Process controllers and control valve dynamics

Chapter 22 provides equations for typical process controllers and control valve dynamics. The controllers considered are the proportional controller, the proportional plus integral (PI) controller and the proportional plus integral plus derivative (PID) controller. Integral desaturation is an important feature of PI controllers, and mathematical mc els are produced for three different types in industrial use. The control valve is almost always the final actuator in process plan. A simple model for the transient response of the control valve is given, which makes allowance for limitations on the maximum velocity of movement. In addition, backlash and velocity deadband methods are presented to model the nonlinear effect of static friction on the valve. 

Control Valve Dynamics. Control valve dynamics tend to be relatively fast compared to the dynamics of the process itself. However, the overall behavior of pneumatic control valves can include nonlinear phenomena such as dead band, stick-slip phenomena, backlash and hysteresis (Blevins et al., 2003 Edgar et al., 2008). Dead band and hysteresis are illustrated in Fig. 9.9. Fortunately, their effects can be reduced significantly by employing valve positioners. 

Hot and cold liquids are mixed at the junction of two pipes. The temperature of the resulting mixture is to be controlled using a control valve on the hot stream. The dynamics of the mixing process, control valve, and temperature sensor/transmitter are negligible and the sensor-transmitter gain is 6 mA/mA. Because the temperature sensor is located well downstream of the junction, an 8 s time delay occurs. There are no heat losses/gains for the downstream pipe. 

From a dynamic-response standpoint, the adjustable speed pump has a dynamic characteristic that is more suitable in process-control apphcations than those characteristics of control valves. The small amphtude response of an adjustable speed pump does not contain the dead baud or the dead time commonly found in the small amphtude response of the control valve. Nonhnearities associated with frictions in the valve and discontinuities in the pneumatic portion of the control-valve instrumentation are not present with electronic... 

Step 9 Apply steps to inlet and bypass valves. Now that the new inlet and bypass valve positions are determined, the outputs to the valves can be changed. Before doing this, however, due to flexibility in the control system, it is still possible to manipulate the step on the valve. For this purpose, the control system provides scaling factors between the actual step and the calculated step. These scaling factors can help compensate for calculation errors and/or process dynamics. This is formulated as ... 

The dynamic response of most transmitters is usually much faster than the process and the control valves. Consequently we can normally consider the transmitter as a simple gain (a step change in the input to the transmitter gives an instantaneous step change in the output). The gain of the pressure transmitter considered above would be... 

In some situations it is very important to be able to increase the flow rate above the design conditions (for example, the cooling water to an exothermic reactor may have to be doubled or tripled to handle dynamic upsets). In other cases this is not as important (for example, the feed flow rate to a unit). Therefore it is logical to base the design of the control valve and the pump on having a process that can attain both the maximum and the minimum flow conditions. The design flow conditions are only used to get the pressure drop over the heat exchanger (or fixed resistance part of the process). 

The design of a chemical engineering system always involves a number of trade-ofls. We have already discussed the conflicts between the process engineer and the control engineer in the question of control valve sizing. There are many other such conflicts between what would be the optimum from only a steadystate standpoint and what is needed to handle the dynamics of the process. 

We know that the temperature control of the shower in a bathroom is not so easy. To have a comfortable shower, a hot water valve needs to be manipulated carefully (control action) however, we usually rely on a trial and error action until the proper temperature of a shower is achieved. How can we achieve the most comfortable shower temperature more quickly This is a common problem in the control action of many processes that are controlled by a feedback loop. The difficulty comes from a delay in the response, which naturally exists in any process - in other words, the dynamic characteristics of a process. Therefore, the control action should be determined based on the dynamics of the process. In particular, some bioprocesses are known to have serious delays in response. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Positioner Application Positioners are widely used on pneumatic valve actuators. Often they provide improved process loop control because they reduce valve-related nonlinearity. Dynamically, positioners maintain their ability to improve control valve performance for sinusoidal input frequencies up to about one-hall of the positioner bandwidth. At input frequencies greater than this, the attenuation in the positioner amplifier network gets large, and valve nonlinearity begins to affect final control element performance more significantly. Because of this, the most successful use of the positioner occurs when the positioner response bandwidth is greater than twice that of the most dominant time lag in the process loop. 

In the conventional control loop, the measurement lag is only part of the total time lag of the control loop. For example, an air heater might have a total lag of 15 minutes. Of this lag, 14 minutes is contributed by the process lag, 50 seconds by the bulb lag, and 10 seconds by the control valve lag. Bypass control is often applied to circumvent the dynamic characteristics of heat exchangers, thus improving their controllability. Bypass control can be achieved by the use of either one three-way valve or two two-way valves. 

This cycling can be eliminated by mounting the control valve in the condensate pipe, but this creates new problems, because when the load decreases, the process is slow steam has to condense before the condensate level is affected, and when the load increases, the process is fast, because blowing out liquid condensate is fast. With such "nonsymmetrical" process dynamics, control is bound to be poor. A better option is to use lifting traps to prevent condensate accumulation. These pumping traps will make temperature control possible even when the heater is under vacuum, but will not improve the problem of low rangeability, and the possible use of two control valves in parallel can still be necessary. 

Greg Shinskey (1988), over the course of a long and productive career at Foxboro, has proposed a number of advanced control" structures that permit improvements in dynamic performance. These schemes are not only effective, but they are simple to implement in basic control instrumentation. Liberal use should be made of ratio control, cascade control, override control, and valve-position (optimizing) control. These strategies are covered in most basic process control textbooks. 

After satisfying all of the basic regulatory requirements, we usually have additional degrees of freedom involving control valves that have not been used and setpoints in some controllers that can be adjusted. These can be utilized either to optimize steady-state economic process performance (e.g., minimize energy, maximize selectivity) or to improve dynamic response. 

Step 8. The previous steps have left us at this point with two unassigned control valves, which are the reflux flows to each column. As discussed in Chap. 6, these are independent variables and can be fixed by flow controllers. We do not need dual composition control for the irreversible case because only one end of both columns is a product stream leaving the process. These two reflux flowrates are available in Step 9 to use as optimizing variables or to improve dynamic response. However, we may need dual composition control in the DIB column for the reversible case as mentioned in Steps 4 and 5. 

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