The
Controller

There
are several different types of controller but all have one thing in common –
they have the same input which is the **error**. The error is the difference between the setpoint
and the process variable, between where you want to be and where you currently
are.

*Error =
Setpoint – Process Variable*

The
differences between the different controllers lies in what each one does with
or to the error. The **On/Off** controller, the simplest, merely
checks the error to see if it is positive or negative. If a positive error means turn the output on,
then a negative error will turn the output off.
The **Proportional** controller
multiplies the error by it’s Proportional Gain and sends the result off as it’s
output. The **Integral** controller integrates the error over time and sends the
result of the integration to its output.
The **Derivative** controller
differentiates or calculates the derivative of the error with respect to time
and this result is it’s output. Each
controller does something different and so the output from each controller is
different even though the input to them all is the same.

On/Off Control

A
presentation on this topic in pdf format.

PowerPoint
presentation on Introduction
to Control

**There
are a number of different types of controller**. These
are:

·
On Off Control (PowerPoint
presentation). One sample problem on this
topic is available.

·
Proportional Control (PowerPoint
presentation)

·
Integral Control (PowerPoint
presentation)

·
Derivative Control (PowerPoint
presentation)

See the Power Point Presentation

and a worked example and a sample problem both based on
the process reaction curve method.

**Modelling
and Laplace**. The
controller is covered by the topics above.
The controller is always connected to a process such as a hot water tank
and is used to control the temperature of the tank, for example. The hot water tank can be modelled to show that it is a first
order system (i.e. relationship between input and output is a first order
equation). (For another example of
modelling, have a look at filling a
tank; or have a look at the model for a RC
Circuit).

The
first order differential equation of the model can be solved using Laplace transforms. See also the power
point presentation on

A sample problem where

**Block
Diagrams**. A block diagram is a very useful way of
representing a control system. You must
first understand the basic features
of a block diagram. The block diagram is
not only useful for providing a graphical image of a control system. It can also be used, in conjunction with the