Control Systems

Definitions

• System: An interconnection of elements and devices for a desired purpose

• Control System: An interconnection of components forming a system configueration that will provide a desired response

  • E.g., a computer.
  • Input (stimulus from external source) --> Control System --> Output (actual response)

• Process: The device, plant, or system under control. The input and output relationship represents the cause-and-effect relationship of the process.

• Actuator: An actuator is a device that provides the motive power to the process (i.e., a device that causes the process to provide the output).

  • E.g., a temperature knob

• Sensor: A sensor most likely has an output, typically a voltage, that is proportional to the physical variable it measures.

  • E.g., a thermometer

• Controller: A controller is a device, possibly in the form of a chip, analogue electronics, or computer, which monitors and physically alters the operating conditions of a given dynamical system

Why

We need control systems so that we can achieve something.

• E.g., keeping a room temperature constant.

Transfer Function

$T(s) = \frac{Y(S)}{U(s)}$ where $Y(s) = L[Y(t)]$ $U(s) = L[U(t)]$

• Proportional values that shows the relationship between magnitude of input and magnitude of the output
• Many systems contain a method by which the gain can be altered, providing more or less "power" to the system. Imagine adding an arbitrary gain term $k$ to the function.

Open Loop System

Utilizes an actuating device to control the process directly without using feedback.

• The system outputs have no effect upon the signals entering the process; the output has no impact on the process.

Benefits:

• Cost effective because you don't need sensors
• Easy to maintain because the structure is simpler

Closed Loop Systems

Systems that use the measurement of the output and feedback to compare the actual output to the desired output response

Feedback

A key tool that can be used to modify the behavior of a system.

• This behavior altering effect is a mechanism used to act on a system to ensure that the desired output is achieved.

Use feedback to:

• Reduce the sensitivity of the performance to deal with variation and imperfections
• Reduce the effects of external disturbances and sensor noises
• Improve transient response characteristics
• Reduce steady-state error

Goal

A good control system is a system that will

• generate a response quickly and without oscillation (good transient response)
• have low error once settled (good steady-state response)
• will not oscillate wildly or damage that system (stability).

Design Process

1. Determine specifications from requirement
2. Draw block diagram
3. Create schematic
4. Obtain block diagram, signal diagram, and state-space representation
5. Reduce diagram to single block diagram or closed-loop system
6. Analyze, design, and test

State space form of the equation

MATLAB

Toolboxes are libraries that customize MATLAB for solving particular classes of problems. You can view algorithms and add your own.

To make a transfer function

1. set your variables and create the transfer function
2. Then create teh output.

DC Motors

stator: field windings, windings in which the main field flux is produced rotor (armature): armature winding, in which voltage is induced. magnetic fields is proportional to the current produced.