Controlled variables

Second card FORMAT(8F10.2), control variables for the regression. This program uses a Newton-Raphson type iteration which is susceptible to convergence problems with poor initial parameter estimates. Therefore, several features are implemented which help control oscillations, prevent divergence, and determine when convergence has been achieved. These features are controlled by the parameters on this card. The default values are the result of considerable experience and are adequate for the majority of situations. However, convergence may be enhanced in some cases with user supplied values. 

MAIN PROGRAM AND DRIVER FOR FITTING BINARY VLF DATA USING METHOD EASED ON THE MAXIMUM LIKELIHCOO PRINCIPLE ONLY CONTROL VARIABLES APE READ IN THIS ROUTINE. 

Vector of indices for the components (I = 1, N) integer initialization control variable (KEY =... 

KV Integer control variable for combining liquid and vapor... 

KAC Integer control variable for acceleration of phase compositions at alternate iterations. 

COMPUTER SIMULATIONS - FINITE ELEMENT PROGRAM Line 2 Basic control variables... 

Despite the variety of methods that had been developed, by 1960 kinetic methods were no longer in common use. The principal limitation to a broader acceptance of chemical kinetic methods was their greater susceptibility to errors from uncontrolled or poorly controlled variables, such as temperature and pH, and the presence of interferents that activate or inhibit catalytic reactions. Many of these limitations, however, were overcome during the 1960s, 1970s, and 1980s with the development of improved instrumentation and data analysis methods compensating for these errors. ... 

The primary control variables at a fixed feed rate, as in the operation pictured in Figure 8, are the cycle time, which is measured by the time required for one complete rotation of the rotary valve (this rotation is the analog of adsorbent circulation rate in an actual moving-bed system), and the Hquid flow rate in Zones 2, 3, and 4. When these control variables are specified, all other net rates to and from the bed and the sequence of rates required at the Hquid... 

Because of the delay in decomposition of the peroxide, oxygen evolution follows carbon dioxide sorption. A catalyst is required to obtain total decomposition of the peroxides 2 wt % nickel sulfate often is used. The temperature of the bed is the controlling variable 204°C is required to produce the best decomposition rates (18). The reaction mechanism for sodium peroxide is the same as for lithium peroxide, ie, both carbon dioxide and moisture are required to generate oxygen. Sodium peroxide has been used extensively in breathing apparatus. 

The primary advantage of the feedforward over the feedback control strategy is that corrective action is initiated before the controlled variable is upset. Feedforward control, however, has its own drawbacks, ie, variables used to characterize the disturbances must be measurable a model of the response of the controlled variable to the disturbance must be available (when the feedforward strategy is used alone, the control performance depends on the accuracy of the model) and the feedforward control strategy does not compensate for any disturbance not measured or modeled. 

In most process plant situations where feedforward control is appropriate, a combination of the feedforward and feedback control is usually used. The feedforward portion reduces the impact of measured disturbances on the controlled variable while the feedback portion compensates for model inaccuracies and unmeasured disturbances. This control strategy is referred to as feedforward control with feedback trim. 

Fig. 12. Cascade control signal flow diagram, where SPP = primary control variable setpoint PVP = primary control variable measurement ...

SPS = secondary control variable setpoint and PVS = secondary control variable measurement. The + and — indicate to multiply the signal by +1 or —1... 

Both control schemes react in a similar manner to disturbances in process fluid feed rate, feed temperature, feed composition, fuel gas heating value, etc. In fact, if the secondary controller is not properly tuned, the cascade control strategy can actually worsen control performance. Therefore, the key to an effective cascade control strategy is the proper selection of the secondary controlled variable considering the source and impact of particular disturbances and the associated process dynamics. 

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 ... 

Fig. 16. Methods of ratio control implementation, where -I- and x indicate the division and multiplication of signals, respectively (a) use of a divider and ratio controller and (b) use of a multiplier. Calculated ratio = actual value of control variable both setpoint and gain are equivalent to the desired ratio.

Multivariable control strategies utilize multiple input—multiple output (MIMO) controUers that group the interacting manipulated and controlled variables as an entity. Using a matrix representation, the relationship between the deviations in the n controlled variable setpoints and thek current values,, and the n controUer outputs, is... 

Similarly, the relationship between the n outputs, and the current values of the controlled variables,i, can be written as a matrix comparable to the inputs, which in matrix shorthand is... 

This equation relates the deviations from setpoints to the observed current values of the controlled variables. 

---