Dynamic responses

The response time ton from the OFF state to the ON state and the response time TOFF from the ON state to the OFF state are given by equations (4.2.4) and (4.2.5), respectively [16]. 

5 2005 KohM Takatoh, MasaM Hasegawa, Mitsuhiro Koden, Nobuyuki Itoh, Ray Hasegawa and Masanori Sakamoto 

Consider next a more general situation where the weak external perturbation is time-dependent, F = F(Z). We assume again that the force is weak so that, again, the system does not get far from the equilibrium state assumed in its absence. In this case, depending on the nature of this external force, two scenarios are usually encountered at long time. 

When a constant force is imposed on an open system, the system will eventually reach a nonequilibrium steady state where the response to the force appears as a time-independent flux. (A closed system in the same situation will reach a new equilibrium state, as discussed above.) 

When the external force oscillates with a given frequency, the system will eventually reach a dynamic steady state in which system observables oscillate with the same frequency and often with a characteristic phase shift. The amplitude of this oscillation characterizes the response the phase shift is associated with the imaginary part of this amplitude. 

The most general linear relationship between the force F(Z) and the response (A5(Z) is then 

Note that causality, that is, the recognition that the response at time t can depend only on past perturbations and not on future ones, is built into (11.18). It is convenient to write 

PERPENDICULAR 33 LOAD O.64k0/cm2 The typical curve of contraction 

---

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... 

As an alternative to deriving Eq. (8-2) from a dynamic mass balance, one could simply postulate a first-order differential equation to be valid (empirical modeling). Then it would be necessary to estimate values for T and K so that the postulated model described the reactor s dynamic response. The advantage of the physical model over the empirical model is that the physical model gives insight into how reactor parameters affec t the v ues of T, and which in turn affects the dynamic response of the reac tor. 

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 ... 

Pneumatic controllers are made of Bourdon tubes, bellows, diaphragms, springs, levers, cams, and other fundamental transducers to accomplish the control function. If operated on clean, diy plant air, they offer good performance and are extremely reliable. Pneumatic controllers are available with one or two stages of pneumatic amphfi-cation, with the two-stage designs having faster dynamic response characteristics. 

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... 

Regulators may be used in gas blanketing systems to maintain a protective environment above anv liquid stored in a tank or vessel as the liquid is pumped out. When the temperature of the vessel is suddenly cooled, the regulator maintains the tank pressure and protects the waUs of the tank from possible collapse. Regulators are known for their fast dynamic response. The absence of time delay that often comes with more sophisticated control systems makes the regulator useful in applications requiring fast corrective action. 

Although dynamic responses of microbial systems are poorly understood, models with some basic features and some empirical features have been found to correlate with actual data fairly well. Real fermentations take days to run, but many variables can be tried in a few minutes using computer simulation. Optimization of fermentation with models and reaf-time dynamic control is in its early infancy however, bases for such work are advancing steadily. The foundations for all such studies are accurate material Balances. 

Although motors and controllers can be bought separately, the trend is to purchase a system from a given manufacturer. There are six types oi variable-speed drives, as own in F ig. 29-73. Dynamic response indicates the ability of the drive to respond to a change in command it is measured in radians/second the higher the number, the faster the drive response. 

Type of Drive Speed Range Starting Torque Maximum Speed Dynamic Response... 

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. 

Fowles, G.R. (1972), Experimental Technique and Instrumentation, in Dynamic Response of Materials to Intense Impulsive Loading (edited by P.C. Chou and A.K. Hopkins), pp. 405-480. 

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. 

Oscarson, J.H. and Graff, K.F., Summary Report on Spall Fracture and Dynamic Response of Materials, Battelle Memorial Institute Report No. BAT-197A-4-3, Columbus, OH, 37 pp., March 1968. 

Figure 5-38 shows plots of the dynamic response to changes in the inlet concentration of component A. The figure represents possible responses to an abrupt change in inlet concentration of an isothermal CFSTR with first order irreversible reaction. The first plot illustrates the situation where the reactor initially contains reactant at and... 

Many HVAC system engineering problems focus on the operation and the control of the system. In many cases, the optimization of the system s control and operation is the objective of the simulation. Therefore, the appropriate modeling of the controllers and the selected control strategies are of crucial importance in the simulation. Once the system is correctly set up, the use of simulation tools is very helpful when dealing with such problems. Dynamic system operation is often approximated by series of quasi-steady-state operating conditions, provided that the time step of the simulation is large compared to the dynamic response time of the HVAC equipment. However, for dynamic systems and plant simulation and, most important, for the realistic simulation... 

The measurement ranges for the base-metal thermocouples are 0 to +750 °C (type J), -200 to +1200 °C (type K), and -200 to +350 °C (type T). The noble-metal thermocouples can be used at higher temperatures up to 1700 °C. The dynamic response of sheathed thermocouples is not very fast however, a probe made from bare, thin wires can have very fast dynamic properties. One of the best features of thermocouples is the simplicity of making new probes by soldering or welding the ends of two wires together. 

---