Controlled variable cycling

The primary control variables at a fixed feed rate, as in the operation pictured in Figure 8, are the cycle time, which is measured by the time required for one complete rotation of the rotary valve (this rotation is the analog of adsorbent circulation rate in an actual moving-bed system), and the Hquid flow rate in Zones 2, 3, and 4. When these control variables are specified, all other net rates to and from the bed and the sequence of rates required at the Hquid... 

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 ... 

Cycling A periodic change in the controlled variable from one value to another. If uncontrolled this is known as hunting. 

The control variables can be constrained to fixed values (e.g. fixed initial temperature in a temperature profile) or constrained to be between certain limits. In addition to the six variables dictating the shape of the profile, ttotai can also be optimized if required. For example, this can be important in batch processes to optimize the batch cycle time in a batch process, in addition to the other variables. 

Control loops can be either stable or unstable. Instability is caused by a combination of process time lags discussed earlier (i.e., capacitance, resistance, and transport time) and inherent time lags within a control system. This results in slow response to changes in the controlled variable. Consequently, the controlled variable will continuously cycle around the setpoint value. 

Marlin and Hrymak (1997) reviewed a number of industrial applications of RTO, mostly in the petrochemical area. They reported that in practice a maximum change in plant operating variables is allowable with each RTO step. If the computed optimum falls outside these limits, you must implement any changes over several steps, each one using an RTO cycle. Typically, more manipulated variables than controlled variables exist, so some degrees of freedom exist to carry out both economic optimization as well as establish priorities in adjusting manipulated variables while simultaneously carrying out feedback control. 

In the heat-exchanger example the controlled variable T cycles as shown in Fig. 7.11a. When a load disturbance in inlet temperature (a step decrease in 7 ) occurs, both the period and the average value of the controlled variable T change. You have observed this in your heating system. When the outside temperature is colder, the furnace runs longer and more frequently, and the room temperature is lower on average. This is one of the reasons why you feel colder inside on a cold day than on a warm day for the same setting of the thermostat. 

ATV is illustrated in Fig. 14.8. A relay of height h is inserted as a feedback controller. The manipulated variable m is increased by h above the steadystate value. When the controlled variable x crosses the setpoint, the relay reduces m to a value k below the steadystate value. The system will respond to this bang-bang control by producing a limit cycle, provided the system phase angle drops below —180°, which is true for all real processes. 

The period of the limit cycle is the ultimate period (PJ for the transfer function relating the controlled variable x and the manipulated variable m. So the ultimate frequency is... 

There is a tendency among control and statistics theorists to refer to trial and error as one-variable-at-a-time (OVAT). The results are often treated as if only one variable were controlled at a time. The usual trial, however, involves variation in more than one controlled variable and almost always includes uncontrolled variations. The trial-and-error method is fortunately seldom a random process. The starting cycle is usually based on manufacturers specifications or experience with a similar process and/or material. Trial variations on the starting cycle are then made, sequentially or in parallel, until an acceptable cycle is found or until funds and/or time run out. The best cycle found, in terms of one or a combination of product qualities, is then selected. Because no process can be repeated exactly in all cases, good cure cycles include some flexibility, called a process window, based on equipment limitations and/or experience. 

In traditional process control, models are often used to predict the deviation of the controlled variable from the desired state, the process error. This assumes that one knows the desired state. In complex batch processes, the desired state of the process is also dependent on history and changing dynamically. Further, most process models have to predict the outcome of an entire cycle to determine if the product will be good, so predictions are not available in real time, even for a slow process like the autoclave cure however, partial models have been used as virtual sensors to expand on the information available from sensors [38]. Saliba et al. used a kinetic model to predict the degree of cure as a function of time and temperature in a mold and used that predicted degree of cure to time pressure application and determine the completion of cure. Others [39] have used the predictions of models together with the measured progress of the process to predict future trends and even project process outcomes. 

A closed-loop system with feedback, which is illustrated in Figure 13.2, is the central feature of a control system in bioprocess control, as well as in other processing industries. First, a set-point is established for a process variable. Then, the process variable measured in a bioreactor is compared with the set-point value to determine a deviation e. Based on the deviation, a controller uses an algorithm to calculate an output signal O that determines a control action to manipulate a control variable. By repeating this cycle during operation, successful process control is performed. The controller can be the operator when manual control is being employed. 

A three-state controller is used to drive either a pair of independent two-state actuators, such as heating and cooling valves, or a Didirec-tional motorized actuator. The controller is comprised of two on/off controllers, each with dead band, separated by a dead zone. While the controlled variable lies within the dead zone, neither output is energized. This controller can drive a motorized valve to the point where the manipulated variable matches the load, thereby avoiding cycling. 

A uniform cycle can also be forced by using on-off control to cycle the manipulated variable between two limits. The period of the cycle will be close to Tn if the cycle is symmetric the peak-to-peak ampli-... 

In an early version a more complex TWG with four variable phase shifted signals with controllable duty cycle [34] was investigated, primarily to determine the optimum signal shape driving the SIS-Separator. From these results the actual version was derived, which due to the concentration of the electronics and signals to the inevitable functions can be minimized with respect to size, cost, and power consumption even further. Still a generator-PCB circuit of 10 x 5 cm2 (Fig. 25a) appears rather large as compared to the PIMMS-Chip. 

To understand how the TCA cycle responds kinetically to changes in demand, we can examine the predictions in time-dependent reaction fluxes in response to changes in the primary controlling variable NAD. Figure 6.4 plots predicted reaction fluxes for pyruvate dehydrogenase, aconitase, fumarase, and malate dehydrogenase in response to an instantaneous change in NAD. The initial steady state is obtained... 

It is assumed that the slip dissolution mechanism [40] adequately describes the crack-tip process. The controlling variables are the stress intensity factor (from mechanical loading) and the crack-tip electrode potential (from electrochemical loading). The crack-tip repassivation process is important, because the kinetics of repassivation determine the fraction of the crack-tip area that remains bare over a slip-dissolution-repassivation cycle. The temperature dependence of the crack-tip process is brought into play through a temperature-dependent crack-tip strain... 

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. 

The MVC, Task 4, adjusts the manipulated variables to satisfy the specifications of the controlled variables. It accomplishes its objective using dynamic response forecasts predicted by the dynamic simulator. The entire computational cycle is repeated every time interval, typically a few minutes, and each cycle is based on data from the previous cycle. In each cycle the controller outputs are computed such as to minimize the difference between the predicted dynamic responses and the desired targets. The MVC action is updated every cycle based on new predicted dynamic responses and new targets. 

---