The basic type of controller is the **Feedback Controller**.

Feedforward controllers also exist but are more complicated to implement. Here we will describe the use of feedback controllers.

In feedback control the variable required to be controlled is measured. This measurement is compared with a given setpoint. The controller takes this error and decides what action should be taken by the manipulated variable to compensate for and hence remove the error.

**Figure 1 - Feedback Control Loop**

The **disadvantage** is that the disturbance has to enter and upset
the system before it is eliminated.

A feedback control loop can have one of two objectives.

- A
**servo**control loop is one which responds to a change in setpoint. The setpoint may be changed as a function of time (typical of this are batch processes), and therefore the controlled variable must follow the setpoint.**Figure 2 - Servo Control** - A
**regulatory**control loop is one which responds to a change in some input value, bringing the system back to steady state. Regulatory control is by far more common than servo control in the process industries.**Figure 3 - Regulatory Control**

The first type of controller that we will study is the proportional controller. This controller sets the manipulated variable in proportion to the difference between the setpoint and the measured variable. The bigger the difference, the greater the change in the manipulated variable.

The equation that describes a proportional controller is

is the output from the controller, i.e. the adjustment*ut*- is the constant of
proportionality, ususally called the controller
**gain** is the output of the controller at its design conditions, sometimes called the*ud***bias**is the required value of*ys*or the*y***setpoint**is the input to the controller, i.e. the measured variable*y*

The **advantage** of proportional control is that it is relatively
easy to implement. However the **disadvantage** is that when
implementing a proportional
only controller there will be an *offset* in the output. Thus there
is always a difference between the setpoint and the actual ouput.
The reason why this is so can be shown by means of an example.

is the flowrate through the pipe*F*is the measured flowrate*Fm*is the required, setpoint flowrate*Fs*is the error between the setpoint and measured value*e*is the valve position or controller output*Fv*

**Figure 4 - Diagram of Flowrate Example**

However, let us now consider what happens when the value of the setpoint
changes from 50 to 60 with ** Fd** staying constant at 50. First
the relevent equation is shown and then the
table below
summerises the results for different gains.

- Choose
to correspond always to the*ud**correct*output - Make the gain very large

The first is hard to achieve since it requires very accurate knowledge of the process, and would require changes whenever the setpoint is moved.

The second leads to problems of rangeability and sensitivity. Suppose the gain is 10, then measurement noise of 1% of the total range will cause the control valve to move over 10% of its total travel. This is unacceptable.

To remove the offset integral action is required and so PI control is
normally used. It works by summing the current controller error and the
integral of
all previous errors. It may be thought of as a way of automatically
calculating the quantity ** ud**. Proper tuning - described in
a subsequent
section - of
the integral part of a PI controller can improve its performance.

If the error ** e** is defined as

- is the reset time of the controller

Alternatively, we can differentiate this expression to get

As before

*F = y = u**e = Fs - F*

So

**Figure 5 - Response Curve**

- As time goes to infinity,
*x = a* - The rate of response of the system increases as
(called the time constant of the equation) becomes smaller*T*

For the flow control system with integral action we see that

will eventually become equal to*F**Fs*- This will happen faster if is small and/or is large