1.0 Overviewsummarize

A  control system is a set of components that is added to an existing system to change, or control, the behavior of that system. A common control system is the thermostat added to the furnace in a house. Without the thermostat, the furnace will heat the house until the heat lost through walls and roof balances the heat added by the furnace. Unless the house is poorly insulated, the inside temperature may be uncomfortably hot before equilibrium is reached. The thermostat is a control system which changes the behavior of the furnace in the house. It monitors the temperature inside the house and then turns the furnace on or off in order to maintain a desired temperature. The figure below shows a simple model of the house and thermostat. Notice how the furnace turns on when the measured temperature drops below the desired temperature and turns off when it exceeds the desired temperature.

HomeThermostat(controller)image/svg+xmlOpen Clip Art LibraryHome2012-05-18T04:05:51   

Desired: 20.0 C    Measured: 25 C
Fig 1.1 Temperature Controller (Thermostat)

The thermostat is a simple on-off controller. In a more sophisticated controller, the controller output would vary with the measured value. An example of this type of control system is a DC motor position controller. The speed of a DC motor can be controlled by changing the voltage applied to the motor. In order to control position one must vary the speed of the motor so that it stops at just the right location. As long as the dynamics of the motor are constant, one can calculate the exact voltage and timing needed to turn the motor and then coast to stop. However, if the motor dynamics change due to something like wear, the voltage and timing no longer stop the motor at the desired location. The solution is to add a control system that monitors the position of the motor and then automatically adjusts the voltage to the motor so that the motor stops at the desired location even when the dynamics of the motor have changed. This type of controller is a linear control system. The voltage to the motor is not simply turned on or off, as in the thermostat. The voltage is varied depending on how far the motor position is from its desired position. You can experiment with a similar systems at the bottom of this page.

1.1 Terminology


The plant is the system whose behavior you are trying to control or modify. The system is usually a dynamic system modeled with differential equations. In the thermostat example, the plant is the furnace and house – we are trying to control the temperature inside the house. In the motor example, the plant is the motor and anything connected to the motor - we are trying to control the position of the motor shaft, but the dynamics of the motor are affected by all of the components connected to it.


The inputs are the values that can be changes to adjust response of plant. In the thermostat example the input is the switch that turns on or off the furnace. In the motor example the input is the voltage level applied to the DC motor.


The output is what you measure to monitor the behavior of the plant. Typically it is the output from a plant that you are trying to control. In the thermostat example, the output is the temperature of the house. In the motor example it is the position of the motor. Some plants have multiple inputs and multiple outputs (MIMO). Most of this site deals with designing control systems for single-input single-output (SISO) system. If the system is MIMO then we will pick the output the best indicates the behavior we are trying to control, and the input that has the most influence on that output. These concepts are related to “observability” and “controllability” of systems and are discussed here.

Controller or Compensator

The controller is the component that is added to the plant to control or modify the behavior of the plant. The controller typically monitors the output from the plant and then changes the input to the plant based on some control algorithm.

Open-loop control

In an open-loop control system the controller does not use knowledge of the plant output to adjust the input. In the thermostat example, and open-loop controller might turn the furnace on for 10 minutes four times every hour regardless of the outside temperature. Open-loop controls have limited usefulness because they assume the plant dynamics are constant. This rarely happens in engineering.

Closed-loop control

In a closed-loop control system the controller monitors the output of the plant and adjusts the input using some mathematical formula or algorithm.

1.2 Experiment

The following two pages will let you experiment with an open-loop and closed-loop motor position controllers. Notice how differently the system respond to changes in the plant model.

img Open-Loop Motor Control img Closed-Loop Motor Control