Proportional controllers

Fig. 2. Flow sheet of lecithin producing unit. Crude soybean oil is heated in the preheater, 1, to 80°C, mixed with 2% water in the proportion control unit, 2, and intensively agitated in 3. The mixture goes to a dweUing container, 4, and is then centrifuged after a residence time of 2—5 min. The degummed oil flows without further drying to the storage tanks. The lecithin sludge is dried in the thin-film evaporator, 6, at 100°C and 6 kPa (60 mbar) for 1—2 min and is discharged after cooling to 50—60°C in the cooler, 8. 9 and 10 are the condenser and vacuum pump, respectively.

Proportional Control A proportional controller moves its output proportional to the deviation in the controlled variable from set point ... 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

This is a control algorithm that attempts to eliminate the offset (caused by proportional control) between the measurement and the setpoint of the controlled process variable. This control mode remembers how long the measurement has been off the setpoint. 

Fig. 4.24 Step response of a first-order plant using proportional control.

Proportional control, gain A lfV/m) Control signal U s) = KfX is) - ZmCv))... 

Fig. 5.22 Proportional control, ship roll stabilization system.

Offset A sustained deviation between the control points and the set point of a proportional control system. 

Proportional band In a proportional controller, the control point range through which the controlled variable must pass in order to move the final control element through its full operating range. 

Proportional control A control algorithm in which the final control element moves to a position proportional to the deviation of the value of the controlled variable from the set point. 

Derivative mode This improves on the proportional-only control by responding solely to the rate of change of the deviation but not in any way to the actual value of the deviation. Derivative action is always used with proportional control. 

The thermostatic expansion valve is substantially an undamped proportional control and hunts continuously, although the amplitude of this swing can be limited by correct selection and installation, and if the valve always works within its design range of mass flow. Difficulties arise when compressors are run at reduced load and the refrigerant mass flow falls below the valve design range. It is helpful... 

Mandrel Speed Manipulation The speed of the mandrel determines the rate of fiber lay down. To control angular velocity, a proportional control algorithm was programmed... 

The error for the proportional control algorithm is determined from the actual position of the carriage PULSEcar-... 

Kcar is the gain used in the proportional control algorithm for the carriage. 

SIGN is used to determine whether the carriage position is incrementing or decremented. TIME is the sampling time of the proportional control algorithm. 

The response of a controller to an error depends on its mode. In the proportional mode (P), the output signal is proportional to the detected error, e. Systems with proportional control often exhibit pronounced oscillations, and for sustained changes in load, the controlled variable attains a new equilibrium or steady-state position. The difference between this point and the set point is the offset. Proportional control always results in either an oscillatory behaviour or retains a constant offset error. 

Consider the case of a proportional controller, which is required to maintain a desired reactor temperature, by regulating the flow of coolant. Neglecting... 

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

The maintenance of constant liquid level in the reflux drum can be expressed by the following proportional control equation... 

When the reactor temperature (Tl) becomes greater than Tmax (=240 F), PERIOD = 2, and the program turns the cooling water on with flow rate Fw. This flow is controlled with a proportional controller using control constant Kc, whose set point (Pset) is varied according to the time ramp function with setting kR and whose output to the valve is Pc. This ramp is horizontal until time period Tihold has passed. Then the setpoint is decreased linearly. The temperature is sensed using a pressure transmitter with output Ptt. 

Proportional control can be based on the temperature of the third stage. Here FO is the base flow rate, KC is the proportional controller gain, and TSET is the temperature set point. Note that in order to guard against the unrealistic condition of negative flow, a limiter condition on F should be inserted into the DYNAMIC region. This can be accomplished with ISIM by the following statement... 

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