Post-Midterm: Intro digital systems + z transform

Question 1

draw the continuous time and continuous control diagram

Question 2

physical system (model)
modelling is a method of identifying:

Answer 2

system parameters in order to find relation (mathematical relation) between input and output

Question 3

examples of physical system (model)

Answer 3

DC motors
mobile robots
inverted pendulum

Question 4

controller
made of ___ or any kind of device that can ___

Answer 4

electronic components (microcontrollers, microprocessors, computers

produce the required control signal

Question 5

measurement unit
measures the ___ and may include

Answer 5

current output
amplification process

Question 6

signal
contains info about

Answer 6

block/system behaviour

Question 7

summator
compares ____ to ___ to produce ___

Answer 7

measured output signal
reference input
error signal

Question 8

summator
in case of analog control, summator is made of ___

Answer 8

operational amplifier

Question 9

summator
cam be included in _____ for the case of using digital control

Answer 9

control algorithm (microcontroller/microprocessor/computer)

Question 10

function and time
function representing a ______

Answer 10

physical quantity or variable

Question 11

function and time
contains info about _____

Answer 11

behaviour or nature of phenomenon

Question 12

function and time
represented as function of _____

Answer 12

independent variable ‘t’

Question 13

function and time
usually ‘__ ‘represents time
thus a signal ‘__’ is denoted by ___

Answer 13

t
x
x(t)

Question 14

digital control system
system (___/__/__) placed within a system to _____ such that a more ____ is obtained based on a ____

Answer 14

digital computer/microcontroller/microprocessor
modify system dynamics
satisfactory response
reference/desired trajectory

Question 15

advantages of digital control systems

Answer 15

accurate and reliable

reduced sensitivity to noise

flexible in programming

low cost and compact (small-size)

most of real life control systems are inherently digital (drones, mobile robots, radar tracking systems)

Question 16

disadvantages of digital control systems

Answer 16

require complex math algorithms

lose info during convos (from Analog–>digital and vice versa

Question 17

common system description methods

Answer 17

continuous time system
discrete time system

Question 18

continuous time systems
type of equations:
transfer function using :
type of state space:

Answer 18

differential equations
transfer functions using laplace transform
continuous state-space

Question 19

discrete time systems
type of equations:
transfer function using :
type of state space:

Answer 19

difference equations
transfer functions using z-transform
discrete state-space

Question 20

why should we study digital control systems
availability of ___ and ___digital computers

Answer 20

inexpensive and powerful

Question 21

why should we study digital control systems
___implementation of ___ and ___ math algorithms in digital form

Answer 21

easy
complicated

Question 22

why should we study digital control systems
they are __ and be used to control both __ and ____

Answer 22

flexible
digital and analog systems (plants)

Question 23

why should we study digital control systems
availability of appropriate _____ equipment that be used to facilitate the interface between ___ and ___

Answer 23

peripheral
digital controller
physical system to be controlled (plant)

Question 24

examples of digital systems

Answer 24

computer
mobile phones
monitor
tv
watch
automotive (vehicles) control and interface
avionics (aircrafts) control and interface

Question 25

advantages of digital control systems

Answer 25

low susceptibility to environment conditions (reduced sensitivity to noise) easier transmission of digital signals accurate and reliable (analog drift eliminated) no parameters drift ability to perform complex tasks at low costs easy modification of software (flexible programming) simple interface with other digital systems (many real-life control systems are inherently digital( eg. radar tracking systems)

Question 26

disadvantages of digital control systems

Answer 26

errors due to finite precision and discrete nature of systems (loss of info during conversion) more sophisticated engineering (development of complex math algorithms) limitation of operation speed (complex algorithms may reduce sampling rate) digital system has probability of failure and depending on application may lead to catastrophic failure

Question 27

what is analog signal __ function of ___ where signal ___ can take any values within the physical limitations of the system

Answer 27

continuous time magnitude

Question 28

sampled-data signal signal defined only at ____

Answer 28

discrete instants of time (usually periodic)

Question 29

sampled-data signal magnitude can take ____

Answer 29

any value within physical limitation of system

Question 30

sampled-data signal time interval between 2 consecutive instants should be ____. this enables the data between the 2 consecutive instants to be approximated using ___

Answer 30

sufficiently small simple interpolations

Question 31

sampling process can be defined as steps 1-6 refer to page 4

Answer 31

1. notation tk=kT (k=0,1,2..) 2.T refers to a fixed sample time , ex T=0.001 sec= 1ms 3. time at any instant is defined using number of samples tk=KT 4.pattern of tk is periodically repeated, tk+n-tk = constant 5. multirate can be used if we have more than 1 sampling rates, kT1, and kT2 where T1=/ T2 6. random sampling can be used as well

Question 32

objective of digital control signal

Answer 32

obtained accumulated satisfactory response

Question 33

accumulated errors sampling has _

Answer 33

2 1. assume change between 2 samples is small enough 2. output value is normally a number

Question 34

quantization is an ___ process which ___ with infinite number of values is represented with a __

Answer 34

approximation analog signal finite of digits (distinct values)

Question 35

quantization quantization level (resolution) defined as the __

Answer 35

range between 2 adjacent decision points

Question 36

quantization given by eq

Answer 36

q=(FSR)/(2^N) where FSR is full scale range n = # of bits

Question 37

quantization since # of bits is infinite, quantization process always results in round off to ___known as ___

Answer 37

nearest digital level quantization error

Question 38

quantization (qe) bounded by __

Answer 38

+/- q/2

Question 39

quantization nature of quantization error is similar to that of ____ and the error is ___ distributed between ___and __ which means the sum of error is _____

Answer 39

random noise uniformly distributed -q/2 and +q/2 white noise

Question 40

transducer device which converts ___ in one from to and ___in another form

Answer 40

input signal output signal

Question 41

analog to digital converter is a ___ where the input signal is a ______ and the output signal is a ____ with __ levels

Answer 41

transducer continuous function of time quantized signal certain distinct

Question 42

digital to analog converter is a ___ where the input signal is a ______ and the output signal is a ____

Answer 42

transducer quantized signal smooth continuous function of time

Question 43

super position is based on

Answer 43

homogenity and additivity

Question 44

time invariant stationary systems systems whose properties ___

Answer 44

do not change with time

Question 45

class of control systems

Answer 45

regulating systems tracking systems

Question 46

regulating systems objective is to ____ even in presence of ___

Answer 46

bring the system output y(t) very close to the origin or to certain point in presence of external disturbances

Question 47

tracking systems objective is for the __ regulation is a special case of tracking where ____ regulation in presence of disturbances is known as ____ regulation in presence of perturbations in plant parameters is known as ____ control system that has disturbance rejection and low sensitivity to perturbations or measurement noise is called ___

Answer 47

system output y(t) to track or follow a desired reference input signal r(t) desired input is zero disturbance rejection low sensitivity to perturbations robust system

Question 48

review difference eq (slide 9)

Question 49

3 approaches used to solve set of differential equations

Answer 49

classical method sequential method z-transform