Control-loop

The four elements described previously are the main components of what by convention is called a control loop, depicted in Fig. 3.2, as follows  

In formal terms, what happens to the information within each block of the control loop is a mathematical transformation that we call a transfer function. Suppose that in the example of the shower, it is not the skin that is used for measuring temperature but a thermometer that is able to deliver the exact temperature of the water. With this assumption, it is easy to explain the transfer function of the comparator (represented by a circle in Fig. 3.2), which is given by the following equation  

To understand this more clearly, consider that the desired temperature, the set point, is 40 °C. If the measured temperature is 44 °C, then the error will be 44 - 40 = +4 °C, i.e., 4 °C above the desired temperature (Fig. 3.3). Now, if the measured temperature was 38 °C, then the error would be 38 -40 = -2 °C, or 2 °C below the desired temperature (Fig. 3.3). In this simple case, it turns out that the transfer function is a straight line, as shown in Fig. 3.3, where the x-axis is the measured temperature and the y-axis is the error. Transfer functions of the other elements of the control loop are a bit more complex therefore they will be addressed in Chap. 9. As in this example, it is easier to use positive feedback error. However, in practice, it is more conmum to use negative feedback error, i.e., the set point (Tsp) minus the measured value (T,n). 

The strategy of formulating a cmitrol problem through a loop has tremendous potential because it is a highly standardized, orderly, and robust procedure to address cmitrol problems. It divides a process into elements with clear boundaries and makes it easy to recognize what should work and how to assemble the parts. 

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A pilot plant typically has significantly more control loops than the average process faciUty. Caution should be used when applying process correlations in the absence of a detailed design. 

Based on a typical medium-sized pilot plant of 10—20 control loops. For smaller units (<10 control loops) reduce the above by 25—40% for larger units (20—40 control loops) increase the costs by 50—100%. 

Instrumentation. Pilot plants are usually heavily instmmented compared to commercial plants. It is not uncommon for a pilot plant to have an order of magnitude more control loops and analytical instmments than a commercial plant because of the need for additional information no longer requked at the commercial stage. A discussion of all the specific types of instmmentation used on pilot plants is beyond the scope of this article. Further information on some of the more common instmmentation is available (1,51). 

Fig. 7. Instmment components of a control loop, where A = process measurement devices, in this case, pressure measurement B = transducer ...

The dynamics of the secondary control loop should be approximately two to four times as fast as the dynamics of the primary control loop in order to achieve stable control. The secondary controller is actually part of the primary controller s process system. Hence, changes in the secondary controller tuning constants change the process system of the primary controller. Therefore, cascade control loops should always be tuned by first tuning the secondary controller and then the primary controller. If the secondary controller tuning is changed for any reason, the primary controller may need to be retuned also. 

Many misconceptions exist about cascade control loops and their purpose. For example, many engineers specify a level-flow cascade for every level control situation. However, if the level controller is tightly tuned, the out-flow bounces around as does the level, regardless of whether the level controller output goes direcdy to a valve or to the setpoint of a flow controller. The secondary controller does not, in itself, smooth the outflow. In fact, the flow controller may actually cause control difficulties because it adds another time constant to the primary control loop, makes the proper functioning of the primary control loop dependent on two process variables rather than one, and requites two properly tuned controllers rather than one to function properly. However, as pointed out previously, the flow controller compensates for the effect of the upstream and downstream pressure variations and, in that respect, improves the performance of the primary control loop. Therefore, such a level-flow cascade may often be justified, but not for the smoothing of out-flow. 

Dead-Time Compensation. Dead time within a control loop can greatiy iacrease the difficulty of close control usiag a PID controller. Consider a classical feedback control loop (Fig. 18a) where the process has a dead time of If the setpoiat is suddenly iacreased at time t, the controller immediately senses the deviation and adjusts its output. However, because of the dead time ia the loop, the coatroUer does aot begia to see the impact of that change ia its feedback sigaal, that is, a reductioa ia the deviatioa from setpoiat, uatil the time t +. Because the deviatioa does aot change uatil... 

Feedback Control In a feedback control loop, the controlled variable is compared to the set point R, with the difference, deviation, or error e acted upon by the controller to move m in such a way as to minimize the error. This ac tion is specifically negative feedback, in that an increase in deviation moves m so as to decrease the deviation. (Positive feedback would cause the deviation to expand rather than diminish and therefore does not regulate.) The action of the controller is selectable to allow use on process gains of both signs. 

Strong process interacHons can cause serious problems if a conventional multiloop feedback control scheme (e g., PI or PID controllers) is employed. The process interacHons canproduce undesirable control loop interac tions where the controllers fight each other. Also, it may be difficult to determine the best pairing of controlled and manipulated variables. For example, in the in-hne blending process in Fig. 8-40(<7), should w be controlled with and x with tt>g, or vice versa ... 

Control Strategies for Multivariable Control Problems If a conventional multiloop control strategy performs poorly due to control loop interactions, a number of solutions are available ... 

Detuning a controller (e.g., using a smaller controller gain or a larger reset time) tends to reduce control loop interactions by sacrificing the performance for the detuned loops. This approach may be acceptable if some of the controlled variables are faster or less important than others. 

The selection of controlled and manipulated variables is of crucial importance in designing a control system. In particular, a judicious choice may significantly reduce control loop interactions. For the blending process in Fig. 8-40(d ), a straightforward control strategy would be to control x by adjusting w, and w by adjusting Wg. But... 

Decoupling Control Systems Decoupling control systems provide an alternative approach for reducing control loop interactions. The basic idea is to use additional controllers called decouplers to compensate for undesirable process interactions. 

In principle, ideal decouphng eliminates control loop interactions and allows the closed-loop system to behave as a set of independent control loops. But in practice, this ideal behavior is not attained for a variety of reasons, including imperfect process models and the presence of saturation constraints on controller outputs and manipulated variables. Furthermore, the ideal decoupler design equations in (8-52) and (8-53) may not be physically realizable andthus would have to be approximated. 

Figure 8-47 presents a P I diagram for a simple temperature control loop that adheres to the ISA symbology. The measurement... 

Distillation columns have four or more closed loops—increasing with the number of product streams and their specifications—all of which interact with each other to some extent. Because of this interaction, there are many possible ways to pair manipulated and controlled variables through controllers and other mathematical functions with widely differing degrees of effectiveness. Columns also differ from each other, so that no single rule of configuring control loops can be apphed successfully to all. The following rules apply to the most common separations. 

Regulatory Control For most batch processes, the discrete logic reqmrements overshadow the continuous control requirements. For many batch processes, the continuous control can be provided by simple loops for flow, pressure, level, and temperature. However, very sophisticated advanced control techniques are occasionally apphed. As temperature control is especially critical in reactors, the simple feedback approach is replaced by model-based strategies that rival if not exceed the sophistication of advanced control loops in continuous plants. 

Sample Transport Transport time, the time elapsed between sample withdrawal from the process and its introduction into the analyzer, shoiild be minimized, particiilarly if the analyzer is an automatic analyzer-controller. Any sample-transport time in the analyzer-controller loop must be treated as equivalent to process dead time in determining conventional feedback controller settings or in evaluating controller performance. Reduction in transport time usually means transporting the sample in the vapor state. 

Automated control schemes employ one or more sets of controls, which will fit into three categories (1) control loops which are used to regulate the addition of tlocciilant, (2) control loops to regulate the withdrawal of Iindertlow, and (3) rake dri e controls. Usually, the feed to a thickener is not controlled and most control systems ha e been designed with some tlexibility to deal with changes in feed characteristics, such as an increase in oliirne or alteration in the nature of the solids thernseh es. In se ere cases, some equalization of the feed is required in order to allow the control system to perform effecth ely. 

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