System identification closed-loop

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 PBL reactor considered in the present study is a typical batch process and the open-loop test is inadequate to identify the process. We employed a closed-loop subspace identification method. This method identifies the linear state-space model using high order ARX model. To apply the linear system identification method to the PBL reactor, we first divide a single batch into several sections according to the injection time of initiators, changes of the reactant temperature and changes of the setpoint profile, etc. Each section is assumed to be linear. The initial state values for each section should be computed in advance. The linear state models obtained for each section were evaluated through numerical simulations. 

This brief overview of separate treatment techniques is not complete, however it can be used for a first inventory and identification of treatment steps which may be considered as part of a complete closed loop water system. It has to be taken in mind that the above-mentioned overview of separate treatment techniques is primarily based on one type of pollutant and one physical state of that pollutant. It will be clear that very often the same treatment step can be applied to remove different types of pollutants. It is also evident that a large percentage of the separate treatment steps mentioned will result in a concentrate containing the pollutants. This concentrate has to be treated subsequently. 

Fifth, the identification of four closed-loop internal circuits that are distinct from the CTSC loops has also modified the classical view. These internal circuits are parallel, somatotopically arranged, and highly collateralized projection systems that integrate striatal, thalamic, and cortical activity. If the CTSC loops are considered vertical, the internal circuits are horizontal and appear to modulate the excitability of the basal ganglia and maintain stability in the system (Obeso et ah, 2000). 

Fig. 7. A simulation of the Hamiltonian identification concept in Fig. 6 for a 10-state quantum system, with the observations being state populations. The data errors were taken as 1%. The closed loop optimal inversion was capable of finding a single experiment, which dramatically filtered out the data noise to produce Hamiltonian matrix elements with an order of magnitude better quality than that of the data noise. In contrast, a standard inversion involving 5000 observations gave significantly poorer results, including amplification of the laboratory noise.

Does not require identification and measurement of any disturbance for corrective action Does not require an explicit process model Is possible to design controller to be robust to process/model errors Control action not taken until the effect of the disturbance has been felt by the system Is unsatisfactory for processes with large time constants and frequent disturbances May cause instability in the closed-loop response... 

Other recent developments in the field of adaptive control of interest to the processing industries include the use of pattern recognition in lieu of explicit models (Bristol (66)), parameter estimation with closed-loop operating data (67), model algorithmic control (68), and dynamic matrix control (69). It is clear that discrete-time adaptive control (vs. continuous time systems) offers many exciting possibilities for new theoretical and practical contributions to system identification and control. 

Van den Hof, P. M. J., and Schrama, R. J. P., Identification and control—closed loop issues, 10th lEAC Symposium on System Identification, Copenhagen, Denmark (July, 1994). 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak... 

An adaptive posi-cast controller has been developed for dynamic systems with large time-delays [17]. Recently, the authors evaluated its performance in the context of a 4-megawatt combustor mod >1 that mimics many of the dynamic characteristics of an actual engine includi g a significant time-delay [18]. Using closed-loop input-output data and syste.n identification (SI), a model of the test-rig was derived. The resulting expression of the SI model is... 

One final point about closed-loop process control. Economic considerations dictate that to derive optimum benefits, processes must invariably be operated in the vicinity of constraints. A good control system must drive the process toward these constraints without actually violating them. In a polymerization reactor, the initiator feed rate may be manipulated to control monomer conversion or MW however, at times when the heat of polymerization exceeds the heat transfer capacity of the kettle, the initiator feed rate must be constrained in the interest of thermal stability. In some instances, there may be constraints on the controlled variables as well. Identification of constraints for optimized operation is an important consideration in control systems design. Operation in the vicinity of constraints poses problems because the process behavior in this region becomes increasingly nonlinear. 

The primary objective is to perform system identification, that is, obtain a plant model, especially that of the process, in order to design a controller. Two different situations can be considered open-loop system identification and closed-loop system identification. 

In open-loop system identification, it is assumed that the controller and reference signal are not present, that is, the control loop has not been closed. In such a case. Fig. 6.1 reduces to Fig. 6.2. The relationship between the input and output can then be written as... 

In closed-loop system identification, the controller is fully functioning and determining the value of the output based on the measured output value. Two different cases can be distinguished depending on the behaviour of the reference signal ... 

On the other hand, if there is an external excitation, then it is easier to perform closed-loop identification. However, if the excitation is much weaker than the disturbance, the model given by Eq. (6.58) will be determined. Thus, the signal-to-noise ratio is extremely important in closed-loop identification. Also, identification depends on the model structure that has been determined for the process. If the model structure chosen for Gp and G/ is different from the structure of G then the model can be identified even if the excitation is weak. Since most controllers do not have any sample time delays, if the structure chosen for Gp has at least one-sample time delay (as it should if it is a discrete system), then the closed-loop system can be easily identified even with a weak excitation. 

There are three different approaches in determining the model structure of a closed-loop system indirect identification, direction identification, and joint input-output identification. 

The second method is called direct identification, where the fact that the process is running in closed loop is ignored. In this type of identification, both the process and error structures must be simultaneously estimated. Thus, either a Box-Jenkins or a general prediction error model should be fit. Since this is one of the more common approaches to closed-loop system identification, it is necessary to examine the properties of this approach. It will be assumed that the prediction error method will be used. 

The third and final method for closed-loop process identification is called the joint input-output identification method, which uses all three signals, y and in order to identify a model of the system in a two-step procedure. In the first step, a model between r, and m, is fit to give... 

Shardt Y (2012a) Data quality assessment for closed-loop system identification and forecasting with application to soft sensors. Doctoral thesis. University of Alberta, Department of Chemical and Materials Engineering, Edmmiton, Alberta, Canada, doi http //hdl.handle.net/10402/ era.29018... 

---