Proportional and integral control

Automatic reset is done by using an electronic integrator to perform the reset function. The deviation or error is integrated with respect to time, and the result is added to the deviation signal to move the proportional band. The block diagram of proportional control with automatic reset is shown in Fig. 4.30. 

The Ki term operates exactly as in a simple proportional controller. The integration term Kj has to be made long enough so that it will be negligible at the frequencies when the control loop has 180 degrees phase shift. These are the critical frequencies for loop stability. If this is done, the K2 term will not have an effect on the stability of the loop, but it will accomplish its task, i.e., eliminate the offset. 

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Allow the tank to achieve steady-state operation in the absence of control (Kc = 0). Use the resulting process reaction curve to estimate combined proportional and integral control parameters. Then use the obtained steady-state values as the initial values for a following sequence of runs. 

We certainly want to respond very differently if the temperature of a chemical reactor is changing at a rate of 100°C/s as opposed to l°C/s. In a way, we want to "project" the error and make corrections accordingly. In contrast, proportional and integral controls are based on the present and the past. Derivative controller action is based on how fast the error is changing with time (rate action control). We can write... 

Proportional plus reset control is a combination of the proportional and integral control modes. 

Combination of proportional and integral control modes leads to the following effects on the response of a closed-loop system ... 

Derivative control action is also referred to as rate action, preact, or anticipatory control. Its function is to anticipate the future behavior of the error signal by considering its rate of change. Derivative action is never used alone, but in conjunction with proportional and integral control. Derivative control is used to... 

The pressure transmitter, located on the discharge header, has a capillary-connected Monel diaphragm seal. It is reverse-acting, with proportional and integral control modes. Normal practice is to include both high- and low-pressure alarms. 

As the hydrogen cools, water condenses and accumulates in the column. The level in the bottom of the column can be measured with a d/p cell. The signal from the level transmitter goes to a direct-acting controller with proportional and integral control modes. The fail-closed control valve is in a side branch off the circulating pump dischaige line. 

The steam flow should be measured with a vortex-shedding meter. Hre linear characteristic of such meters provides greater rangeability. A fail-closed steel globe valve with an equal percentage characteristic and a positioner should be used. Tire controller would be reverse-acting with proportional and integral control functions. 

Derivative control action is also referred to as rate action, preact, or anticipatory control. Its function is to anticipate the future behavior of the error signal by computing its rate of change thus, the shape of the error signal influences the controller output. Derivative action is never used alone, but in conjunction with proportional and integral control. Derivative control is used to improve the dynamic response of the controlled variable by decreasing the process response time. If the process measurement is noisy, however, derivative action will ampHfy the noise unless the measurement is filtered. Consequently, derivative action is seldom used in flow controllers because flow control loops respond quickly and flow measurements tend to be noisy. In the chemical industry, there are more PI control loops than PID. 

The function of derivative control action is to anticipate the future behavior of the error signal by considering its rate of change. In the past, derivative action was also referred to as rate action, pre-act, or anticipatory control For example, suppose that a reactor temperature increases by 10 °C in a short period of time, say, 3 min. This clearly is a more rapid increase in temperature than a 10 °C rise in 30 min, and it could indicate a potential runaway situation for an exothermic reaction. If the reactor were under manual control, an experienced plant operator would anticipate the consequences and quickly take appropriate corrective action to reduce the temperature. Such a response would not be obtainable from the proportional and integral control modes discussed so far. Note that a proportional controller reacts to a deviation in temperature only, making no distinction as to the time period over which the deviation develops. Integral control action is also ineffective for a sudden deviation in temperature, because the corrective action depends on the duration of the deviation. 

PID control The modes of control used to control processes or part of a process. The three basic modes of control are proportional control, integral control, and derivative control. Derivative control is always used in combination with proportional control or both proportional and integral control. Integral control is generally used in combination with proportional or with both proportional and derivative control. PID control is also known as three-term control. 

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