• 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.
• Some of the things we do naturally (like the rules above) can be done with mathematics
• 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).
• The figure below shows a basic PID controller in block diagram form.
• The PID controller is the most common controller on the market.
• 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’
• There are two very common systems assumed - first and second order.
• First order systems are very simple, as is shown below.
• Condsider the example of a DC servo motor controlled by a computer. The purpose of the controller is to position the motor. The system below shows a reasonable control system arrangement. Some elements such as power supplies and commons for voltages are omitted for clarity.
• This system can then be redrawn with a block diagram.
• The block diagram can now be filled out with actual values for the components. Do this below.
• Convert the block diagram into a transfer function for the entire system.
• Pick a value of the gain ’K’ to give a system performance with the damping factor = 1.0.
