1.1 CONTROL SYSTEMS
• 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
1.1.1 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).
• The figure below shows a basic PID controller in block diagram form.
• The PID controller is the most common controller on the market.
1.1.2 Analysis of PID Controlled Systems With Laplace Transforms
1.1.3 Manipulating Block Diagrams
1.1.3.1 - Commercial PID Tuners
• WARNING: Don’t assume results from these systems are perfect, proper engineering methods must be used to avoid failures in critical systems.
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1.1.4 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’
1.1.5 System Response
• There are two very common systems assumed - first and second order.
• First order systems are very simple, as is shown below.
1.1.6 A Motor Control System Example
• 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.
1.1.7 System Error
• We typically will be interested in system error and feedback error.
• Consider a simple negative feedback system with various inputs,
• Practice problem - find the steady state system error for the transfer function and ramp below,
1.1.8 Controller Transfer Functions
• The table below is for typical control system types,