Ch 1: Introduction to Control Systems Flashcards
Three Major
Theories
Classical Control Theory
Modern Control Theory
Robust Control Theory
Classic Control Theory:
Important Features and Methods
- Use of Differential Equations to describe systems
- Analysis of stability of closed loop systems based on open-loop, steady state sinusoidal input
- Root-Locus Method
- Frequency Response
- Developed stable systems
- Did not deal with multiple input/output systems
- Primary focus on Linear Time Invariant, single input/output systems
Note: This list is NOT comprehensive
Modern Control Theory:
Important Features/Methods
Introduced
- Analysis in Time Domain
- Synthesis with State Variables
Basic Definitions:
Controlled Variable
The quantity or condition that is measured and controlled
Basic Definitions:
Control Signal
Also called the ‘Manipulated Value’
The quantity or condition that is varied by the controller to affect the value of the controlled variable.
Basic Definitions:
Control
The action of measuring the Controlled Variable, then applying the Control Signal to correct or limit deviation of the Controlled Variable from a desired value
Basic Definitions:
Plants
In the context of Control Systems,
a Plant is any physical object that is to be controlled.
A piece of equipment functioning to perform some operation.
Could be anything from a simple tool to a whole factory or power grid, or financial system.
Basic Definitions:
Process
Any operation that is to be controlled
Basic Definitions:
Systems
A combination of components that act together to achieve a certain objective.
Basic Definitions:
Disturbances
A signal that tends to adversely affect the value of the output of a system.
Two Types:
- Internal
- Generated from within the system
- External
- Generated from outside the system, treated as a kind of input
- Examples: noise, kicking a robot
Basic Definitions:
Feedback Control
An operation that uses the output of a system to reduce the difference between output and some Reference Input.
Makes corrections.
This reduces the impact of Disturbances in the system.
Robust Control Theory:
Basic Idea
- System models don’t perfectly reflect the actual, real world system
- Robust Control Theory attempts to account for the difference by including an Uncertainty or Error Value estimate in the model
Robust Control Theory:
Estimating Uncertainty
Very basic Mathematical Approach
Assume G(s) is a perfect model of a system, and ~G(s) is a model with some uncertainty ∆(s)
The error can be related as either a
- Multiplicative Factor
- ~G(s) = G(s) [1 + ∆(s)]
- Additive Factor
- ~G(s) = G(s) + ∆(s)
Exact uncertainty is unknowable, so we use an upper bound estimate, W(s)
Feedback Control System:
Summary
A system that maintains a prescribed relationship between the output and the reference input,
by comparing them and using the difference as a means of control
Closed-Loop Control Systems:
Summary
Term is used interchangeably with Feedback Control System. The ‘Loop’ IS the feedback.
The Actuating Error Signal(the difference) is fed to the controller to reduce the error and bring the output of the system to a desired value.
“Closed Loop” always implies the use of feedback
Open-Loop Control Systems:
Summary
Systems in which the output has no effect on the control action.
Output is not fed back for comparison or even measured.
Accuracy of the system must depend on calibration and the system will not compensate for disturbances.
Note: Any system that operates with only time as the input is open-loop
Compensation:
Definition
Modification of the system dynamics to satisfy given specifications.
This is done in three ways:
- Adjusting Gain - primary method
- Installing a Compensator device
- Performing redesign/restructuring of the system
Control System Design:
Three Approaches to Design and Analysis used in this book
Root-Locus Approach
Frequency Response Approach
State-Space Approach
Control System Design:
Basic Considerations
Performance Specifications
System Compensation
Design Procedures
Control System Design:
Major Performance Specifications/Requirements and some examples
Define what the system must do and under which performance constraints.
Requirements may be given as numeric values, or as more general qualitative statements
- Transient Response Requirements
- Maximum overshoot
- Settling time in Step Response
- Steady State Requirements
- Steady State Error following Ramp Input
- Frequency Response Requirements
- Operating frequency range
- Dealing with high/low frequency
Control System Design:
Basic steps of designing a system
- Set up a mathematical model, starting as simply as possible
- Adjust parameters of a compensator
- Construct prototype and test the open-loop system
- If open-loop test goes well, close the loop and test the prototype
- Repeat steps, adjusting parameters and design based on trials
- Attempt to catch biggest issues early
