Continuous controller modes proportional control

In industrial practice it is common to combine all three modes. The action is proportional to the error (P) and its change (D) and it continues if residual error is present (I). This combination gives the best control using conventional feedback equipment. It retains the specific advantages of all three modes proportional correction (P), offset elimination (1) and stabilising, quick-acting character, especially suitable to overcome lag presence (D). 

Proportional control. The simplest continuous control mode is proportional. The control signal produced by the controller is proportional to the error signal e, defined as... 

Proportional control is the simplest continuous control mode that can damp out oscillations in the feedback control loop. This control mode normally stops the process variable PV from cycling, but it does not necessarily return it to the set point. 

Classical Feedback Control. The majority of controllers ia a continuous process plant is of the linear feedback controller type. These controllers utilize one or more of three basic modes of control proportional (P), iategral (I), and derivative (D) action (1,2,6,7). In the days of pneumatic or electrical analogue controllers, these modes were implemented ia the controller by hardware devices. These controllers implemented all or parts of the foUowiag control algorithm ... 

Integral mode controller (I) output is proportional to the sum of the error over the time. It can be seen that the corrections or adjustments are proportional to the integral of the error and not to the instantaneous value of the error. Moreover, the corrections continue until the error is brought to zero. However, the response of integral mode is slow and therefore is usually used in combination with other modes. 

In the proportional (throttling) mode, there is a continuous linear relation between value of the controlled variable and position of the final control element. In other words, amount of valve movement is proportional to amount of deviation. 

The main advantage of the integral control mode is that the controller output continues to reposition the final control element until the error is reduced to zero. This results in the elimination of the residual offset error allowed by the proportional mode. 

The term T is the integral or reset time setting of the controller. If the bias (b) is zero, this mode acts as a pure integrator, the output of which reaches the value of the step input during the integral time. The integral mode eliminates the offset of plain proportional control because it continuously looks at... 

The Integral mode is sometimes referred to as reset because it continues to take action over time until the error between measurement and setpoint is eliminated. The parameter to specify this action is Integral time, which can be thought of as the length of time for the controller to repeat the initial proportional response if the error remained constant. Note that as this parameter is made smaller, the reset increases as the control action is repeated in a shorter period of time. Some controllers use an alternate parameter, Reset, that is the reciprocal of Integral time and is referred to as repeats/unit time. This latter approach is perhaps more intuitive in that as the Reset parameter is increased, there is more reset action being applied. 

The reset (or integral) mode is designed to reduce the difference between the setpoint and the process variable by adjusting the controller output continuously until the offset is eliminated. The reset mode responds proportionally to the size of the error, the length of time that it lasts, and the integral gain setting. 

If the reactor is stable, based on its heat transfer characteristics, as discussed earlier with regard to continuous reactors, control of temperature will be simplified. The reactor will respond rapidly, with a period of perhaps 20 min, and 10 percent proportional band may be sufficient for effective damping. All three control modes should be adjusted while at the operating temperature. 

Now we consider the combination of the proportional, integral, and derivative control modes as a PID controller. PI and PID control have been the dominant control techniques for process control for many decades. For example, a survey has indicated that large-scale continuous processes typically have between 500 and 5,000 feedback controllers for individual process variables such as flow rate and liquid level (Desborough and Miller, 2001). Of these controllers, 97% utilize some form of PID control. 

A second mode of operation involves the use of an exit slit with an ion collector positioned immediately behind it to measure the intensity of the isolated ion beam. By continuously varying either the accelerating voltage, V, or the magnitude of the magnetic field, H, as a function of time, the separate m/z ion beams can be scanned past the exit slit. When the response of the detector is plotted as a function of time, a spectrum is obtained in which m/z is proportional to H. The width of the slit controls the spectral resolution of the measurement. 

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