Fig 6 - uploaded by Péter Zoltán Csurcsia
Content may be subject to copyright.
The number of parameters for the first, second and third order kernels is shown as a function of the memory length (truncation lag).
Source publication
This paper presents an efficient nonparametric time domain nonlinear system identification method applied to the measurement benchmark data of the cascaded water tanks. In this work a method to estimate efficiently finite Volterra kernels without the need of long records is presented. This work is a novel extension of the regularization methods tha...
Context in source publication
Context 1
... this point we comment on the computational complexity which increases with increasing degree of the Volterra series (increasing number of parameters, see Fig. 6). In this particular situation, the time needed for a regularized FIR estimate is in order of milliseconds. The first degree case has a computational time in the magnitude of seconds, the second degree Volterra kernel is around minutes, and finally the third degree Volterra kernels requires hours. The exact computational time depends ...
Similar publications
This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates...
System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying (LTV) systems. To tackle this challenge, we develop an episodic block model for the LTV system where the model...
Citations
... A coupled or cascaded two-tank dynamical system, which is investigated in [17,[66][67][68][69] (state-space approach, PI, PID), [11,12,23,25,30,36] (transfer function approach), [35,70,71] (FL, PSO, NN), [72] (autoregressive model), [73] (multidimensional regularization), [74] (model-predictive control of a geometry-varying conical tank), and [75,76] (SMC); 3. ...
... Let us enumerate some dedicated approaches, the specific applications of which are present in the related literature, e.g.: (i) a model reference control driven from the experimental data of MIMO cascaded tank systems, including the tuning of a virtual reference feedback [83]; (ii) nonlinear control of a three-tank CTS with mismatched uncertainties [79]; (iii) a robust high-gain observers-based water level and leakage flow rate estimation [77]; (iv) the control of two conical tanks with interacting levels based on a dynamic matrix approach [74]; (v) a Volterra series estimate of the CTS using multidimensional regularization [73]; (vi) black and white box approaches for a CTS identification [72]; and (vii) a few references [8,12,18] described in Section 2. ...
... A physical model of the cascaded configuration of a two-tank system with one inlet and two outlets, see[17,23,67,68,[71][72][73]. ...
In this paper, a unique overview of intelligent machines and mathematical methods designed and developed to measure and to control the water level in industrial or laboratory setups of coupled and cascaded configurations of tanks is made. A systematized and concise overview is made of the mechatronic systems used in the measurement, identification, and control of the water level enumerates, the software used in the associated scientific research, modern techniques and sensors, and mathematical models, as well as analysis and control strategies. The broad overview of applications of the last decade is finalized by a proposition of a control system that is based on a parameter estimation of a new experimental setup, an integral dynamic model of the system, a modern mechatronic machine such as the Watson-Marlow peristaltic pump, the Anderson Negele sensor of level, the NI cRIO-9074 controller, and LabVIEW virtual instrumentation. The results of real experimental tests, exploiting a hybrid proportional control, being improved by a numerically predicted water level, are obtained using a few tools, i.e., the static characteristics, the classical step response, and a new pyramid-shaped step function of a discontinuous path-following reference input, being introduced to evaluate the effectiveness and robustness of the regulation of the level height.
... ere are a few attempts to apply nonlinear system identification techniques to common applications in different engineering fields reported in the literature. In the area of chemical process control, Aljamaan et al. [12] identified the dynamics of the continuously stirred tank reactor (CSTR) in the presence of nonstationary disturbances, Zhu [13] identified a distillation column, and Birpoutsoukis et al. [14] estimated a Volterra series model of the cascaded two-tank system. Similarly, in biomedical engineering applications, Vlaar et al. [15] identified brain signals by electroencephalography (EEG) while Cescon et al. [16] identified models of the blood sugar level inside the human body. ...
... is work is limited to the cascaded two-tank system, where different identification approaches have been proposed in the literature. Unlike the nonlinear state-space method proposed by Relan et al. [1], Birpoutsoukis et al. [14] developed a nonparametric Volterra series-based approach. In this latter method, cancelling the undesired transient part played an important role in minimizing the error. ...
... e phase direction and length were measured together in the L-M iteration. e update is defined in (14). ...
A common process control application is the cascaded two-tank system, where the level is controlled in the second tank. A nonlinear system identification approach is presented in this work to predict the model structure parameters that minimize the difference between the estimated and measured data, using benchmark datasets. The general suggested structure consists of a static nonlinearity in cascade with a linear dynamic filter in addition to colored noise element. A one-step ahead prediction error-based technique is proposed to estimate the model. The model is identified using a separable least squares optimization, where only the parameters that appear nonlinearly in the output of the predictor are solved using a modified Levenberg–Marquardt iterative optimization approach, while the rest are fitted using simple least squares after each iteration. Finally, MATLAB simulation examples using benchmark data are included.
Aiming at the problem of object model identification of modern industrial process control systems, a new closed-loop moment parameter identification online method based on the data of normal operation of the running system is proposed. In this method, only one step response data of the system is required, and appropriate convergence factors are introduced into the Laplace formula, the trapezoidal integral method is used to calculate the values of two derivatives of the transfer function, then the four unknown parameters of the second-order model can be solved by fitting the data with the least square method, and the target model can be identified. Finally, the simulation results of building different objects through Matlab show that the identification method has general applicability and good robustness with high recognition, and it is not sensitive to noise signals.
This paper introduces a user-friendly estimation toolbox for (industrial) measurements of (vibro-acoustic) systems with multiple inputs. The vibration testing methods are very important because they help to improve the product quality and to avoid safety and comfort issues. The time-consuming testing procedures are nowadays fully substituted by techniques that evaluates the frequency response functions (FRFs).
The toolbox provides a user-friendly nonparametric estimation method that uses a special combined Local Polynomial/Rational approach. The toolbox can be used even in case of multiple inputs with only one measured period – that would be not possible with the classical FRF estimator frameworks.
Scientists and engineers want accurate mathematical models of physical systems for understanding, design, and control. To obtain accurate models, persistently exciting rich signals are needed. The MUMI Matlab toolbox creates multisine signals to assess the underlying systems in a time efficient, user-friendly way. In order to avoid any spectral leakage, to reach full nonparametric characterization of the noise, and to be able to detect nonlinearities and time-variations, multisine signals can be used. By the use of the toolbox, inexperienced users can easily create state-of-the-art excitation signals to be used to perturbate almost any physical systems.
Volterra series approximate a broad range of nonlinear systems. Their identification is challenging due to the curse of dimensionality: the number of model parameters grows exponentially with the complexity of the input–output response. This fact limits the applicability of such models and has stimulated recently much research on regularized solutions. Along this line, we propose two new strategies that use kernel-based methods. First, we introduce the multiplicative polynomial kernel (MPK). Compared to the standard polynomial kernel, the MPK is equipped with a richer set of hyperparameters, increasing flexibility in selecting the monomials that really influence the system output. Second, we introduce the smooth exponentially decaying multiplicative polynomial kernel (SED-MPK), that is a regularized version of MPK which requires less hyperparameters, allowing to handle also high-order Volterra series. Numerical results show the effectiveness of the two approaches.
