- , the controller gain
- , the integral reset time

In the second section on modelling processes we looked at

- First order input output processes
- Mechanistic models of actual processes

For the first of these we saw that there were three parameters necessary to define the process. These are

, the dead time*T*- , the process gain
- , the process time constant

The aim of this section is to introduce a method of **matching the
personality** of the controller to that of the process so as to achieve
the optimum controllability. In other words how do we go from the
process parameters to the controller parameters. The method introduced
uses the open loop response of a process and works best with a
delay-followed-by-first-order-lag. There are many other *tuning*
methods which look at other aspects of the process in order to tune the
controller. A couple of these will be discussed in a later section.

**Instantaneous Response**processes are easy to control. Large gains may be used, subject to noise constraints. Integral action should be used.**First Order Response**Processes are also easy to control. The tuning method described below is based on a first order response.**Time Delay**processes are difficult to control. A**pure**time delay becomes unstable in principle if a dimensionless gain greater than 1 is used in a proportional only controller.**Inverse Response**processes exhibit a response to an adjustment like this:You will see later in the interactive exercises that this is very difficult to control!

The method is outlined below.

- Look at the open loop response of the process to a step change in the manipulated variable.
- Evaluate
- The steady-state gain,
**(y2 - y1) / (u2 - u1)** - The time delay,
**Td** - The time constant,
**Ts**

The diagram above shows how to obtain these values.

- The steady-state gain,
- Finally substitute these values into the table below to obtain the
relevent controller parameters.
Controller Type *Gain*Reset Derivative P Ts / Td - - PI 0.9 Ts / Td 3.3 Td - PID 1.2 Ts / Td 2.0 Td 0.5 Td

Therefore by substituting all the values in for the above and re-arranging we get the following values for the controller parameters:

Controller Type | Controller Gain, | Reset | Derivative |
---|---|---|---|

P | (Ts ) / (Td ) | - | - |

PI | (0.9 Ts ) / (Td ) | 3.3 Td | - |

PID | (1.2 Ts ) / (Td ) | 2.0 Td | 0.5 Td |

**Advantages** of this method are

- Only a single experimental test is needed.
- It does not require trial and error
- The controller settings are easily calculated.

However there are also **Disadvantages**

- Experiment is under open loop response and so disturbances may affect the results.
- Results tend to be oscillatory.
- Does not work well for complex responses - leads to inaccurate tuning model.

If we are lucky it may be similar in form but different in detail as shown below.

However if we are unlucky the response may be like this...

In a process the measurement ** y** is strictly speaking a
dimensioned quantity: temperature, pressure, flow etc.

The adjustment ** u** is usually a flow, so that the
process gain,
, will in general have
odd dimensions! This also makes it hard
to interpret or compare gain values.

In practice, both measurement and adjustment have a
**maximum
range** determined by the measuring instrument or valve.
It is best to work with **scaled** quantities always expressed as a
fraction or percentage of range, e.g.

Alternatively, if the gain is very small, say 0.01, then for a large change
in ** u** there is hardly any response in

What is required is a gain of around 1. This enables both input and output to be used to their full ranges which in turn improves the controllability.

So if this definition of the gain is used it is clear from a
glance if a
suitable value has been obtained or not.
In this case simply use the value of the *gain* from the first
table above along with the dimensionless process gain above to obtain
the dimensionless controller gain.

Firstly remember that you have a value of the ** dimensionless
gain** for the controller as evaluated above.

Now we define the **Proportional Band**, ** P**, as the
reciprocal of the dimensionless controller gain.

**Return to Start of Module 2.4: Controller
Design and System Modelling**