# Proportional Controller Versus Proportional And Derivative Controller Course Work Sample

Published: 2021-06-25 23:55:04

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Usually, the design of control systems is based on proportional control. The main difference between a proportional controller and a proportional plus derivative controller is that the latter has a derivative section added. According to Cooper (2007), this derivative action is responsive to the rate of change of the error signal. In order to compare the two, it is important to examine the characteristics and mode of operation of each, as well as their industrial application.

Proportional Controller

Of all controllers used in control systems, the proportional controller is the most simple. In this method of control, the control system behaves in a manner that the control effort is proportional to the error. A simple block diagram of such a control system is shown in figure 1 below;

The critical characteristics of a proportional controller lie in its computation of the control effort. Usually, the output is subtracted from the input to obtain the error signal. In this case, the output value is the measured output value while the input value is the desired output value. According to Cooper (2007), an ideal proportional controller has G1 as the transfer function and a gain constant Kp whereby the manipulated variable is directly proportional to the actuating signal E. Doebelin (1985) observes that a proportional controller is capable of varying the energy sent to the controlled process in a continuous fashion hence matching its needs instead of having to cycle back and forth between 2 or 3 fixed levels of supply. Therefore, it is this lack of limit cycling that gives the proportional controller an edge over the on-off controllers. Proportional controllers are stable. However, their disadvantage is that they have a higher cost, are complex and there is lower reliability of the hardware in comparison to the on-off controllers.

Proportional Plus Derivative Controller

This is a control system in which there is a derivative section that is added to the proportional controller. This section is usually responsive to the rate of change of the error signal and not the amplitude. This is unlike in a proportional controller whereby the response is to the error signal. The derivative action is responsive to the rate of change immediately it begins. This means that the output of the controller is initially larger in direct relation with the rate of change of the error signal (Doebelin, 1985). If the rate of change of the error signal is higher, this causes the final control element to be quickly positioned to the desired output value. This added derivative control decreases the initial overshoot of the variable that is measured, and this helps in making the process stable.

A PD controller has a differentiator which produces the derivative signal. The differentiator gives an output that is directly proportional to the input’s rate of change, and a constant specifying the differentiation function (Cooper, 2007). It is the derivative constant that defines the output of the differential controller and is expressed in seconds. The differentiator transforms a varying signal to a constant magnitude signal. When the rate of change of the input is constant, the output magnitude is constant. Alone, derivative cannot be utilized as a control mode because a steady-state input gives a zero output in a differentiator. As such, a combination of derivative control and proportional action is used in a way that the output of the proportional section becomes the input of the derivative section. PD controllers combine the benefits of both rate control and proportional modes.

Comparing the Two

In terms of characteristics, the dynamic characteristic of a proportional controller shows a number of points. First, the step response corresponds to the proportional relationship between the output and input signals. Second, the proportional controller is load-dependent due to this proportional relationship. Third, the control correction instantly follows the corresponding control difference, making the proportional controller a fast controller. Fourth, the correction magnitude is limited meaning that the proportional controller is intrinsically stable, meaning that it is capable of also stably controlling non-self-regulating controlled systems (Doebelin, 1985). On the other hand, a proportional plus derivative controller incorporates a proportional controller and a derivative action element. Unlike proportional controllers whereby the control effort is proportional to the error signal, in a PD controller, the control effort is proportional to the rate of change of the error signal. For this reason, a PD controller is fast and more effective than a proportional controller.

According to Cooper (2007), PD controllers are capable of correcting a control difference more quickly than proportional controllers. However, this can result in a residual deviation, also referred to as an offset. While proportional controllers are load-dependent, PD controllers are load-dependent though this load-dependence is less pronounced since the stabilizing effect of the derivative component allows for a smaller proportional band to be selected. In terms of their industrial applications, PD controllers are rarely used in HVAC systems. However, they can find application in air conditioning, heating control and room temperature control. P-controllers can find application in HVAC systems.

References

Cooper, D.J. (2007) The P-Only Control Algorithm. Retrieved on 20 Oct. 2013 from http://www.controlguru.com/wp/p62.html
Doebelin, E.O. (1985) Control System: Principles and Design. New York: John Wiley & Sons, Inc.

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