Delay Time Parameter Estimation

For example, for both the analysed transportation systems there were no possibility to define if, and what kind of components dependency occur. The system reliability structure wasn t also defined. Additionally, there were also no possibilities of delay time parameter estimation. The problem with economic data gathering process is also visible for the case of Skoda trams. 

The implementation of the on-line optimization strategy requires the knowledge of current states and/or parameters in nonlinear process models in order to modify a new optimal profile defined as a set point for a controller. It is known that some measurements i.e. concentration are available at low sampling rate with significant time delay. To overcome this difficulty, state and parameter estimation is incorporated into the proposed on-line optimization algorithm. 

Since the concentrations of reactants (Ma, Mp, Me and Mp,) in batch reactor are assumed to be measurable with a delay of one sampling time that is, at time k of the reactor, only information at time A — 1 is available. Thus, the EKF is applied to estimate the value of reactant concentration at current time k from their delayed measurements at sampling time k — 1. However, since it is expected to exhibit uncertainly in reaction rate constant (i.e. k and fcj) in real plant, the EKF is also used to estimate these uncertain parameters. The following equations, therefore, are appended for parameter estimation... 

The linear characteristics can be noticed on the left side of the equation however in gy the inherent nonlinearities of the estimation error dynamics are enclosed. This means that, by suitable choices of the gains, the left side is stable, but gy is a potentially destabilizing factor of the dynamics. Except for gy, Eq. (8) establishes a clear relationship between the choice of the tuning parameters and the sampling-delay time value in front of the desired kind of estimation error response. 

Comparing the coefficients set of this characteristic polynomial of reference with those of the output estimation error dynamics (Eq. 8), the gains were obtained in well-defined terms of the sampling-delay time and the tuning parameters (fo, CO) ... 

To show the performance of the estimator, a simulation study was realized. The model parameters for the DA bacteria are (Jsix, Ip/x, ICmax, = (0.25, 0.25/0.95, 0.035 h", 0.9 g L ), which are the corresponding for the bioreactor considered as the actual plant. These parameters were obtained from a previous regression fitting over a set of experimental runs. For the estimator, a parametric error was introduced ks = 0.8 instead of 0.9. Attending practical considerations, the sampling-delay time was set at > = 1 h. 

A wavelet model for the data consisted of the following regressors i, y/ 2> y, 3, and yt 4, plus for each of the inputs the terms between rtk+X and 11 + 5. The total time delay was assumed to be one for the process between the i and hi and two between the and hi. Note that the time delay used here must include the one-sample time delay introduced by sampling a system, that is, the total time delay equals The estimated model parameters will not be included here as they are... 

Jodejko-Pietruczuk, A., Werbihska-Wojciechowska, S. (2014a). Analysis of maintenance models parameters estimation for technical systems with delay time. Eksploatacja i Niezawodnosc—Maintenance and Reliability 16(2) 288-294. 

The estimated parameters have been used for the maintenance decision rule described in section 4. The delay time rhas been considered equal to 19 (approximatively equal to 4 A/). 

Model parameters for second-order systems which include time delays can be estimated using graphical or numerical methods. A method due to Smith (1972) utilizes a model of the form... 

Sundaresan, K. R., and R. R. Krishnaswamy, Estimation of Time Delay, Time Constant Parameters in Time, Frequency, and Laplace Domains, Can. J. Chem. Eng., 56,257 (1978). 

As seen previously for some specific applications such as wastewater treatment plants, software sensors can be envisaged to provide on-line estimation of non-measurable variables, model parameters or to overcome measurement delays [81-83]. Software sensors have been developed mainly for monitoring bioprocesses because the control system design of bioreactors is not straightforward due to [84] significant model uncertainty, lack of reliable on-line sensors, the non-linear and time-varying nature of the system or slow response of the process. 

The formulation described above provides a useful framework for treating feedback control of combustion instability. However, direct application of the model to practical problems must be exercised with caution due to uncertainties associated with system parameters such as and Eni in Eq. (22.12), and time delays and spatial distribution parameters bk in Eq. (22.13). The intrinsic complexities in combustor flows prohibit precise estimates of those parameters without considerable errors, except for some simple well-defined configurations. Furthermore, the model may not accommodate all the essential processes involved because of the physical assumptions and mathematical approximations employed. These model and parameter uncertainties must be carefully treated in the development of a robust controller. To this end, the system dynamics equations, Eqs. (22.12)-(22.14), are extended to include uncertainties, and can be represented with the following state-space model ... 

In order to perform the on-line optimization strategy, the knowledge of current state variables and/or parameters in the process models is required. Due to the fact that some of these variables cannot be known exactly or sometime can be measured with time delay, it is essential to include an on-line estimator to estimate these process variables using available process measurements as well. The sequence of an estimation and optimization procedure is known as an estimation-optimization task [6], As in several estimation techniques, an Extended Kalman Filter (EKF) has become increasingly popular because it is relatively easy to implement. It has been found that the EKF can be applied to a number of chemical process applications with great success. Once the estimate of unknown process variables is deter-... 

In contractile experiments the time from the stimulation of the nerve to the CMAP recorded in muscle provides an estimate of NCV. The length of the nerve from the stimulating electrode to the muscle can simply be measured and divided by the time. However, the time recorded in this way includes the delay for synaptic transmission, which may be increased in models with synaptic defects. If this is a concern or if the only parameter desired is NCV, then the measurement can be obtained non-invasively with a relatively simple setup (e.g., (3)). Using the sciatic nerve, NCV can be calculated by measuring the latency of compound motor action potentials recorded in the muscle of a rear paw. Action potentials are produced by subcutaneous stimulation at two separate sites proximal stimulation at the sciatic notch and distally at the ankle. NCV is then calculated by using the two latencies and conduction distance. Decreases in nerve conduction velocity most often reflect defects in myelination, but may also be the result of changes in internodal distance, decreased axon diameters, or altered excitability. 

It is important to notice that all the relations characterizing these three CFMs have been established by considering that a first order chemical reaction takes place in volume V and according to the accepted structure of the flow. So, here, k represents the kinetic reaction constant. When the reaction is not taken into account, we consider k = 0. In relations (3.83)-(3.85),Xrt is the time delay expressed in a natural value, s describes the system phase difference in time units and T] is the mixing coefficient. This last parameter equals one for a perfect mixing flow and zero for plug flow. In other cases, q can be estimated with m/(m + b + d) as shown in Fig. 3.27. 

An alternative model, including a lag-time to allow for distributional effects embedded in the observed time delay of the onset of the effect after warfarin administration, was published by Pitsui et al. (1993). Setting the baseline value of clotting factor activity in the absence of warfarin (P0) to a fixed mean of three predose measurements, the program can estimate that parameter. 

Transit Models The development of indirect effect models (32) facilitated the evaluation of many disease-mediated processes such as changes in biomarker levels over time. Control streams and example databases for these models are presented elsewhere in Chapters 22 and 23 and will not be covered here. However, as was discussed, when applying these indirect response models, it is possible to increase the delay in response by the addition of extra compartments. The addition of these extra effect compartments also creates additional parameters that need to be estimated, which are often not identifiable. 

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