7.1 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
7.1.1 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.
7.1.2 Analysis of PID Controlled Systems With Laplace Transforms
7.1.3 Manipulating Block Diagrams
7.1.3.1 - 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.
EXPERTUNE
will automatically adjust gain and time constant
LT/TUNE
7.1.4 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'
7.1.5 System Response
There are two very common systems assumed - first and second order.
First order systems are very simple, as is shown below.
7.1.6 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.
7.1.7 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,
7.1.8 Controller Transfer Functions
The table below is for typical control system types,
