Determining Manipulated Variables

After selecting the inventory controls, the remaining manipulated variables (HAc feed, organic reflux flow, and strippCT heat duty) are used for maintaining the stoichiometric balance and for product quality control (purities of the ethyl acetate and water products). In the stripper, the acetate product purity is controlled by the stripper heat input 2r,str. nd a temperature is used to infer the product compositiem. From the RCM (Fig. 16.22), the water purity is determined by the tie line of the LL equilihrium, so it is left uncontrolled. In order to maintain the stoichiometric balance, we use a temperature control to adjust the feed ratio Fhac/ boh (FR). Thus, we have a 2 x 2 multivariable system. From a unitwise perspective, the pairing for the manipulated variables and the controlled variables are FR-7rd and 2 ,str-Tstr- 

We have two manipulated variables left, side draw flow Fss and organic reflux flowrate Rorg. For the side stream flowrate, one can choose to ratio the side stream flowrate to the feed or simply fix Fss lo its setpoint. The latter is utilized here because it is a relatively large flowrate (Fss = 1500 kmol/h) compared to the reflux flowrate (R = 407 kmol/h) and frequent perturbations may introduce unnecessary disturbances to the lower section of the column. Two possible approaches can be taken for the organic reflux. One is to fix the reflux ratio RR. The other is to ratio the reflux to the feed (R/F fon)- Therefore, we 

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The feedforward control strategy (Fig. lb) addresses the disadvantages of the feedback control strategy. The feedforward control strategy measures the disturbance before it affects the output of the process. A model of the process determines the adjustment ia the manipulated variables(s) to compensate for the disturbance. The information flow is therefore forward from the disturbances, before the process is affected, to the manipulated variable iaputs. 

Stea.dy-Sta.teFeedforwa.rd, The simplest form of feedforward (FF) control utilizes a steady-state energy or mass balance to determine the appropriate manipulated variable adjustment. This form of feedforward control does not account for the process dynamics of the disturbance or manipulated variables on the controlled variable. Consider the steam heater shown ia Figure 15. If a steady-state feedforward control is designed to compensate for feed rate disturbances, then a steady-state energy balance around the heater yields ... 

Constraint control strategies can be classified as steady-state or dynamic. In the steady-state approach, the process dynamics are assumed to be much faster than the frequency with which the constraint control appHcation makes its control adjustments. The variables characterizing the proximity to the constraints, called the constraint variables, are usually monitored on a more frequent basis than actual control actions are made. A steady-state constraint appHcation increases (or decreases) a manipulated variable by a fixed amount, the value of which is determined to be safe based on an analysis of the proximity to relevant constraints. Once the appHcation has taken the control action toward or away from the constraint, it waits for the effect of the control action to work through the lower control levels and the process before taking another control step. Usually these steady-state constraint controls are implemented to move away from the active constraint at a faster rate than they do toward the constraint. The main advantage of the steady-state approach is that it is predictable and relatively straightforward to implement. Its major drawback is that, because it does not account for the dynamics of the constraint and manipulated variables, a conservative estimate must be taken in how close and how quickly the operation is moved toward the active constraints. 

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 ... 

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 ... 

Equation (6.8) is a functional. There are several functions, a(t), b(t), T(t), that contribute to the integral, but T(t) is the one function directly available to the reactor designer as a manipulated variable. Functional optimization is used to determine the best function T t). Specification of this function requires that T t) be known at every point within the interval 0[Pg.208]

Our selection of the initial state, x0, and the value of the manipulated variables vector, u(t) determine a particular experiment. Here we shall assume that the input variables u(t) are kept constant throughout an experimental run. Therefore, the operability region is defined as a closed region in the [xoj.xo, , Xo,n, U u2,...,u,]T -space. Due to physical constraints these independent variables are limited to a very narrow range, and hence, the operability region can usually be described with a small number of grid points. 

The original optimal control problem can also be simplified (by reducing its dimensionality) by partitioning the manipulated variables u(t) into two groups U and u2. One group U could be kept constant throughout the experiment and hence, the optimal inputs for subgroup u2(t) are only determined. 

The proportional band determines the range of output values from the controller that operate the final control element. The final control element acts on the manipulated variable to determine the value of the controlled variable. The controlled variable is maintained within a specified band of control points around a setpoint. 

The DMC method uses the same statistical mathematics that are used in a standard least-squares procedure for determining the best values of parameters of an equation to fit a number of data points. In the DMC approach, we would like to have NP future output responses match some optimum trajectory by finding the best values of NC future changes in the manipulated variables. This is exactly the concept of a least-squares problem of fitting NP data points with an equation with NC coefficients. This is a valid least-squares problem as long as NP is greater than NC. 

There are usually many more state variables that manipulated variables. In a distillation column there are typically over 100 state variables N = 100), while there are only 5 manipulated variables (it = S). There is only one load disturbance shown in Eq. (15.54) for simplicity. If there were more than one, the effects of each could be determined individually. 

Decoupling. K is determined to decouple some blocks of process/ manipulated variables. This is usually complemented by a decentralized control or a pole placement strategy. 

The two possible control configurations for a system with two inputs and two outputs are shown in Fig. 7.77. One example of this is illustrated in Fig. 7.73 where the overhead and bottoms product compositions of a distillation process are controlled using the reflux and steam-to-reboiler flowrates respectively as the manipulated variables. Theoretically, we could employ the reflux flowrate to control the bottoms product composition and the steam-to-reboiler flowrate to control the overhead product composition. It is possible to determine which configuration produces the least interaction by forming the system relative gain array A, where ... 

Process design modifications usually have a bigger impact on operability (dynamic resilience). Dynamic resilience depends on controller structure, choice of measurements, and manipulated variables. Multivariable frequency-response techniques have been used to determine resilience properties. A primary result is that closed-loop control quality is limited by system invertability (nonmin-imum phase elements). Additionally, it has been shown that steady-state optimal designs are not necessarily optimal in dynamic operation. 

Figure 4 illustrates the operation of an internal model control system (5) designed to use Pd as a manipulated variable to minimize the variance of the purity error APp while optimizing Y. As shown in the figure, the effect of the change in Pd at the time point k-1 is subtracted from the measured output variable (i.e., the purity error) at the time point k in order to determine an estimate of ADk, i.e.,... 

In the simplest case, only the stoichiometry of chemical reactions is known, but no kinetic information is available. This allows designing the control structure, which is choosing the controlled and manipulated variables and their pairing. Note that the knowledge of stoichiometry is also necessary for designing the structure of the separation system, which is determined by the composition and the thermodynamic properties of the reactor-outlet mixture. 

After the variables are selected, the structure of the controller itself is chosen. This determines which manipulated variables are changed and on which errors the changes are based. Proper control system structuring can have a significant effect on its reliability. In industry, strategies that work well all the time provide more benefits than those that work optimally but are frequently on manual control. 

Once we have fixed a flow in each recycle loop, we then determine what valve should be used to control each inventory variable. This is the material balance step in the Buckley procedure. Inventories include all liquid levels (except for surge volume in certain liquid recycle streams) and gas pressures. An inventory variable should typically be controlled with the manipulated variable that has the largest effect on it within that unit (Richardson rule). Because we have fixed a flow in each recycle loop, our choice of available valves has been reduced for inventory control in some units. Sometimes this actually eliminates the obvious choice for inventory control for that unit. This constraint forces us to look outside the immediate vicinity of the holdup we are considering. 

The central element in any control loop is the process to be controlled. Therefore, the control objectives must be defined (e.g., maintain a desired outlet temperature and/or composition, maintain the level in a tank at a certain height, etc.). Once the control objective is specified, variables are measured in order to monitor the operational performance of the process (sensing element). Next, the input variables. that are to be manipulated are determined. Finally, after the control objectives, the possible measurements, and the available manipulated variables have been identified, the control configuration is defined. The control configuration is the information structure used to connect the available measurements to the available manipulated variables. The two general types of control configurations are feedback control and feedforward control. Details on feedback control are discussed below in this problem. Feedforward control is discussed in the next problem, CTR.2. 

Sample Scientists may use a sample or a portion of the total number as a type of estimation. To sample is to take a small, representative portion of the objects or organisms of a population for research. By making careful observations or manipulating variables within that portion of the group, information is discovered and conclusions are drawn that might apply to the whole population. A poorly chosen sample can be unrepresentative of the whole. If you were trying to determine the rainfall in an area, it would not be best to take a rainfall sample Irom under a tree. 

A kinetic study is not complete unless the effects of various experimental variables on the experimental rate functions are determined. By systematically changing experimental variables and determining the effect on the rate function, valuable clues are obtained that will aid in deducing mechanisms to explain the observed rate function. The most commonly manipulated variables in soil kinetic studies include reactant concentrations (both solute and solid phase), temperature, pH, ionic strength, and solution composition (other than pH, ionic strength, and solute concentration). 

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