• 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,