Flashcards in Semester 1 Deck (37):

1

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

### Linear and non-linear

2

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

###
1) Differential equations

2)Input-output relationship

3)Transfer functions

3

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

### x

4

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

### u, the inputs are the signals coming from the actuators

5

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

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

6

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

### n

7

## What is another name for linear systems?

### time invariant systems

8

## What type of system can be described by transfer function?

### Linear, time-invariant systems

9

## How is a linear system described by transfer function?

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

10

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

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

11

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

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

12

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

### Look at the order of the system (the number of x's)

13

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

### Look at the number of y's

14

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

### Look at the number of u's

15

## 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.

16

## How do you analyse the stability of a system?

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

17

## 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)

18

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

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

19

## 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.

20

## 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.

21

## How do you check whether a system is state controllable?

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

22

## How do you check whether a system is output controllable?

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

23

## 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.

24

## 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.

25

## What does proportional gain do in an analog PID controller?

### Gives rise to a steady state error.

26

## What does integral gain do in an analog PID controller?

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

27

## What does derivative gain do in an analog PID controller?

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

28

## How can a discrete PID be implemented in practice?

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

29

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

### 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.

30

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

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

31

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

### 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.

32

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

###
1 - Model the system

2- Identify the parameters

3- Analyse properties of the system (stability, controllability etc)

4- Start designing the controller

33

## Why is a proportional controller not recommended in practice?

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

34

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

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

35

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

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

36

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

### u=k1x1+k2x2+v

37