Temperature Control Theory Essay Research Paper Process

Temperature Control Theory Essay, Research Paper

Process control systems serve two different purposes. Generally the first of these purposes is to effect a change in a certain output variable, commonly encountered in the startup of a process. The second of these is to regulate or hold an output variable constant despite any changes in an input variable, which usually cannot be easily managed [1].

In order to discuss process control, in detail it is necessary to define several terms. A control loop is comprised of several variables. Among these are manipulated variables (MV), process variables (PV), and disturbance variables (DV). Manipulated variables refer to variables that are easily controlled, such as stream flowrates. Process variables are those that are desired to be set at a certain datum level, commonly a desired temperature. Disturbance variables create deviations in the process variable from the desired datum level or set point (SP). The controller receives process variable information and in turn attempts to maintain the process variable at the set point.

In particular there are two types of control systems, feedforward and feedback control. Feedback control operates by feeding back process variable data to the controller. In feedback process control, the controller receives process variable data and makes appropriate changes in the manipulated variable via the final control element (FCE). The uniqueness of feedback control is that it utilizes prevailing process variable information in order to determine what measures need to be taken to return the process variable to the set point [2]. Figure I illustrates a typical feedback control loop.

The modus operandi of a feedfoward controller is that the controller receives a direct signal of the disturbance variable. Here the disturbance variable is measured directly rather than the output variable that is desired to be regulated. The disturbance variable is measured before the process is perturbed and the controller endeavors to neutralize the disturbance s effects, usually by some prescribed process model. The controller does not receive any output variable information and consequently has no information pertaining to the actual effect or accuracy of the control action [2]. Figure II depicts a typical feedfoward configuration. A feedback controller was used in this investigation and henceforth only feedback controllers will be discussed.

There are three general categories of feedback controllers, namely proportional control, proportional-plus-integral (PI), and proportional-plus-integral-plus-derivative (PID). Each type will be treated separately.

A proportional-only controller changes its output in such a way that the output is proportional to the deviation of the process variable from the set point. The deviation of the process variable from the set point is referred to as the error and denoted,

Despite the simplicity of proportional control, it has one major deficiency. Under proportional-only control, steady-state offset is observed for non-zero set points [1]. By the definition of steady state, all time derivatives must be equal to zero. It is possible for de(t)/dt to equal zero so long as the error has reached some steady-state value or the error is zero. However, looking back to equation 3 it is apparent that if e(t) is zero so must be the value for the controller output c (t). The difficulty here is that the c (t) can never be zero for non-zero set points; and therefore, for proportional only controllers, steady-state offset will always be observed. Moreover, from equation 3 as the system reaches steady state, the error stabilizes and consequently the controller output, c(t), would also stabilize. Thus at steady state, the proportional only controller does not attempt to counterbalance the error [1].

Under steady-state conditions the controller output and the error will remain constant. Equation 4 implies that the c(t) will change with time until e(t) is zero. Therefore, under integral control c(t) will, at steady state, assume a value such that e(t) reaches zero [4]. Depending upon the capability of the equipment that is being used, this always occurs. However, it is possible for the controller or the final control element to saturate and reach a limiting value. Should saturation occur, the controller or the final control element will become stuck and will be unable to return the controlled variable back to the set-point [4].

Integral control action is seldom used alone, since little correction is achieved until the error signal has endured for a period of time. Since proportional control action occurs immediately at the detection of error, integral control and proportional control are often used in tandem.

Proportional-plus-integral control exhibits the quick response of proportional control and the effective treatment of offset as observed under integral control conditions. Despite this fact, PI control does exhibit some limitations. PI control affords an undulating response pattern and hence can cause disturbances in the system, increasing system instability [4]. Usually small disturbances can be tolerated by virtue of the faster response time. This phenomenon can be corrected by proper tuning of the instrument or by incorporating derivative control into the control system [4].

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