Describe any two discontinuous controller modes.

There are two discontinuous controller modes are :-

1. Two position (on-off controller)
2. Three position (multi-position controller)

1. On-Off Controller :- This controller works as switch controller only in two steps ON and OFF.

$$P = 0 \%\ (OFF)\ ;\ e_p \lt 0$$

$$P = 100 \%\ (ON)\ ;\ e_p \gt 0$$

$$where,\ e_p = error$$

$$error\ =\ set\ point\ -\ measured\ variable$$

From the above relation we know that the measure value is less than set point i.e. positive error.

That is when the error occurs, the controller output results full. And if the measure Variable value is more than set point a negative error will occur. Then the controller output is zero.

Example :- The Heaters is used for water heating.

1. Multi-position controller :- The multi-position committer are discontinuous controller in three positions.

Let P be the % of error. Thus this can be expressed in three forms such as

$$P = 100\%\ ;\ e_p \gt +e_1,$$

$$P = 50\%\ ;\ -e_1 \lt e_p \lt + e_1$$

$$P = 0\%\ ;\ e_p \lt -e_1$$

When the percentage of error is between $+e_1$, and $-e_1$, the Controller settles down to a nominal controller output of 50%. If the percentage of error exceed to $+e_1$ or more than it then the controller O/P is increased to 100%. If the percentage error is less than $-e_1$, then the controller O/P goes to zero. These three conditions are represented graphically below -

These type of controller are more complicated to design and it takes time to obtain the final control element of the process.

Example :-

1. Control of Servo-meter for any application
2. Locomotive Control.