Semester 1

Question 1

What are the two main categories that systems can be broadly classified into?

Answer 1

Linear and non-linear

Question 2

What are the main 3 ways a system can be described?

Answer 2

1) Differential equations
2) Input-output relationship
3) Transfer functions

Question 3

What letter is used to represent the state of a system?

Answer 3

x

Question 4

What letter is used to represent the input of a system?

Answer 4

u, the inputs are the signals coming from the actuators

Question 5

What letter is used to represent the output/measurements of a system?

Answer 5

y, the outputs/measurements are the signals coming from the sensors.

Question 6

What letter is used to describe the order of a system?

Answer 6

n

Question 7

What is another name for linear systems?

Answer 7

time invariant systems

Question 8

What type of system can be described by transfer function?

Answer 8

Linear, time-invariant systems

Question 9

How is a linear system described by transfer function?

Answer 9

H(s) = Y(s)/U(s) = N(s)/D(s)

Question 10

What is U(s) in a linear systems transfer function?

Answer 10

U(s) = L [u(t)]

Question 11

What is Y(s) in a linear systems transfer function?

Answer 11

Y(s) = L [y(t)]

Question 12

How can you tell how many state variables a system has?

Answer 12

Look at the order of the system (the number of x’s)

Question 13

How can you tell how many outputs (sensors) a system has?

Answer 13

Look at the number of y’s

Question 14

How can you tell the number of inputs there are in a system?

Answer 14

Look at the number of u’s

Question 15

What is the main difference between a linear system and a non-linear system?

Answer 15

A linear system can be described by transfer function whereas a non linear system can’t.

Question 16

How do you analyse the stability of a system?

Answer 16

Use the characteristic equation P(s) = det(sI-A) to compute the eigenvalues of a.

Question 17

How can you tell from the eigenvalues whether a system is stable or not?

Answer 17

If the system is stable the eigenvalues will lie in the left-half complex plane (be negative)

Question 18

What is the transfer function of a system, involving the term (sI-A)?

Answer 18

H(s) = C 1/(sI-A) B

Question 19

Why is it necessary to analyse the state controllability of a system before designing the controller for the system?

Answer 19

You cannot design a state feedback for a system that isn’t state controllable.

Question 20

Why is it necessary to analyse the output controllability of a system before designing the systems controller?

Answer 20

If it is not output controllable then an output feedback cannot be designed for the controller.

Question 21

How do you check whether a system is state controllable?

Answer 21

Check whether the rank of the matrix [B, AB] is equal to 2.

Question 22

How do you check whether a system is output controllable?

Answer 22

Check whether the rank of the matrix [CB, CAB] is equal to 1.

Question 23

What are the advantages and disadvantages of a state feedback controller?

Answer 23

It is not directly implementable since it doesn’t measure x2, however there is a greater degree of freedom when designing the controller.

Question 24

What are the advantages and disadvantages of the output feedback controller?

Answer 24

It is readily implementable however there is a lesser degree of freedom in designing the controller than a state feedback controller.

Question 25

What does proportional gain do in an analog PID controller?

Answer 25

Gives rise to a steady state error.

Question 26

What does integral gain do in an analog PID controller?

Answer 26

Eliminates the steady state error caused by the proportional gain, but it slows down the response time.

Question 27

What does derivative gain do in an analog PID controller?

Answer 27

Increases the rapidity of the response but might give rise to overshoots.

Question 28

How can a discrete PID be implemented in practice?

Answer 28

With an AD converter on the front and DA converter on the back.

Question 29

What are the advantages and disadvantages of describing a system using a transfer function?

Answer 29

The stability can easily be analysed by computing the poles of the system, but since the initial conditions are assumed to be zero it id only suitable for linear, time-invariant systems.

Question 30

What is the drawback of describing a system by input-output relationship?

Answer 30

It’s generally described using an nth order differential equation, making it difficult to analyse.

Question 31

What is the main advantage of describing a system by state-space approach?

Answer 31

It is a general approach and can be employed for both linear and non linear systems that can decompose an nth order differential into n first order differential equations.

Question 32

What step-by-step procedure would you follow when designing a controller in an industrial environment?

Answer 32

1 - Model the system
2- Identify the parameters
3- Analyse properties of the system (stability, controllability etc)
4- Start designing the controller

Question 33

Why is a proportional controller not recommended in practice?

Answer 33

It gives rise to steady state error, causing the output to not reach its target.

Question 34

What is the transfer function of a system in terms of its input and output?

Answer 34

H(s) = Output (S) / input (S)

Question 35

How do you check that the rank of a 2x2 matrix is 2?

Answer 35

it has a rank of 2 if it has a non-zero determinant

Question 36

When u(t) = Kx(t) + v(t), what is the controller design given by?

Answer 36

u=k1x1+k2x2+v

Question 37

When u(t) = Kx(t) + v(t), what is the closed loop system given by?

Answer 37

dx/dt = (A+BK)+Bv