1) Introduction - Feed Back Control

Components in feedback control system

Figure 1 shows the main components in a control system.


Figure 1: Main components and signals in a feedback control system

y is the process state variable, that we want to control so it equals - in the best way - the set point SP .

To do the job, we measure the output by the sensor, and compare this measured signal with the set point. The difference between the two is called the error, e.

The error is input to the controller that send a controller output, u to some kind of actuator, that controls some input variable to the process.

This part of the course deals with the design of the controller.

Example:

Let say the process is a gas fired boiler. The out put of the boiler is hot water and the input is natural gas. We want to control the output temperature of the hot water, i.e. y is the temperature of the water. To measure the temperature we have a electronic temperature transmitter, i.e. a device that measure the temperature and send a standard signal to the comparator point, where it is subtracted from the set point. If the error is high and positive (as a result of a low temperature of the water) , the controller send a high control output to the actuator. The actuator could be a gas valve, and with a high input signal from the controller, the valve will by open to a high degree, thus sending a high gas flow to the boiler, giving - after some time - a higher temperature!

Performance of the control system


Figure 2: Step response

To test a control system it is common to change the set point in form of a "unit step" (or just a step of some kind).

Figure 2 shows the result of such an experiment. The performance can be expressed in more ways. As shown on the figure some values could be:

In the next lessons you will see, how we could design a controller, that - to some extend - can manage the task.

History

Watt invented - among more - the flyball governor, see figure 3.


Figure 3: Watt's flyball governor

The principle is as follows:

If the load of the steam engine is increased, the rotational speed is reduced. The task for the controler is to try to compensate for that - try to keep the speed constant what ever the load is.

To solve this task, the main shaft of the steam engine is connected to the above shown apparatus.

If the speed is reduced, then the two flyballs - because of less centrifugal forces - will come closer to the center.

This will infer the top lever to raise - to the left - and then desend to the right. And then open more for the steam valve - thus adding more steam to the engine - to compensat for the load.

And vica versa.