In this lecture we demonstrate some control conepts through a detailed example. No mathematical relations are used in explaining the example. The system (or process) that we will consider consists of a tank that contains oil. The tank sits on a heater which supplies energy to the oil. The energy supplied by the heater depends on the input voltage to the heater which is controlled by a knob. Please refer to Figure 1 for a sketch of this thermal system.

Figure 1: The oil, tank and heater system.

In this application we are interested in regulating the oil temperature. The system can be represented by a block diagram as shown in Figure 2. The input to the system is the voltage to the heater or knob position, whereas the output of the system is the oil temperature.

Figure 2: Block diagram of the oil, tank and heater system.

Let us suppose that this process is in a factory and a worker adjusts the voltage knob to set the oil temperature at a desired value determined by his boss. The boss decides the desired temperature based on the factory requirements. The worker uses a lookup table to position the knob. The table contains knob positions and the corresponding values of steady state temperature (we mean by steady state the final value since it takes some time to heat the oil to the desired temperature). An experiment was performed in the past to obtain the lookup table. The knob was adjusted at the different positions and the corresponding values of temperature were measured by a temperature sensor such as a thermometer or a thermocouple. See Figure 3.

Figure 3: Open loop control of the oil temperature. Note that there is no device to measure the oil temperature.

The situation in Figure 3 can be represented by a block diagram as shown in Figure 4. The boss decides the desired temperature which he tells the worker to adjust. Therefore, the input to the worker is the desired temperature. The worker uses the lookup table to select the knob position. If everything is OK the oil temperature should go to a value close to the desired value. The actual oil temperature will usually be different from the desired value due environmental and operating condition changes. The worker does not know the final temperature since there is no sensor to provide the temperature measurement. The worker just adjusts the knob once and he hopes that the temperature will go to the desired value. This is called an open loop system. In this kind of system the output (temperature here) is controlled directly using an actuating device (human worker here) without measuring this output.

Figure 4: Block diagram representation of the open loop system.

The boss would like to have the oil temperature more accurate, that is, the oil temperature should be very close to the desired value. He buys a thermometer (temperature sensor) so that the worker could read the oil temperature and thus adjusts the knob appropriately to make the temperature as close as possible to the desired value. If the measured tempearture is less than the desired one he will raise the knob, otherwise he will lower it. He keeps doing this until the desired value of temperature is achieved. The worker is able to do a better job because he has a sensor or feedback information about the oil temperature. In this case we have a closed loop system.

Figure 5: Closed loop control of the oil temperature. Note that there is a thermometer to measure the oil temperature.

Click here to experiment with the system yourself (Java)

Click here to see an animation (swf)
Click here to see the mechanical temperature control animation.

The situation in Figure 5 can be represented by a block diagram as shown in Figure 6. The boss decides the desired temperature which he tells the worker to adjust. The worker uses the desired and measured temperatures to calculate the error=desired-measured. If the error is positive he raises the knob, otherwise he lowers it. He repeats this procesdure until the error is zero, i.e., desired temp. = measured temp. Note that the lookup table is unnecessary in the closed loop case. Nevertheless, the lookup table gives the worker the initial guess for the knob position depending on the desired temperature and then he makes the appropriate changes to take the error to zero.

Figure 6: Block diagram representation of the closed loop (feedback) system.

In the above example the controller was a human (worker). The controller is the part of the system that makes decisions based on an objective. The objective in the thermal system was to achieve the desired value of oil temperature. This was done by making the difference between the desired and measured values of temperature equal to zero. The human could be replaced by an electronic circuit, computer or a mechanical controller. We used a thermometer for the tempearture measurement. A thermocouple which converts temperature to voltage could be used for the electronic circuit or computer controller. No sensor is needed for the mechanical controller. The relationship between pressure and temperature could be used to design a mechanism for moving the knob up and down to achieve the desired value of tempearature.