Valve, control dynamic model

We showed through nonlinear dynamic simulations how the process reacts to various disturbances and changes in operating conditions. We have not shown any attempts to optimize process performance, to improve the process design, or to apply any advanced control techniques (model-based, nonlinear, feedforward, valve-position, etc.). These would be the natural next steps after the base-level regulatory control system had been developed to keep the process at a stable desired operating point. 

A simple example can be used to illustrate the concept of the use of dynamic models in simulation and control. Consider the water tank shown in Figure 3.4, where the valve at the bottom discharges water at a rate proportional to the head /z. It is well known that the discharge is proportional to -Jh-, however, we use the assumption that it is proportional to h in order to make the equations linear and, therefore, illustrate the ideas in a simple manner. 

Consider the horizontal cylindrical tank shown in Fig. E16.27a, which is based on the model presented in Example 4.7. The output of the system, the controlled variable, is the height of the tank, h(t), and the input of the system, the manipulated variable, is the opening of the valve, x, which is proportional to the input flow, qi. The nonlinear dynamic model of the system is represented by the following equation ... 

Consider the model s reactor assuming saturation in the control valve and negligible dynamic s jacket as shows in Eq.(43). The steady states of system (43) can be obtained considering that the derivatives of the left hand of Eq.(43) are nil and... 

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. 

In a dynamic simulation, controllers are used to model the real control valves of the process. When converting a steady-state simulation to a dynamic simulation, some care is needed to ensure that the controller functions correspond to physically achievable control structures. 

An important design tool is the use of "Dynamic Simulation". This computer modeling technique was used to verify that the control systems were adequate for the purchased equipment (such as pumps, compressors, control valves, heat exchangers and pipe sizing) and were in fact going to meet our stated control objective. 

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. 

Equations (2.21) have been written in the order and manner above to bring out the dynamic interdependence of the states that will normally emerge as a feature of models of typical industrial processes. While the derivative of one state may depend only on the current value of that state, as in the case of the valve travels, x and Xi, others will depend not only on their own state but also on a number of others. This latter situation arises above in the cases of control valve travel, Xi, and the liquid mass in the tank, m. The dependence may be linear in some cases, but in any normal process model, there will be a large number of nonlinear dependencies, as exhibited above by the derivative for tank liquid mass, which is dependent on a term multiplying the square of one state by the square-root of another. This is an important point to grasp for those more accustomed to thinking of linear, multivariable control systems such systems are idealizations only of a nonlinear world. 

In Appendix 11A we developed the mathematical model that describes the dynamic behavior of a pneumatic control valve. This was shown to be of second-order. But the response to changes, of most small... 

The process reaction curve for this system provides us with an experimental model of the overall process which we can use to tune the controller without requiring detailed knowledge of the dynamics for the reactor, heating jacket, thermocouple, and control valve. 

The simple human task that we want to model is of an operator responding to an annunciator. The procedure requires that the operator compare readings on two meters. Based on the relative values of these readings, the operator must either open or close a valve until the values on the two meters are nearly the same. The task network in Figure 9 represents the operator activities for this model. Also, to allow the study of the effects of different plant dynamics (e.g., control lags), a simple one-node model of the line in which the valve is being opened is included in Figure 10. 

However, to date, it is generally agreed, by both researchers and practitioners that bottle testing is still a good guide (257). The bottle test is static and does not model closely the dynamic effects of water droplets dispersed or coalescing in the actual equipment such as control valves, pipes, inlet delivery, baffles, water wash, ete. If the point of injection of chemicals is upstream of the settler, then the test approximates the situation better. It is, however, still crucial that the characteristies of the emulsion be understood before the treatment system is selected (273, 274). 

An Aspen Flash model is used for the reflux drum with pressme set at 1 bar and design specification of a vapor fraction of 10 , which makes the drum essentially adiabatic. A small vapor flow rate is necessary so that the control valve in this vent line can be sized. In the Aspen Dynamics simulation, the valve is completely closed. The liquid holdup in the drum is set to give 5 min at 50% full (diameter 3 m and length 6 m). 

The purpose is to develop a steam balance for operational supervision as well as for identification of improvement opportunities in the steam system. Models for boilers, turbines, deaerators (DAs), letdown valves, desuperheaters, and steam flash tanks are discussed in the previous chapter. Historian and distributed control system (DCS) data will be coimected to steam balance so that the steam balance is capable of dynamically balancing the steam and power demands due to process variations, units on or off, and weather change. 

In many industrial control problems, notably those involving temperature, pressure, and flow control, measurements of the controlled variable are available, and the manipulated variable is adjusted via a control valve. In feedback control, corrective action is taken regardless of the source of the disturbance. Its chief drawback is that no corrective action is taken until after the controlled variable deviates from the set point. Feedback control may also result in undesirable oscillations in the controlled variable if the controller is not tuned properly, that is, if the adjustable controller parameters are not set at appropriate values. The tuning of the controller can be aided by using a mathematical model of the dynamic process, although an experienced control engineer can use trial-and-error tuning to achieve satisfactory performance in many cases. Next, we discuss the two types of controllers used in most commercial applications. 

---