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.

 

• EXPERTUNE

• address

G.E.S.

4734 Soneearhray Dr.

Hubertus, WI 53033

tel: (414) 628-0088

• approx. $1500 (U.S.)

• will automatically adjust gain and time constant

 

• LT/TUNE

• address

Control Soft Inc.

4122 Wyncote Rd.

Cleveland, OH 44121

tel: (216) 234-5759

 

 

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,