Process dynamic response

By this point, the reader should have an understanding of the need for and function of feedback control, should understand the elements of the feedback loop, and understand some of the qualitative features of the process dynamic response. While standard feedback control does not require extensive understanding of the process being controlled, some process understanding is important. In fact, the more we understand about the process, the easier our overall control system design may become. We will touch on 

3 FUNDAMENTALS OF SINGLE INPUT-SINGLE OUTPUT SYSTEMS Set-Point Change Load Disturbance 

Up to now, we have looked primarily at control as a means of maintaining the PV at a fixed set-point in the presence of load disturbances. Set-point changes are also types of disturbances that a control loop must be able to handle. Production rate changes, for example, require that a flow rate set-point be changed. We will use the set-point change disturbance and the load disturbance as a means of illustrating process dynamic response. 

It is possible to adjust the feedback control loop to give any of the above responses. The form of the response desired depends on the process being controlled. For the most part, responses Ci to C3 would give desired behaviour, since each results in a return of 

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Dyna.micPerforma.nce, Most models do not attempt to separate the equiUbrium behavior from the mass-transfer behavior. Rather they treat adsorption as one dynamic process with an overall dynamic response of the adsorbent bed to the feed stream. Although numerical solutions can be attempted for the rigorous partial differential equations, simplifying assumptions are often made to yield more manageable calculating techniques. 

Mathematically speaking, a process simulation model consists of a set of variables (stream flows, stream conditions and compositions, conditions of process equipment, etc) that can be equalities and inequalities. Simulation of steady-state processes assume that the values of all the variables are independent of time a mathematical model results in a set of algebraic equations. If, on the other hand, many of the variables were to be time dependent (m the case of simulation of batch processes, shutdowns and startups of plants, dynamic response to disturbances in a plant, etc), then the mathematical model would consist of a set of differential equations or a mixed set of differential and algebraic equations. 

Open-Loop versus Closed-Loop Dynamics It is common in industry to manipulate coolant in a jacketed reacdor in order to control conditions in the reacdor itself. A simplified schematic diagram of such a reactor control system is shown in Fig. 8-2. Assume that the reacdor temperature is adjusted by a controller that increases the coolant flow in proportion to the difference between the desired reactor temperature and the temperature that is measured. The proportionality constant is K. If a small change in the temperature of the inlet stream occurs, then depending on the value or K, one might observe the reactor temperature responses shown in Fig. 8-3. The top plot shows the case for no control (K = 0), which is called the open loop, or the normal dynamic response of the process by itself. As increases, several effects can be noted. First, the reactor temperature responds faster and faster. Second, for the initial increases in K, the maximum deviation in the reactor temperature becomes smaller. Both of these effects are desirable so that disturbances from normal operation have... 

The PI controller is by far the most commonly used controller in the process industries. The summation of the deviation with its integral in the above equation can be interpreted in terms of frequency response of the controller (Seborg, Edgar, and Melhchamp, Process Dynamics and Control, Wiley, New York, 1989). The PI controller produces a phase lag between zero and 90 degrees ... 

Feedforward Control If the process exhibits slow dynamic response and disturbances are frequent, then the apphcation of feedforward control may be advantageous. Feedforward (FF) control differs from feedback (FB) control in that the primary disturbance or load (L) is measured via a sensor and the manipulated variable (m) is adjusted so that deviations in the controlled variable from the set point are minimized or eliminated (see Fig. 8-29). By taking control action based on measured disturbances rather than controlled variable error, the controller can reject disturbances before they affec t the controlled variable c. In order to determine the appropriate settings for the manipulated variable, one must develop mathematical models that relate ... 

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... 

Basic process control system (BPCS) loops are needed to control operating parameters like reactor temperature and pressure. This involves monitoring and manipulation of process variables. The batch process, however, is discontinuous. This adds a new dimension to batch control because of frequent start-ups and shutdowns. During these transient states, control-tuning parameters such as controller gain may have to be adjusted for optimum dynamic response. 

Numerical simulations are designed to solve, for the material body in question, the system of equations expressing the fundamental laws of physics to which the dynamic response of the body must conform. The detail provided by such first-principles solutions can often be used to develop simplified methods for predicting the outcome of physical processes. These simplified analytic techniques have the virtue of calculational efficiency and are, therefore, preferable to numerical simulations for parameter sensitivity studies. Typically, rather restrictive assumptions are made on the bounds of material response in order to simplify the problem and make it tractable to analytic methods of solution. Thus, analytic methods lack the generality of numerical simulations and care must be taken to apply them only to problems where the assumptions on which they are based will be valid. 

The dynamic response used to describe fluid motion in the system is bulk velocity. Kinematic similarity exists with geom.etric similarity in turbulent agitation [32]. To duplicate a velocity in the kinematically similar system, the kno m velocity must be held constant, for example, the velocity of the tip speed of the impeller must be constant. Ultimately, the process result should be duplicated in the scaled-up design. Therefore, the geometric similarity goes a long way in achieving this for some processes, and the achievement of dynamic and/or kinematic similarity is sometimes not that essential. 

Because the most common impeller type is the turbine, most scale-up published studies have been devoted to that unit. Almost all scale-up situations require duplication of process results from the initial scale to the second scaled unit. Therefore, this is the objective of the outline to follow, from Reference [32]. The dynamic response is used as a reference for agitation/mixer behavior for a defined set of process results. For turbulent mixing, kinematic similarity occurs with geometric similarity, meaning fixed ratios exist between corresponding velocities. 

The aim of dynamic simulation is to be able to relate the dynamic output response of a system to the form of the input disturbance, in such a way that an improved knowledge and understanding of the dynamic characteristics of the system are obtained. Fig. 2.1 depicts the relation of a process input disturbance to a process output response. 

The strategy depends on the situation and how we measure the concentration. If we can rely on pH or absorbance (UV, visible, or Infrared spectrometer), the sensor response time can be reasonably fast, and we can make our decision based on the actual process dynamics. Most likely we would be thinking along the lines of PI or PID controllers. If we can only use gas chromatography (GC) or other slow analytical methods to measure concentration, we must consider discrete data sampling control. Indeed, prevalent time delay makes chemical process control unique and, in a sense, more difficult than many mechanical or electrical systems. 

The few examples of deliberate investigation of dynamic processes as reflected by compression/expansion hysteresis have involved monolayers of fatty acids (Munden and Swarbrick, 1973 Munden et al., 1969), lecithins (Bienkowski and Skolnick, 1974 Cook and Webb, 1966), polymer films (Townsend and Buck, 1988) and monolayers of fatty acids and their sodium sulfate salts on aqueous subphases of alkanolamines (Rosano et al., 1971). A few of these studies determined the amount of hysteresis as a function of the rate of compression and expansion. However, no quantitative analysis of the results was attempted. Historically, dynamic surface tension has been used to study the dynamic response of lung phosphatidylcholine surfactant monolayers to a sinusoidal compression/expansion rate in order to mimic the mechanical contraction and expansion of the lungs. 

The studies described in the preceding two sections have identified several processes that affect the dynamic behavior of three-way catalysts. Further studies are required to identify all of the chemical and physical processes that influence the behavior of these catalysts under cycled air-fuel ratio conditions. The approaches used in future studies should include (1) direct measurement of dynamic responses, (2) mathematical analysis of experimental data, and (3) formulation and validation of mathematical models of dynamic converter operation. 

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