information. To do so, the proposed algorithm is initially evaluated in a simulated room with several sound sources active at the same time. Finally, an experimental validation is proposed for the cases of a semi-anechoic chamber and an arbitrary room. Special attention is dedicated to the algorithm convergence behavior, considering different meta parameters settings. Results are eventually compared with the other normalized version of the least mean square algorithm.

A Multiple-Input Multiple-Output Cepstrum

This letter extends the concept of scalar cepstrum coefficients from single-input single-output linear time invariant dynamical systems to multiple-input multiple-output (MIMO) models, making use of the Smith–McMillan form of the transfer function. These coefficients are interpreted in terms of poles and transmission zeros of the underlying dynamical system. We present a method to compute the MIMO cepstrum based on input/output signal data for systems with square transfer function matrices (i.e., systems with as many inputs as outputs). This allows us to do a model-free analysis. Two examples to illustrate these results are included: a simple MIMO system with three inputs and three outputs, of which the poles and zeros are known exactly, that allows us to directly verify the equivalences derived in this letter, and a case study on realistic data. This case study analysis data coming from a (model of) a non-isothermal continuous stirred tank reactor, which experiences linear fouling. We analyze normal and faulty operating behavior, both with and without a controller present. We show that the cepstrum detects faulty behavior, even when hidden by controller compensation. The code for the numerical analysis is available online.

Covariance analysis in SISO linear systems identification

In this paper, we analyze the asymptotic covariance of models of causal single-input single-output linear time invariant systems. Expressions for the asymptotic (co)variance of system properties estimated using the prediction error method are derived. These expressions delineate the impacts of model structure, model order, true system dynamics, and experimental conditions. A connection to results on frequency function estimation is established. Also, simple model structure independent upper bounds are derived. Explicit variance expressions and bounds are provided for common system properties such as impulse response coefficients and non-minimum phase zeros. As an illustration of the insights the expressions provide, they are used to derive conditions on the input spectrum which make the asymptotic variance of non-minimum phase zero estimates independent of the model order and model structure.

Parameterised controller synthesis for SISO-LTI uncertain plants using frequency domain information

This paper extends the results of a new model-free approach which has been applied to guarantee nominal stability and performance. In this paper, using a particular controller structure, the robust stability (RS) and robust performance (RP) criteria for single input single output linear time invariant (SISO-LTI) plants with multiplicative uncertainty are transformed to affine functions in terms of controller parameters. It is shown that solving the feasibility problem of these new criteria will lead to controllers that guarantee the RS and performance. There is no need for a plant mathematical model. The required data for controller synthesis are just the frequency responses corresponding to limited samples of the uncertain plant. Also, there is no need for exact data at each frequency for the whole set of frequency responses. The approach is also applicable for designing both low- and high-order controllers. The effectiveness of the proposed technique is illustrated by simulation results.

Effect of Initialization on a Class of Fractional Order Systems: Experimental Verification and Dependence on Nature of Past History and System Parameters

The objectives of this work are (i) to verify experimentally the theoretical claim that neither Riemann–Liouville nor Caputo fractional derivative can be used to predict the time response of fractional order systems without proper correction for the system’s past history in terms of an initialization function and (ii) to study quantitatively how the error incurred due to ignoring initialization depends on the nature of the past history and the system parameters. The entire analysis is restricted to a special class of single input single output linear time invariant fractional order system which can be realized by a simple electrical circuit consisting of a resistance and a fractance in series. This work involves two different realizations of fractances or constant phase elements whose characteristic parameters are first determined based on their respective impedance frequency responses and then used to simulate the time responses of the circuit with the input same as the one used for experimentation using a numerical method for two cases: (i) taking past history into account and (ii) without taking past history into account. Thereafter, an integral square error criterion is presented and variation of the same is studied with respect to system parameters and nature of the history function to have a relative idea of how much partial past history in the absence of a complete one should suffice in practical applications.

Stability analysis of a combined direct and variable structure adaptive control

This study presents the proofs of robust stability of a direct adaptive controller with a variable structure (VS) parcel. The control law parameters are adjusted based on a method proposed by Narendra and Boskvic (1990). In this approach, two sets of parameters must be obtained. One set is used to attain the control objective which is, in this case, to track the output of a reference model as closely as possible. The other set is of VS type, which is used to improve performance and robustness. A slight modification of the adaptive law for the VS parameters with proofs of robust stability is proposed here. With this modified law, all mathematical proofs already existing in the literature for robust direct adaptive controllers can be extended to the case under study. The combined controller is applied to a single input single output linear time invariant (SISO LTI) plant with unmodelled dynamics of multiplicative and additive types. It is proven that the combined controller can arbitrarily improve the convergence of the error while keeping the system robustness, if compared to the non-combined case. Simulation results illustrate the efficiency of the proposed control strategy.

Consistent output estimate with wavelets: An alternative solution of least squares minimization problem for identification of the LZC system of a large PHWR

A novel technique for estimating system parameters based on consistent output estimate in wavelet domain is proposed as an alternative solution to the classical least squares minimization problem, in this paper. The algorithm is computationally efficient and exhibits excellent performance in cross validation. An iterative algorithm, alternately projecting the solution in time and wavelet domain for penalized minimization of local error in wavelet coefficients, is presented in the paper. As a case study, the paper addresses the problem of modeling a complex process in a large Pressurized Heavy Water Reactor (PHWR) based on the evolution of input and output. Xenon-induced spatial oscillations are kept from growing in large PHWRs, by means of the Liquid Zone Control System (LZCS). In this work, an identification scheme of a single input single output linear time invariant model of the LZCS is studied. Shift invariant orthogonal wavelets are used for consistent output estimate of the LZCS process. The technique is verified on the real experimental data obtained from the LZCS test set-up. It is observed that even a low order wavelet based model gives excellent approximation from fewer numbers of input–output data points.

A new output regulation using sliding-mode technique for a class of SISO linear time-varying systems

In this brief, we propose a new output regulator using the sliding-mode technique for a class of single-input single-output linear time- varying (LTV) systems. It is seen that a bounded -similarity-transforma- tion matrix is first designed, which is necessary for the transformed LTV system to retain the dynamical features of the original LTV system. The up- date law of the transformation matrix based on the eigenstructure-assign- ment technique is developed to guarantee the uniformly exponential con- vergence of the closed-loop dynamics on the sliding mode. A sliding-mode output regulator using only the output measurements is then designed to drive both the sliding variable and the system output to converge to zero in a finite time. A simulation example is given in support of the proposed scheme.

適応スライディング面によるモデル規範型可変構造制御に関する研究

In this paper, for single-input single-output linear time invariant systems with unknown parameters, a new model reference variable structure control which has an adaptive sliding surface is proposed. This control is feasible using only input and output measurements. Under some usual assumptions in model reference adaptive control (MRAC) by applying the so-called e/sub 1/-modification, the resulting closed loop system is shown to be globally stable in the presence of bounded input disturbances. Also disturbance attenuation is possible, to some extent, by changing the parameter of the sliding surface. In addition, since the identification error model can be suitably changed without prefilter and the relative degree of it is smaller by 1 compared with ordinary MRACs, the tracking performance can be improved. Simulation results are presented to show these advantages.