• Control systems use some output state of a system and a desired state to make control decisions.

• In general we use negative feedback systems because,

- they typically become more stable

- they become less sensitive to variation in component values

- it makes systems more immune to noise

• Consider the system below, and how it is enhanced by the addition of a control system.


Figure 19.1 An example of a feedback controller


Figure 19.2 Rules for a feedback controller

• Some of the things we do naturally (like the rules above) can be done with mathematics

19.2.1 PID Control Systems

• The basic equation for a PID controller is shown below. This function will try to compensate for error in a controlled system (the difference between desired and actual output values).


Figure 19.3 The PID control equation

• The figure below shows a basic PID controller in block diagram form.


Figure 19.4 A block diagram of a feedback controller



• The PID controller is the most common controller on the market.

19.2.2 Analysis of PID Controlled Systems With Laplace Transforms







19.2.3 Finding The System Response To An Input

• Even though the transfer function uses the Laplace ‘s’, it is still a ratio of input to output.

• Find an input in terms of the Laplace ‘s’








19.2.4 Controller Transfer Functions

• The table below is for typical control system types,