Closed-loop method

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

A pilot pattern should be chosen so that the injected fluid is well controlled within the pattern. Otherwise, the fluid may be lost through directional flow channels. Then any interpretation or evaluation of the pilot performance would be difficult. When evaluation wells are drilled, cores should be taken in a closed-loop method so that reservoir conditions are maintained. These cores are used to evaluate alkaline consumption, measure relative permeabilities, and so on. Formation evaluation tests are conducted at evaluation wells. Finally, simulation models (sector models) are built to integrate all the data taken to evaluate the alkaline flooding performance. 

Apart from galvanic separation and the possibility of measuring both dc and ac currents, the closed-loop method has several other advantages. The range of currents being measured is much larger than in open-loop devices and only limited by how much current the feedback circuit can deliver. Since the sensor always... 

We also examined the effects of NO donors on the intestinal absorption of calcitonin by using an in situ closed loop method in rats. A significant hypocalcemic effect was observed after the administration of calcitonin and NO donors to the intestinal loops of rats (Fig. 5.3). Similar results were also obtained in the case of 5(6)-carboxy-fluorescein (CF) [27] and insulin. Thus, NO donors may be useful for enhancing the intestinal absorption of poorly absorbable drugs (e.g., some peptide biopharmaceuticals), and indeed they may be one of the most ideal enhancers in practical use. 

One good feature of the Ziegler-Nichols closed-loop method is that it can be learned more quickly than starting with trial and error alone. There is a procedure to be followed, and the pattern of sustained cycling is easy to recognize. The Ziegler-Nichols method is often completely acceptable for tuning control loops that respond quickly, for example, liquid flow rate control loops that respond with an ultimate peak-to-peak time period (UTP) of 5 to 15 s. 

The development of the Robbins closed-loop tuning methodology was the result of about 11 years of development with collaboration and feedback of comments from others. A number of different methods for tuning process control loops were tested along the way, and this new closed-loop method using pattern recognition was determined to be the most cost-effective. 

In contrast to the DC motors, which employ current switching and therefore perform poorly at low speeds, this closed-loop method of controlling stepping motors performs quite accurately even at very low velocities. On the other hand, the generation of the sinusoidally modulated input currents requires both accurate position measurement and separate current choppers for each phase. Thus the implementation cost is somewhat higher than a servo system utilizing DC motors. 

Perhaps the most well known and most frequently published method is that by Ziegler and Nichols (Reference 3). They developed an open loop method in addition to the more frequently published closed loop method. The criterion used by both methods is the quarter decay ratio. This is illustrated in Figure 3.21 following a SP change the PV response should be slightly oscillatory with the height of the second peak being one-quarter of that of the first. 

Othman et al. [86] proposed a closed-loop method to control molecular weight. They used NIR to estimate conversion. They developed a nonlinear estimator to get the reaction rate necessary for the control loop. This method reUes on the quality of off-line measurements necessary for NIR calibration. They used nonlinear high-gain observers to identify model parameters and the reaction rates which were used to obtain desired monomer feeds to keep constant. This feedback control produced high molecular masses which could not be achieved in open-loop cases but the approach still relies on the quality of the model. 

Constant cycling methods Ziegler—Nichols closed-loop method... 

When tuning using the Ziegler-Nichols closed-loop method, values for proportional, integral, and derivative controller parameters may be determined from the ultimate period and ultimate gain. These are determined by disturbing the closed-loop system and using the disturbance response to extract the values of these constants. 

The following is a step-by-step approach to using the Ziegler-Nichols closed-loop method for controller tuning ... 

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