Integral mode, controllers

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. 

Therefore, the integral mode control action is given by... 

The pressure controller (controller block) amplifies the transmitter signal and sends a modified signal to the final element. Depending on the system requirements, the controller block may include additional correction factors, integral and derivative (reset and rate). This is called a three-mode controller. 

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... 

Three principal functional control modes are proportional (P), integral (I) and derivative (D) control. These are performed by the ideal three-mode controller (PID), described by the equation... 

The main disadvantage of the integral mode is that the controller output does not immediately direct the final control element to a new position in response to an error signal. The controller output changes at a defined rate of change, and time is needed for the final control element to be repositioned. 

The combination of the two control modes is called the proportional plus reset (PI) control mode. It combines the immediate output characteristics of a proportional control mode with the zero residual offset characteristics of the integral mode. 

Proportional-plus-Integral-plus-Derivative (PID) Control The derivative mode moves the controller output as a function of the rate of change of the controlled variable, which adds phase lead to the controller, increasing its speed of response. It is normally combined with proportional and integral modes. The noninteracting or ideal form of the PID controller appears functionally as... 

A controller compares its measurement (y) to its set point (r), and based on the difference (e = error) sends an output signal (m - manipulated variable) to the final control element (e.g., control valve) to eliminate the error. The control mode options include on-off, floating, proportional (P), integral (I), differential (D), and many others. The proportional mode considers the present state of the process error, the integral mode looks at the past history of the error, and the derivative mode anticipates the future values of the error... 

The integral (I) control mode (sometimes called reset mode, because after a load change it returns the controlled variable to set point and eliminates the offset) generates an output (m) according to the equation ... 

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... 

In selective and cascade control loops, external feedback is the most-often-applied solution. Here, instead of looking at its own output, which can be blocked, the integral mode of the controller looks at an external feedback signal (such as the opening of the valve), which cannot be blocked. In surge control or reactor heat-up applications, the chosen solution usually is to use the slave measurement as the external reset signal to prevent saturation. 

Flow as a secondary cannot only overcome the effects of valve hysteresis, but also insures that line pressure variations or badly selected valve characteristics will not affect the primary loop. For these reasons, in composition control systems, flow is usually set in cascade. Cascade flow loops are also useful in feedforward systems. Flow controllers invariably have both proportional and integral modes. If their proportional band exceeds 100%, they must have an integral mode. 

Part (c) in Figure 2.85 illustrates a triple cascade loop, where a temperature controller is the slave of an analyzer controller while the reflux flow is cascaded to temperature. Because temperature is an indicator of composition at constant pressure, the analyzer controller serves only to correct for variations in feed composition. Cascade loops will work only if the slave is faster than the master, which adjusts its set point. Another important consideration in all cascade systems (not shown in Figure 2.85) is that an external reset is needed to prevent the integral mode in the master from saturating, when that output is blocked from reaching and modulating the set point of the slave (when the slave is switched to local set point). 

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. 

During normal operation the flare valve is closed and the pressure in the gasifier is controlled through a by-pass valve at the booster compressor. Quite naturally is the gasifier a slow system concerning both pressure and temperature control. The output control of the gas turbine is completely different and it responds more or less instantaneously. Operation in the fully integrated mode made the pressure, temperature and gas quality in the system vary a bit when the gas turbine suddenly compensated for a small change in either parameter. 

With the exception of derivative action any of these control modes may be used alone in certain applications. Integral and derivative actions are most usually combined with proportional control to give proportional plus integral control (proportional control with automatic reset) proportional plus derivative control or three-mode control, which is proportional plus integral plus derivative. 

---