Proportional band

Actuator pressure Vapor pressure Proportional band (%)... 

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 ... 

An example is shown in Figure 4-84, whieh represents the regenerator pressure following a malfunetion of the expander bypass valve. The bypass valve trips open in 1 see while the expander inlet valve maintains eontrol. Tlie regenerator pressure drops approximately 2.0 psi before starting to reeover. The inlet valve stroking time was 10 see and the eontroller settings were 5% proportional band and 30 see reset. 

The speed of the controller is adjusted by the proportional band and reset rate (proportional and integral gains). These parameters also influence the stability of the control loop. All control loops are limited to a gain of less than one at their critical frequency. Higher closed-loop gain will make the loop unstable. 

Proportional band, % 20 20 Equation 1 Proportional band, % Equation 2 Equation 2... 

P.B. = proportional band setting overshoot = amount - -l- of setpoint, °F span = transmitter span, °F... 

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. 

Stable control of reduced pressures is readily achieved by the use of two (or more) pressure-reducing valves in parallel (Figure 22.10). At full load and loads not too much below this level both valves are in use. As the load diminishes, the controlled pressure begins to increase and the valve which is set at the lower pressure begins to close. When the load can be supplied completely by the valve set at the higher pressure, the other valve closes. Any further load reduction causes the remaining valve to modulate through its proportional band. 

Dry bulb sensors may be bi-metal strips, thermistors or refrigerant-filled phials or bellows responding to pressure differences caused by temperature change. These, in turn, provide an electrical or mechanical signal. The mechanical items are used to alter the value of potentiometers or make-or-break contacts. The signals are transmitted to amplifiers, which respond to the degree of error. An important feature is the proportional band of temperature over which the controls call for up to full plant capacity. 

Generally, the proportional gain is dimensionless (i.e.. p(t) and e(t) have the same units). Many controller manufacturers use the percent proportional band, which is defined as... 

PI controllers are most common. They eliminate offsets and have acceptable speeds of response in most industrial settings. We usually pick a low to intermediate gain (wide proportional band, PB 150) to reduce the effect of noisy signals (from flow turbulence also why we do not use D control). We also use a low reset time ( 0.1 min/repeat i.e. relatively large I action) to get fast set-point tracking. 

Three terms commonly used to describe the proportional mode of control are proportional band, gain, and offset. 

Proportional band, (also called throttling range), is the change in value of the controlled variable that causes full travel of the final control element. Figure 14 shows the relationship between valve position and temperature band for two different proportional bands. 

The proportional band of a particular instrument is expressed as a percent of full range. For example, if full range of an instrument is 200°F and it takes a 50°F change in temperature to cause full valve travel, the percent proportional band is 50°F in 200°F, or 25%. Proportional bands may range from less than 1% to well over 200%. However, proportional bands over 100% cannot cause full valve travel even for full range change of the controlled variable. 

Gain, also called sensitivity, compares the ratio of amount of change in the final control element to amount of change in the controlled variable. Mathematically, gain and sensitivity are reciprocal to proportional band. 

With proportional control, the final control element has a definite position for each value of the measured variable. In other words, the output has a linear relationship with the input. Proportional band is the change in input required to produce a full range of change in the output due to the proportional control action. Or simply, it is the percent change of the input signal required to change the output signal from 0% to 100%. 

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 proportional band is the input band over which the controller provides a proportional output and is defined as follows ... 

The controller has a proportional band of 100%, which means the input must change 100% to cause a 100% change in the output of the controller. 

If the fulcrum setting was changed so that a level change of 2 in, or 50% of the input, causes the full 3-in stroke, or 100% of the output, the proportional band would become 50%. The proportional band of a proportional controller is important because it determines the range of outputs for given inputs. 

The controller has been set for a proportional band of 50%. Therefore, a 50% change in the 200°F span, or a change of 100°F, causes a 100% controller output change. 

At time tb the measured variable increases by 100°F, or 50%, of the measured variable span. This 50% controller input change causes a 100% controller output change due to the controller s proportional band of 50%. The direction of the controller output change is decreasing because the controller is reverse-acting. The 100% decrease corresponds to a decrease in output for 15 psi to 3 psi, which causes the control valve to go from fully open to fully shut. 

If the measured variable drops below the setpoint, a positive error is developed, and the control valve opens further. If the measured variable goes above the setpoint, a negative error is developed, and the control valve throttles down (opening is reduced). The 50% proportional band causes full stroke of the valve between a +50°F error and a -50°F error. 

When the error equals zero, the controller provides a 50%, or 9 psi, signal to the control valve. As the error goes above and below this point, the controller produces an output that is proportional to the magnitude of the error, determined by the value of the proportional band. The control valve is then capable of being positioned to compensate for the demand disturbances that can cause the process to deviate from the setpoint in either direction. 

The proportional band is the change in input required to produce a full range of change in the output due to the proportional control action. 

A proportional plus integral controller is used to control the level in the reflux accumulator of a distillation column by regulating the top product flowrate. At time t = 0, the desired value of the flow controller which is controlling the reflux is increased by 3 x 10-4 m3/s. If the integral action time of the level controller is half the value which would give a critically damped response and the proportional band is 50 per cent, obtain an expression for the resulting change in level. 

The proportional band (= 50 per cent) = 100 x (error required to move the valve from fully open to fully shut)/(full range of level)... 

Many instrument manufacturers use an alternative term, proportional band (PB), instead of gain. The two are related by... 

The common types of control loops are level, flow, temperature, and pressure. The type of controller and the settings used for any one type are sometimes pretty much the same from one application to another. For example, most flow control loops use PI controllers with wide proportional band and fast integral action. 

A- FLOW LOOPS. PI controllers are used in most flow loops. A wide proportional band setting (PB — ISO) or low gain is used to reduce the effect of the noisy flow signal due to flow turbulence. A low value of integral or reset time (t, - 0.1 minute per repeat) is used to get fast, snappy setpoint tracking. 

The tuning of proportional level controllers is a trivial job. For example, we could set the bias value at 50 percent of full scale, the setpoint at 50 percent of full scale, and the proportional band at 50. This means that the control valve will be half open when the tank is half full, wide open when the tank is 75 percent full, and completely shut when the tank is 25 percent full. Changing the proportional band to 100 would mean that the tank would be completely full to have the valve wide open and completely empty to have the valve shut. 

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