Semester 1 Flashcards
What are the two main categories that systems can be broadly classified into?
Linear and non-linear
What are the main 3 ways a system can be described?
1) Differential equations
2) Input-output relationship
3) Transfer functions
What letter is used to represent the state of a system?
x
What letter is used to represent the input of a system?
u, the inputs are the signals coming from the actuators
What letter is used to represent the output/measurements of a system?
y, the outputs/measurements are the signals coming from the sensors.
What letter is used to describe the order of a system?
n
What is another name for linear systems?
time invariant systems
What type of system can be described by transfer function?
Linear, time-invariant systems
How is a linear system described by transfer function?
H(s) = Y(s)/U(s) = N(s)/D(s)
What is U(s) in a linear systems transfer function?
U(s) = L [u(t)]
What is Y(s) in a linear systems transfer function?
Y(s) = L [y(t)]
How can you tell how many state variables a system has?
Look at the order of the system (the number of x’s)
How can you tell how many outputs (sensors) a system has?
Look at the number of y’s
How can you tell the number of inputs there are in a system?
Look at the number of u’s
What is the main difference between a linear system and a non-linear system?
A linear system can be described by transfer function whereas a non linear system can’t.
How do you analyse the stability of a system?
Use the characteristic equation P(s) = det(sI-A) to compute the eigenvalues of a.
How can you tell from the eigenvalues whether a system is stable or not?
If the system is stable the eigenvalues will lie in the left-half complex plane (be negative)
What is the transfer function of a system, involving the term (sI-A)?
H(s) = C 1/(sI-A) B
Why is it necessary to analyse the state controllability of a system before designing the controller for the system?
You cannot design a state feedback for a system that isn’t state controllable.
Why is it necessary to analyse the output controllability of a system before designing the systems controller?
If it is not output controllable then an output feedback cannot be designed for the controller.
How do you check whether a system is state controllable?
Check whether the rank of the matrix [B, AB] is equal to 2.
How do you check whether a system is output controllable?
Check whether the rank of the matrix [CB, CAB] is equal to 1.
What are the advantages and disadvantages of a state feedback controller?
It is not directly implementable since it doesn’t measure x2, however there is a greater degree of freedom when designing the controller.
What are the advantages and disadvantages of the output feedback controller?
It is readily implementable however there is a lesser degree of freedom in designing the controller than a state feedback controller.