Open-loop experiments

Based on what we have obtained in Example 5.7, if we did an open-loop experiment as suggested in Eq. (6-1), our step response would fit well to the function ... 

It is the ratio of the partial derivative evaluated under two different circumstances. On top, we look at the effect of in, while holding m2 constant. The calculation represents an open-loop experiment... 

Here, max and jrm n denote, respectively, the maximum and the minimum values of the muscular activation, a determines the slope of the feedback curve, S is the displacement of the curve along the flow axis, and Fneno is a normalization value for the Henle flow. The relation between the glomerular filtration and the flow into the loop of Henle can be obtained from open-loop experiments in which a paraffin block is inserted into the proximal tubule and the rate of glomerular filtration (or, alternatively, the so-called tubular stop pressure at which the filtration ceases) is measured as a function of an externally forced rate of flow of artificial tubular fluid into the loop of Henle. Translation of the experimental results into a relation between muscular activation and Henle flow is performed by means of the model, i.e., the relation is adjusted such that it can reproduce the experimentally observed steady state relation. We have previously discussed the significance of the feedback gain a in controlling the dynamics of the system, a is one of the parameters that differ between hypertensive and normotensive rats, and a will also be one of the control parameters in our analysis of the simulation results. 

Pattern factor control using fuel control requires a combustion system that incorporates individual fuel-injection site control to allow for fuel modulation to produce the desired temperature pattern. Thus, an advanced combustor with zonal fuel control capability has been selected for demonstrating APFC. Activities associated with the preparation for APFC open-loop experiments with this combustor are described along with results from supporting numerical simulations. 

Theoretically, the main concerns lie with identifiability of a process, that is, given a data set and model structure (order of polynomials), what are the conditions for there to be a unique solution to the parameter estimates. For open-loop experiments, the identifiability constraint for a prediction error model can be simply written as... 

A related approach to estimating the time delay is to determine the impulse response coefficients, h, for the model. Similar to the cross-correlation plot, the first nonzero value would be assumed to be equal to the time delay. A typical impulse response plot is shown in Fig. 6.5 (right). In this plot, the time delay would be estimated as being four, since that is the last nonzero value before the significant peak. This method requires that the data be obtained from an open-loop experiment. 

The CCD detector and the potentiostat were synchronized in an open-loop configuration by starting the experiment with a common trigger. Careful measurements... 

Another advantage of frequency response analysis is that one can identify the process transfer function with experimental data. With either a frequency response experiment or a pulse experiment with proper Fourier transform, one can construct the Bode plot using the open-loop transfer functions and use the plot as the basis for controller design.1... 

Now, from its essential notion, we have the feedback interconnection implies that a portion of the information from a given system returns back into the system. In this chapter, two processes are discussed in context of the feedback interconnection. The former is a typical feedback control systems, and consists in a bioreactor for waste water treatment. The bioreactor is controlled by robust asymptotic approach [33], [34]. The first study case in this chapter is focused in the bioreactor temperature. A heat exchanger is interconnected with the bioreactor in order to lead temperature into the digester around a constant value for avoiding stress in bacteria. The latter process is a fluid mechanics one, and has feedforward control structure. The process was constructed to study kinetics and dynamics of the gas-liquid flow in vertical column. In this second system, the interconnection is related to recycling liquid flow. The experiment comprises several superficial gas velocity. Thus, the control acting on the gas-liquid column can be seen as an open-loop system where the control variable is the velocity of the gas entering into the column. There is no measurements of the gas velocity to compute a fluid dynamics... 

A set of experiments on gas-liquid motion in a vertical column has been carried out to study its d3mamical behavior. Fluctuations volume fraction of the fluid were indirectly measured as time series. Similar techniques that previous section were used to study the system. Time-delay coordinates were used to reconstruct the underl3ung attractor. The characterization of such attractor was carried out via Lyapunov exponents, Poincare map and spectral analysis. The d3mamical behavior of gas-liquid bubbling flow was interpreted in terms of the interactions between bubbles. An important difference between this study case and former is that gas-liquid column is controlled in open-loop by manipulating the superficial velocity. The gas-liquid has been traditionally studied in the chaos (turbulence) context [24]. 

We will first concentrate on studying the process dynamics, so let us consider a numerical experiment that consists of starting a dynamic simulation of the process from initial conditions that are slightly perturbed from the nominal, steady-state values of the state variables. Although material holdups are stabilized using the proportional controllers in Equation (4.40), in view of the process-level operating objective stated above, this can be considered an open-loop simulation. 

To date, similar experiments on dissociative ionization of molecules by adaptively shaped ultrashort laser pulses have been reported, where specific ion ratios were targeted during iterative control using GA and SA [14,15]. However, less detailed comparisons between adaptive control and open-loop control experiments regarding the laser pulse width, pulse train, and peak intensity exist. Moore et al. claimed that not only accelerated specific bondbreaking, but even new bond formation, can specified by adaptive pulse shape control [14]. Because ethanol molecules have a relatively simple main struc-... 

The desired purity for the experiment reported below was set to 55.0% and the controller was started at the 60th period. As in the simulation study, a diagonal matrix R = 0.02 I (3,3) was chosen for regularization. The control horizon was set to Hr = 1 and the prediction horizon was Hv = 60 periods. Figure 9.10 shows the evolution of both the product purity and the controlled variables. In the open-loop mode, where the operating point was calculated based on the initial model, the product purity constraint was violated at periods 48 and 54. After one cycle, the controller drove the purity above 55.0% and kept it there. The controller first reduces the desorbent consumption. This action seems to contradict the intuitive idea that more desorbent injection should enhance separation. However, in the presence of a reaction, this is not true, as shown by this experiment. The controlled variables converge towards a steady state, but they still change from period to period, due to the non-ideality of the plant. 

Fig. 12.20 O2 conversion data versus temperature for the oxidation of CH4 for three microreactor channels. Open-loop temperature control was used in this experiment with each heater set to the same heater voltage. The temperature used for the plot is the average of the measured RTD temperatures. These results come from one AIMS experiment with three...

After washing the columns in an open-loop system for 4-6 h with PBS, and then overnight in a closed-loop system with 20 mL of PBS, a further 30% of the initially bound protein was removed, until an equilibrium had been established between the bound and unbound proteins. On changing the PBS eluent to heat-defibrinated plasma (containing antithrombin III), the desorption of both 125I-thrombin and 125I-antithrombin III from the column increased dramatically. In the experiments with radiolabeled antithrombin III, the column had been exposed previously to thrombin, therefore, the displaced radiolabeled antithrombin III should more properly be described as labeled inactive complex. Because defibrinated plasma contains anti-... 

The desired purity for the experiment reported below was set to 55.0% and the controller was started at the 60th period. Figure 7.47 shows the evaluation of the product purity as well as of the controlled variables. In the open loop mode where the operating point was calculated based on the initial model, the... 

Equations S.2-8.8 constitute an open-loop observer/estimator that is completely dependent on model responses and whose rate of convergence is not adjustable (no feedback action) [ 132 ]. Note that if the observer error at t = 0 is equal to zero (the initial conditions are known with very high precision), it will remain equal to zero during the rest of the process, provided that the model is correct. All the model contributions to the estimator are included in D12, where the only parameters are the reactivity ratios and the heat of polymerization. These parameters can be obtained by independent experiments with a good accuracy. 

Extensions of Kalman filters and Luenberger observers [131 Solution polymerizations (conversion and molecular weight estimation) with and without on-line measurements for A4w [102, 113, 133, 134] Emulsion polymerization (monomer concentration in the particles with parameter estimation or not (n)) [45, 139[ Heat of reaction and heat transfer coefficient in polymerization reactors [135, 141, 142] Computationally fast, reiterative and constrained algorithms are more robust, multi-rate (having fast/ frequent and slow measurements can be handled)/Trial and error required for tuning the process and observation model covariance errors, model linearization required The number of industrial applications is scarce A critical article by Wilson eta/. [143] reviews the industrial implementation and shows their experiences at Ciba. Their main conclusion is that the superior performance of state estimation techniques over open-loop observers cannot be guaranteed. 

Often, batch polymerization control is a matter of specifying an open-loop policy for the introduction of various materials. Due to the fact that there is no steady state around which to regulate, and to the fact that by the time a problem is detected, the batch may have progressed beyond the point of possible corrective action, it is often useful to track the behavior of a polymerization from batch to batch, and re-optimize the current batch based on the experience gained in preceding batches. An example is shown in Figure 5.10. Here a mathematical model is used to specify the optimal initiator... 

The ability of the controller to handle process disturbances was examined by simulating abrupt variations in feed quality. This was simulated by increasing the concentration of inhibitor in the monomer from zero to 10 ppm. The variation in feed quality is a common problem in industrial practice and results from the deliberate addition of inhibitor to monomer to prevent premature polymerization. If monomer purification to remove inhibitor is not done (and it often is not in commercial operations), the switching of monomer feed tanks can produce undesirable and unexpected effects on the process outputs. In the open loop, the increase in inhibitor concentration from zero to 10 ppm causes a drop in the monomer conversion from 0.247 to 0.169. The particle size output also experiences a decline from 0.762 to 0.737. The reduction in polymerization rate is a direct result of the decreased initiator flux into the polymer particles, and the drop in particle size reflects the diminished... 

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