Control Systems Ch 1 Flashcards
Control Systems Introduction:
Terms/Concepts in this Chapter
- Control Systems
- Types of Signals
- Control System Classifications
- Open Loop System
- Closed Loop System
Definition:
System
An arrangement of physical components,
which act together as a unit to achieve a certain objective
Definition:
Excitation
The input stimulus, or signal, to a control system
Definition:
Response
The signal produced by a Control System.
The output of the control system.
Definition:
Disturbance
Any signal that adversely affects the output of a system.
A good example is noise in the excitation signal.
Important Classifications
of Control Systems
- Time Varying and Time Invariant Systems
- Linear Systems and Non-Linear Systems
- Continuous Time and Discrete Time Systems
- Open and Closed Loop Systems
Time Invariant Control Systems
Those control systems in which the system parameters are independent of time.
The system behavior does not change with time.
Time Varying Control Systems
Systems whose parameters are functions of time.
The behavior depends not only on the input, but the time at which input is applied.
Considerabley more complex in design than Time Invariant Control Systems.
Linear System
A Linear System
is one that obeys the Superposition Property.
Adding and scaling the inputs results in the same output as adding and scaling the original output in the same way.
a x1(t) + b x2(t) → a y1(t) + b y2(t)
Basic System Properties
Superposition Property:
A combination of two system properties:
- Additivity Property
- Homogeneity or Scaling Property
System Properties:
Additivity Property
A system is said to be Additive
if the response of a system
when 2 or more inputs are applied together
is equal to
the sum of responses when the signals are applied individually.
if x1(t) → y1(t) and x2(t) → y2(t),
Then the system is additive if, x1(t) + x2(t) → y1(t) + y2(t)
System Properties:
Homogeneity or Scaling Property
A system is said to obey the Homogeneity Property
if the response of a system to a scaled input
is the same as the scaled response to the unscaled input.
if x(t) → y(t),
then the system obeys homogeneity if
a x(t) → a y(t), where a is constant.
System Properties:
Superposition Property
A system is said to obey the Superposition Property if it obeys both the Additivity and Homogeneity Properties.
if x(t) → y(t),
then the system obeys the Superposition Property if
a x1(t) + b x2(t) → a y1(t) + b y2(t)
where a and b are constants.
Why is it reasonable to model non-linear real world systems as
Linear Time Invariant(LTI) Systems?
- Most practical systems are non-linear to a certain extent
- Analyzing and finding solutions to non-linear time variant systems is extremely difficult and time-consuming
- When the non-linearity is negligible and does not affect the system response badly, the system can be treated as linear
- This makes the math a lot easier
- The advantages of the approximation far outweigh the disadvantages in almost all cases.
Continuous Time
vs
Discrete Time
Functions and Systems
Functions:
Continuous Time Functions are defined for every instant of time.
Discrete Time Functions are only defined for certain instants of time, such as every minute or hour.
Systems:
In a Continuous Time System, all the system variables are continuous time functions.
In a Discrete Time System, at least one of the system variables is a discrete function.
