System identification step

The system identification step in the core-box modeling framework has two major sub-steps parameter estimation and model quality analysis. The parameter estimation step is usually solved as an optimization problem that minimizes a cost function that depends on the model s parameters. One choice of cost function is the sum of squares of the residuals, Si(t p) = yi(t) — yl(t p). However, one usually needs to put different weights, up (t), on the different samples, and additional information that is not part of the time-series is often added as extra terms k(p). These extra terms are large if the extra information is violated by the model, and small otherwise. A general least-squares cost function, Vp(p), is thus of the form... 

The determination of has many advantages. First, it is a way to compare in-vivo and in-vitro parameters for the same system [11]. Second, it gives an interpretation of the results obtained in the system identification step of the core model. Nevertheless, the final step in the core-box modeling framework is not achieved until the gray-box model has obtained all the estimated features of the estimated core model,... 

The identification of plant models has traditionally been done in the open-loop mode. The desire to minimize the production of the off-spec product during an open-loop identification test and to avoid the unstable open-loop dynamics of certain systems has increased the need to develop methodologies suitable for the system identification. Open-loop identification techniques are not directly applicable to closed-loop data due to correlation between process input (i.e., controller output) and unmeasured disturbances. Based on Prediction Error Method (PEM), several closed-loop identification methods have been presented Direct, Indirect, Joint Input-Output, and Two-Step Methods. 

The very basis of the kinetic model is the reaction network, i.e. the stoichiometry of the system. Identification of the reaction network for complex systems may require extensive laboratory investigation. Although complex stoichiometric models, describing elementary steps in detail, are the most appropriate for kinetic modelling, the development of such models is time-consuming and may prove uneconomical. Moreover, in fine chemicals manufacture, very often some components cannot be analysed or not with sufficient accuracy. In most cases, only data for key reactants, major products and some by-products are available. Some components of the reaction mixture must be lumped into pseudocomponents, sometimes with an ill-defined chemical formula. Obviously, methods are needed that allow the development of simple... 

For effective control of crystallizers, multivariable controllers are required. In order to design such controllers, a model in state space representation is required. Therefore the population balance has to be transformed into a set of ordinary differential equations. Two transformation methods were reported in the literature. However, the first method is limited to MSNPR crystallizers with simple size dependent growth rate kinetics whereas the other method results in very high orders of the state space model which causes problems in the control system design. Therefore system identification, which can also be applied directly on experimental data without the intermediate step of calculating the kinetic parameters, is proposed. 

To determine the state space model with system Identification, responses of the nonlinear model to positive and negative steps on the Inputs as depicted in Figure 4 were used. Amplitudes were 20 kW for P,, . 4 1/s for and. 035 1/s for Q. The sample interval for the discrete-time model was chosen to be 18 minutes. The software described In ( 2 ) was used for the estimation of the ARX model, the singular value analysis and the estimation of the approximate... 

Response of vr to a step of +20 kW on P, obtained with the nonlinear model, system identification and method of lines... 

For continuous process systems, empirical models are used most often for control system development and implementation. Model predictive control strategies often make use of linear input-output models, developed through empirical identification steps conducted on the actual plant. Linear input-output models are obtained from a fit to input-output data from this plant. For batch processes such as autoclave curing, however, the time-dependent nature of these processes—and the extreme state variations that occur during them—prevent use of these models. Hence, one must use a nonlinear process model, obtained through a nonlinear regression technique for fitting data from many batch runs. 

Model development (also called system identification) involves several critical activities including design of experiments and collection of data, data pretreatment, model fitting, model validation and acceptability of the model for its use. A vast literature has been developed over the last 50 years in various aspects of model identification [99, 170, 174, 246, 278]. A schematic diagram in Figure 4.2 where the ovals represent human activities and decision making steps and the rectangles represent computer-based computations and decisions illustrates the links between critical activities. 

FIGURE 16.6 Velocity estimates for the saccadic eye movement illustrated in Figure 16.5. Solid line is the saccadic eye movement model velocity prediction with the final parameter estimates computed using the system identification techniques. The dots are the two-point central difference estimates of velocity computed with a step size of 3 and a sampling interval of 1 msec. (From Enderle, J.D. and Wolfe, J.W. 1987. IEEE Trans. Biomed. Eng. 34 43-55. With permission.)... 

The reconstruction accuracy of the measurement system depends on the step frequency of the input signals A/ and the load impedance. Clearly, additional study is required to explore the promise of this method including application this method to estimate faults in different wiring and cables with considering of mechanical variations estimation of much more complicated wiring systems identification of the factors affecting the reconstruction accuracy and a detailed estimation and comparison of different optimization techniques. 

Having successfully implemented conventional MRAC techniques, the next logical step was to try to incorporate the MRAC techniques into a neural network-based adaptive control system. The ability of multilayered neural networks to approximate linear as well as nonlinear functions is well documented and has foimd extensive application in the area of system identification and adaptive control. The noise-rejection properties of neural networks makes them particularly useful in smart structure applications. Adaptive control schemes require only limited a priori knowledge about the system to be controlled. The methodology also involves identification of the plant model, followed by adaptation of the controller parameters based on a continuously updated plant model. These properties of adaptive control methods makes neural networks ideally suited for both identification and control aspects [7-11]. 

The system identification framework shown in Fig. 6.3 extends the general regression framework shown in Fig. 3.1 to take into account the specific issues in process system identification. The framework consists of three steps ... 

Data Collection During the data collection step, the required data are collected and analysed to determine if there are any obvious problems with the data set, such as missing data, faulty sensors, faulty values, or multiple operating modes. The framework presented in Fig. 6.3 assumes that a separate experiment will be designed in order to obtain the data required for system identification. In industry, the ability to perform such experiments can be limited due to various factors, including safety, economic, or reluctance on the part of the plant operators. Instead, historical data from the data historian are extracted and preprocessed to determine their usefulness for the given problem. 

The states in Eqn (25.2) are now being formed as linear combinations of the -step ahead predicted outputs k= 1, 2,. ..). The literature on state space identification has shown how the states can be estimated directly from the process data by certain projections. (Verhaegen, 1994 van Overschee and de Moor, 1996 Ljung and McKelvey, 1996). The MATLAB function n4sid (Numerical Algorithms for Subspace State Space System Identification) uses subspace methods to identify state space models (Matlab 2000, van Overschee and de Moor, 1996) via singular value decomposition and estimates the state x directly from the data. 

The ring system identification currently implemented in AUTONOM is a two-step process initiated by the ring system perception. The reliability of the ring perception routine is the crux of the naming algorithm. 

There is an all-Italian project, meeting all the primary prerequisites so far illustrated, which is a system developed by Govoni based on Tecoplast s experience. It consists of a platform for selection according to plastics typology, where all the identification steps are performed twice and where the efficiency of selection following detection is always subjected to check (Figure 1). 

Nonlinear System Identification Particle-Based Methods, Fig. 3 The particle filter implementation steps... 

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