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)

# Tuning a PID controller

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 Laplace.

A sample problem where Laplace is used to solve the first order differential equation for a thermometer.

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 Laplace transformed versions on the components within it (i.e. controller and process) to determine overall information on the system.  A first order process (e.g. heating a tank) controlled by a proportional controller is analysed, and the results are that 1. the system is first order, 2. the time constant of the system is less that that of the process, and 3. there is an error at steady state (to be expected with P control).  A similar analysis of a first order process controlled by a proportional plus integral controller is also included.
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