Proportional action

The proportional action of the controller is for instantaneous controller output that is proportional to the error between the process variable and the setpoint in the controller (Equation 8.1)  

CO = controller output K = proportional gain e, error = process variable - setpoint subscript b = bias (initial) value subscript c = controller 

If the water temperature out of the process is too hot, the steam valve will be closed in direct proportion to the error. Similarly, if the water temperature out of the process is too cold, the steam valve will be opened in direct proportion to the error. However, if there is a change to increase the temperature setpoint or a change to increase the load (process water flow rate), the proportional action by itself cannot eliminate the error. The new steady-state steam valve position would need to be further open to eliminate error. This is a result of the fact that when the error is zero, the valve would only be open far enough to heat the water to the lower setpoint or the lower flow rate. As a result, the temperature would drop by an amount called offset. The amount of offset can be reduced by increasing the proportional gain in the controller, K but the increased gain can cause oscillation and cycling in the process variable. 

Some controllers use proportional gain, K, as the tuning constant. Other controllers use the reciprocal or 100/K as the proportional band in percent as the tuning constant. A 10% proportional band will change the controller output from 0% 

The integral (reset) action in the controller is primarily for eliminating the offset error at steady state (Equation 8.2)  

The principle behind proportional control is to keep the controller output (AO in proportion to the error ( ). 

The controller as specified in Equation (3.2) is known as the full position form in that it generates the actual controller output. A more useful form is the incremental or velocity form which generates the change in controller output (AA/). We can convert the controller to this form by considering two consecutive scans. If E is the current error and E i is the error at the previous scan then 

The advantage of this version is that first it eliminates C which is usually not a constant and would require adjustment as process conditions vary. Secondly the controller will have bumpless initialisation. When any controller is switched from manual to automatic mode it 

Some systems require the proportional band (PB) rather than gain. It is defined as the percentage change in error required to move the output 100 %. Conversion between the two is straightforward. 

While it will respond to changes in PV, the main purpose of proportional action is to generate a proportional kick whenever the SP is changed. If we assume PV is constant then from Equation (3.1) 

---

ProportionaJ-plus-Integral (PI) Control Integral action eliminates the offset described above by moving the controller output at a rate proportional to the deviation from set point. Although available alone in an integral controller, it is most often combined with proportional action in a PI controller ... 

Proportional-action governor is a governor with inherent regulation and a continuous hnear relation between the input (speed change) and the output of the final control element, the governing valve. 

Proportional-action governor with reset is a governor with inherent regiilation so that the momentary output is proportional to input change, and subsequently a reset action initiated by the output acts on the speed changer or its equivalent to make the settled regulation less than the inherent regulation. 

In equation (4.68), T is called the integral action time, and is formally defined as The time interval in which the part of the control signal due to integral action increases by an amount equal to the part of the control signal due to proportional action when the error is unchanging . (BS 1523). 

Integral mode This improves on the proportional-only control by repeating the proportional action within a unit time while a deviation from set point exists. The regulating unit is only allowed to be at rest when set point and... 

Proportional plus integral plus derivative action Proportional action provides a controller output proportional to the error signal. Integral action supplies a controller output which changes in the direction to reduce a constant error. Derivative action provides a controller output determined by the direction and rate of change of the deviation. When all these are combined into one controller (three-term or PID), there is an automatic control facility to correct any process changes. 

Roughly, the reset time is the time that it takes the controller to repeat the proportional action. This is easy to see if we take the error to be a constant in the integral. 

The proportional action of the proportional plus reset controller, if acting alone, would respond to the disturbance and reposition the control valve to a position that would return the hot water out to a new control point, as illustrated by the response curves. You ll note that a residual error would still exist. 

By adding the reset action to the proportional action the controller produces a larger output for the given error signal and causes a greater adjustment of the control valve. This causes the process to come back to the setpoint more quickly. Additionally, the reset action acts to eliminate the offset error after a period of time. 

Proportional plus reset controllers act to eliminate the offset error found in proportional control by continuing to change the output after the proportional action is completed and by returning the controlled variable to the setpoint. 

Derivative cannot be used alone as a control mode. This is because a steady-state input produces a zero output in a differentiator. If the differentiator were used as a controller, the input signal it would receive is the error signal. As just described, a steady-state error signal corresponds to any number of necessary output signals for the positioning of the final control element. Therefore, derivative action is combined with proportional action in a manner such that the proportional section output serves as the derivative section input. 

As seen in Figure 27, proportional action provides an output proportional to the error. If the error is not a step change, but is slowly changing, the proportional action is slow. Rate action, when added, provides quick response to the error. 

Figure 31 demonstrates the combined controller response to a demand disturbance. The proportional action of the controller stabilizes the process. The reset action combined with the proportional action causes the measured variable to return to the setpoint. The rate action combined with the proportional action reduces the initial overshoot and cyclic period. 

A. PROPORTIONAL ACTION. A proportional-only feedback controller changes its output signal, CO, in direct proportion to the error signal, E, which is the difference between the setpoint, SP, and the process measurement signal, PM,... 

B. INTEGRAL ACTION (RESET). Proportional action moves the control valve in direct proportion to the magnitude of the error. Integral action moves the control valve based on the time integral of the error, as sketched in Fig. 7.9b. 

Proportional-lntegral-Derivative Control The most common algorithm for control action in the feedback loop of processing industries is the PID control, which is a combination of proportional action (P), integral action (1), and differential action (D). 

A proportional action (P action) provides an output signal O in proportion to the deviation e according to the following equation. 

However, the ideal control algorithm would have no overshoot, no offset, and a quick response characteristic. For this purpose, a proportional action (P), an integral action (I), and a differential action (D) were combined as a PID controller as follows. 

A capsule summary of the merits of the three kinds of corrective action can be made. The proportional action is rapid but has a permanent offset that increases as the action speeds up. The addition of integral action reduces or entirely eliminates the offset but has a more sluggish response. The further addition of derivative action speeds up the correction. The action of a three-mode PID controller can be made rapid and without offset. These effects are illustrated in Figure 3.3 for a process subjected to a unit step upset, in this case a change in the pressure of the control air. The ordinate is the ratio of the displacements of the response and upset from the set point. 

The response has a high maximum deviation and there is a significant time of oscillation (response time). The period of this oscillation is moderate. For a sustained change in load, the controlled variable is not returned to its original value (the desired value) but attains a new equilibrium value termed the control point. This difference between the desired value and the control point is called the offset or droop. The reason for offset with proportional action can be seen if it is remembered that the control action is proportional to the error. 

Thus, the pressure of the output to the valve P is the sum of Pi and the pressure produced by the wide-band proportional action contributed by the proportional bellows and the flapper-nozzle system (cf. equation 7.3). Note that for t > 0, P/ is no longer equal to P0 and thus equation 7.268 only strictly applies at t = 0. The value of 3 i (and consequently r/) depends upon the capacity C/B of the integral bellows and the the resistance to flow R/r through the integral restrictor. It is generally assumed that C/fi changes little and r/ is varied by adjusting R/r. 

Son very small linear stem-motion valves. A solenoid is usually gned as a two-position device, so this valve control is on/off. Special solenoids with position feedback can provide proportional action for modulating control. Force requirements of medium-sized valves can be met with piloted plug designs, which use process pressure to assist the solenoid force. Piloted plugs are also used to minimize the size of common pneumatic actuators, especially when there is need for high seating load. 

Proportional Action. Control action is proportional to the size of the error, and Equation 2 becomes ... 

FLC system approach can be used to solve problems. Many applications of FLC are related to simple control algorithms such as the PID controller. In a natural way, nonlinearities and exceptions are included which are difficult to realize when using conventional controllers. In conventional control, many additional measures have to be included for the proper functioning of the controller anti-resist windup, proportional action, retarded integral action, etc. These enhancements of the simple PID controller are based on long-lasting experience and the interface of continuous control and discrete control. The fuzzy PID-like controller provides a natural way to applied controls. The fuzzy controller is described as a nonlinear mapping. 

---