RISHARD DORF _ MODERN CONTROL SYSTEMS CHAPTER 1 Multiple Choice This activity contains 10 questions.
Early applicatio! o" "ee#$ac% cotrol iclu#e &hich o" the "ollo&i'( Drebbel’s temperature regulator Water clock of Ktesibios Watt’s flyball governor All of the above
I)portat )o#er applicatio! o" cotrol !y!te)! iclu#e &hich o" the "ollo&i'( Fuel-efficient and safe automobiles Autonomous robots Automated manufacturing All of the above
Co)plete the "ollo&i' !etece* Cotrol o" a i#u!trial proce!! $y auto)atic rather tha )aual )ea! i! o"te calle# ________* automation. a specification. negative feedback.
a design gap.
Co)plete the "ollo&i' !etece+ _________ are itrii!ic i the pro're!!io "ro) a iitial cocept to the "ial pro#uct* Closed-loop feedback systems pen-loop control systems Design gaps Flyball governors
Co)plete the "ollo&i' !etece+ Cotrol e'ieer! are cocere# &ith u#er!ta#i' a# cotrolli' !e')et! o" their e,iro)et!o"te calle# ________ ________** trade-offs. risk. design synthesis. systems.
Early pioeer! i the #e,elop)et o" !y!te)! a# cotrol theory iclu#e+ !. ". #lack !. $y%uist !. W. #ode All of the above
a design gap.
Co)plete the "ollo&i' !etece+ _________ are itrii!ic i the pro're!!io "ro) a iitial cocept to the "ial pro#uct* Closed-loop feedback systems pen-loop control systems Design gaps Flyball governors
Co)plete the "ollo&i' !etece+ Cotrol e'ieer! are cocere# &ith u#er!ta#i' a# cotrolli' !e')et! o" their e,iro)et!o"te calle# ________ ________** trade-offs. risk. design synthesis. systems.
Early pioeer! i the #e,elop)et o" !y!te)! a# cotrol theory iclu#e+ !. ". #lack !. $y%uist !. W. #ode All of the above
Co)plete the "ollo&i' !etece+ A ope.loop cotrol !y!te) utili/e! a actuati' #e,ice to cotrol a proce!! _______* using feedback. &ithout using feedback. in engineering synthesis. in engineering design.
A !y!te) &ith )ore tha oe iput ,aria$le or )ore tha oe output ,aria$le i! %o& $y &hat a)e( Closed-loop feedback system 'ultivariable control system pen-loop feedback system (obust control system
Cotrol e'ieeri' i! applica$le to &hich "iel#! o" e'ieeri'( 'echanical and aerospace Chemical and environmental environmental )lectrical and biomedical All of the above
Clo!e#.loop cotrol !y!te)! !houl# ha,e &hich o" the "ollo&i' propertie!+ Desirable responses to commands *ood regulation against disturbances +o& sensitivity to changes in the plant parameters All of the above
)arly applications of feedback control include &hich of the follo&ing,
1*
All of the above Your A!&er+
0*
mportant modern applications of control systems include &hich of the follo&ing, Autonomous robots Your A!&er+ All of the above Correct A!&er+
*
Complete the follo&ing sentence. Control of an industrial process by automatic rather than manual means is often called . automation. Your A!&er+
2*
Complete the follo&ing sentence/ are intrinisic in the progression from an initial concept to the final product. pen-loop control systems Your A!&er+ Design gaps Correct A!&er+
3*
Complete the follo&ing sentence/ Control engineers are concerned &ith understanding and controlling segments of their environments0 often called . trade-offs. Your A!&er+ systems. Correct A!&er+
)arly pioneers in the development of systems and control theory include/
4*
All of the above Your A!&er+
5*
Complete the follo&ing sentence/ An open-loop control system utili1es an actuating device to control a process . &ithout using feedback. Your A!&er+
A system &ith more than one input variable or more than one output variable is kno&n by &hat name,
6*
'ultivariable control system Your A!&er+
Control engineering is applicable to &hich fields of engineering,
7*
All of the above Your A!&er+
Closed-loop control systems should have &hich of the follo&ing properties/
18 *
All of the above Your A!&er+
True or Fal!e This activity contains 5 questions.
The "ly$all 'o,eror i! 'eerally a'ree# to $e the "ir!t auto)atic "ee#$ac% cotroller u!e# i a i#u!trial proce!!* 2rue False
A clo!e#.loop cotrol !y!te) u!e! a )ea!ure)et o" the output a# "ee#.$ac% o" the !i'al to co)pare it &ith the #e!ire# iput*
2rue False
E'ieeri' !ythe!i! a# e'ieeri' aaly!i! are the !a)e* 2rue False
Thi! i! a e9a)ple o" a clo!e#.loop "ee#$ac% !y!te)*
2rue False
A )ulti,aria$le !y!te) i! a !y!te) &ith )ore tha oe iput a#:or )ore tha oe output* 2rue False
'atch the term &ith it3s definition
1*
Optio
Your A!&er+
Correct A!&er+
The output !i'al i! "e# $ac% !o that it !u$tract! "ro) the iput !i'al*
A. ptimi1ation
4. $egative feedback
A !y!te) that u!e! a )ea!ure)et o" the output a# co)pare! it &ith the #e!ire# output*
#. (isk
F. Closed-loop feedback control system
A !et o" pre!cri$e# per"or)ace criteria*
C. Comple5ity of design
!. "pecifications
1*2
A )ea!ure o" the output o" the !y!te) u!e# "or "ee#$ac% to cotrol the !y!te)*
*. Flyball governor
K. Feedback signal
1*3
A !y!te) &ith )ore tha oe iput ,aria$le or )ore tha oe output ,aria$le*
(. 4roductivity
'. 'ultivariable control system
The re!ult o" )a%i' a ;u#'e)et a$out ho& )uch co)pro)i!e )u!t $e )a#e $et&ee co"licti' criteria*
6. 2rade-off
6. 2rade-off
A itercoectio o" ele)et! a# #e,ice! "or a #e!ire# purpo!e*
6. 2rade-off
D. "ystem
A repro'ra))a$le-)ulti"uctioal )aipulator u!e# "or a ,ariety o" ta!%!*
. 4ositive feedback
+. (obot
A 'ap $et&ee the co)ple9 phy!ical !y!te) a# the #e!i' )o#el itri!ic to the pro're!!io "ro) the iitial cocept to the "ial pro#uct*
$. Design gap
$. Design gap
The itricate patter o" iter&o,e part! a# %o&le#'e re
+. (obot
C. Comple5ity of design
The ratio o" phy!ical output to phy!ical iput o" a i#u!trial proce!!*
!. "pecifications
(. 4roductivity
1*1
1*0
1*
1*4
1*5
1*6
1*7
1*18
1*11
The proce!! o" #e!i'i' a techical !y!te)*
C. Comple5ity of design
". )ngineering design
#. (isk
1*1
A !y!te) that utili/e! a #e,ice to cotrol the proce!! &ithout u!i' "ee#$ac%*
7. pen-loop control system
D. "ystem
#. (isk
1*12
=certaitie! e)$o#ie# i the uite#e# co!e
". )ngineering design
). Design
The #e,ice-plat-or !y!te) u#er cotrol*
$. Design gap
2. 4rocess
The output !i'al i! "e# $ac% !o that it a##! to the iput !i'al*
'. 'ultivariable control system
. 4ositive feedback
A itercoectio o" co)poet! "or)i' a !y!te) co"i'uratio that &ill pro,i#e a #e!ire# re!po!e*
!. "pecifications
8. Control system
The cotrol o" a proce!! $y auto)atic )ea!*
!. "pecifications
9. Automation
The a#;u!t)et o" the para)eter! to achie,e the )o!t "a,ora$le or a#,ata'eou! #e!i'*
+. (obot
A. ptimi1ation
The proce!! $y &hich e& phy!ical co"i'uratio! are create#*
D. "ystem
. "ynthesis
A )echaical #e,ice "or cotrolli' the !pee# o" a !tea) e'ie*
$. Design gap
*. Flyball governor
1*10
1*13
1*14
1*15
1*16
1*17
1*08
1*01
1*00
CHAPTER 2
Multiple Choice This activity contains 10 questions.
The po!itioi' !y!te) o" a priter ca $e )o#ele# a!
&here the iput R >! ? repre!et! the #e!ire# po!itio a# Y >! ? i! the output po!itio* I" the iput i! a uit !tep iput- the "ial ,alue o" the output i!+
$one of the above
Co!i#er a !y!te) &ith the clo!e#.loop tra!"er "uctio
&ith iput R (s) a# output Y (s)* @he all iitial co#itio! are /ero a# the iput i! a i)pul!e- the the output y (t) i!
Co!i#er a !y!te) repre!ete# $y the $loc% #ia'ra)+
The clo!e#.loop tra!"er "uctio T(s)Y(s): R(s) i!
$one of the above
Co!i#er the $loc% #ia'ra) $elo& "or Pro$le)! 2 throu'h 4+
2* The clo!e#.loop tra!"er "uctio T(s) = Y(s)/R(s) i!+
The clo!e#.loop uit !tep re!po!e i!+
The "ial ,alue o" y(t) i!+
Co!i#er the #i""eretial e
@here
i! a uit !tep* The pole! o" thi! !y!te) are+
$one of the above
A car o" )a!! m 1888%' i! attache# to a truc% u!i' a !pri' o" !ti""e!! K 08888 N:) a# a #a)per o" co!tat b 088 N!:)* The truc% )o,e! at a co!tat acceleratio o" a 8*5 ):!0*
The tra!"er "uctio $et&ee the !pee# o" the truc% a# the !pee# o" the car i! +
$one of the above
Co!i#er the clo!e#.loop !y!te)+
Co)pute the clo!e#.loop tra!"er "uctio a# the clo!e#.loop /ero! a# pole!*
2he positioning system of a printer can be modeled as
1*
&here the input ( :s ; represents the desired position and < :s ; is the output position. f the input is a unit step input0 the final value of the output is/ $one of the above Your A!&er+
Correct A!&er+
Consider a system &ith the closed-loop transfer function
0*
&ith input R (s) and output Y (s). When all initial conditions are 1ero and the input is an impulse0 then the output y (t) is
Your A!&er+
Correct A!&er+
Consider a system represented by the block diagram/
*
2he closed-loop transfer function T(s)=Y(s) > R(s) is
Your A!&er+
Correct A!&er+
Consider the block diagram belo& for 4roblems ? through @/
2*
2* 2he closed-loop transfer function T(s) = Y(s)/R(s) is/
Your A!&er+
2he closed-loop unit step response is/
3* Your A!&er+
Correct A!&er+
2he final value of y(t) is/
4* Your A!&er+
Correct A!&er+
Consider the differential e%uation
5* Where system are/
is a unit step. 2he poles of this
Your A!&er+
6*
A car of mass m =BBBkg is attached to a truck using a spring of stiffness K = BBBB $>m and a damper of constant b = BB $s>m. 2he truck moves at a constant acceleration of a = B. m>s.
2he transfer function bet&een the speed of the truck and the speed of the car is /
Your A!&er+
Consider the closed-loop system/
7*
Compute the closed-loop transfer function and the closed-loop 1eros and poles.
Your A!&er+
Correct
A!&er+
Consider the feedback system/
18*
Assuming R(s) = B0 the closed-loop transfer function from the disturbance D(s) to the output Y(s) is/
Your A!&er+
Correct A!&er+
9ery fe& physical systems are linear &ithin some range of the variables.
1*
Your A!&er+ 2rue
Correct False A!&er+
5
0*
2he s-plane plot of the poles and 1eros graphically portrays the character of the natural response of a system.
Your 2rue A!&er+
*
2he roots of the characteristic e%uation are the 1eros of the closedloop system.
Your A!&er+ 2rue
Correct False A!&er+
2*
A linear system satisfies the properties of superposition and homogeneity.
Your 2rue A!&er+
3*
2he transfer function is the ratio of the +aplace transform of the output variable to the +aplace transform of the input variable0 &ith all initial conditions e%ual to 1ero.
Your 2rue A!&er+
1.
Match the term with it's definition:
Optio
1*1
The #e,ice that cau!e! the proce!! to pro,i#e the output* The #e,ice that pro,i#e! the )oti,e po&er to the proce!!*
Your A!&er+
A. DC motor
Correct A!&er+
). Actuator
=i#irectioal-operatioal $loc%! that repre!et the tra!"er "uctio! o" the ele)et! o" the !y!te)*
#. Damped oscillation
1*
The relatio "or)e# $y e
2. Assumptions !. Characteristic e%uation
1*2
The ca!e &here #a)pi' i! o the $ou#ary $et&ee u#er#a)pe# a# o,er#a)pe#*
2. Assumptions 4. Critical damping
A o!cillatio i &hich the a)plitu#e #ecrea!e! &ith ti)e*
2. Assumptions #. Damped oscillation
A )ea!ure o" #a)pi'* A #i)e!iole!! u)$er "or the !eco#.or#er characteri!tic e
A. DC motor
C. Damping ratio
A electric actuator that u!e! a iput ,olta'e a! a cotrol ,aria$le*
A. DC motor
A. DC motor
1*0
1*3
1*4
1*5
1*6
1*7
1*18
1*11
1*10
1*1
7. #lock diagrams
A tra!"or)atio o" a "uctio " >t ? A. DC motor "ro) the ti)e #o)ai ito the co)ple9 "re! ?*
". +aplace transform
A appro9i)ate )o#el that re!ult! A. DC motor i a liear relatio!hip $et&ee the output a# the iput o" the #e,ice*
'. +inear appro5imation
A !y!te) that !ati!"ie! the propertie! o" !uperpo!itio a# ho)o'eeity*
A. DC motor
+. +inear system
A rule that ea$le! the u!er to o$tai a tra!"er "uctio $y traci' path! a# loop! &ithi a !y!te)*
A. DC motor
(. 'ason loop rule
De!criptio! o" the $eha,ior o" a !y!te) u!i' )athe)atic!*
A. DC motor
. 'athematical models
A #ia'ra) that co!i!t! o" o#e! coecte# $y !e,eral #irecte# $rache! a# that i! a 'raphical repre!etatio o" a !et o" liear relatio!*
A. DC motor
$. "ignal - flo& graph
A. DC motor
*. "imulation
1*12
A )o#el o" a !y!te) that i! u!e# to i,e!ti'ate the $eha,ior o" a !y!te) $y utili/i' actual iput !i'al!*
A. DC motor
1*13
The ratio o" the Laplace tra!"or) o" the output ,aria$le to the Laplace tra!"or) o" the iput ,aria$le*
D. 2ransfer function
State)et! that re"lect !ituatio! a# co#itio! that are ta%e "or 'rate# a# &ithout proo"*
A. DC motor
2. Assumptions
A ratio o" the output !i'al to the iput !i'al "or a itercoectio o" !y!te)! &he all the loop! ha,e $ee clo!e# or other&i!e accoute# "or*
A. DC motor
6. Closed-loop transfer function
A e
A. DC motor
F. Differential e%uation
The #i""erece $et&ee the #e!ire# output a# the actual output*
). Actuator
. )rror signal
The "re
'. +inear appro5imation
K. $atural fre%uency
1*14
1*15
1*16
1*17
1*08
'atch the term &ith it3s definition/
0*
Optio
Your A!&er+
The theore) that !tate!
0*1
that
#. Final value #. Final value theorem theorem
&here
Laplace tra!"or) o"
i! the
*
The property o" a liear !y!te) i
0*0
&hich the !y!te) re!po!ea iput
lea#! to the
Correct A!&er+
- to
A. verdamped
. !omogeneity
re!po!e *
0*
0*2
&he the iput i!
Ma#e liear or place# i a liear "or)*
A. verdamped
4. +ineari1ed
A co#itio or !tate)et that )u!t $e !ati!"ie# to achie,e a #e!ire# e""ect or re!ult*
A. verdamped
!. $ecessary condition
The ca!e &here the #a)pi' ratio
A. verdamped
A. verdamped
A. verdamped
$. 4oles
0*3
i!
0*4
The root! o" the #eo)iator polyo)ial >i*e*- the root! o" the characteri!tic e
0*5
0*6
0*7
0*18
0*11
0*10
0*1
*
The la& that !tate! that i" t&o iput! A. are !cale# a# !u))e# a# route# verdamped throu'h a liear- ti)e.i,ariat !y!te)- the the output &ill $e i#etical to the !u) o" output! #ue to the i#i,i#ual !cale# iput! &he route# throu'h the !a)e !y!te)*
7. 4rinciple of superposition
The iput to a cotrol !y!te) o"te repre!eti' the #e!ire# output*
A. verdamped
K. (eference input
A. verdamped
+. (esidues
The ,alue that the output achie,e! a"ter all the tra!iet co!tituet! o" the re!po!e ha,e "a#e#*
A. verdamped
F. "teady state
The co)ple9 plae &here- 'i,e the
A. verdamped
D. splane
A po&er !erie! &hich i! u!e# to lieari/e "uctio! a# !y!te) )o#el!*
A. verdamped
). 2aylor series
The ti)e iter,al ece!!ary "or a !y!te) to cha'e "ro) oe !tate t o
A. verdamped
*. 2ime constant
The co!tat! a!!ociate# &ith the partial "ractio e9pa!io o" the output Y>!? &he the output i! &ritte i a re!i#ue.pole "or)at*
co)ple9 u)$er - the x .a9i! >or hori/otal a9i!? i! the s.a9i!- a# they .a9i! >or ,ertical a9i!? i! the jw . a9i!*
aother $y a !peci"ie# perceta'e*
The ca!e &here the #a)pi' ratio
0*12
0*13
0*14
A. verdamped
'. 8nderdamped
A "ee#$ac% cotrol !y!te) &herei the 'ai o" the "ee#$ac% loop i! oe*
A. verdamped
C. 8nity feedback
The root! o" the u)erator polyo)ial o" the tra!"er "uctio*
A. verdamped
. Eeros
i!
*
CHAPTER 3 – State Variables Multiple Choice This activity contains 10 questions.
For Pro$le)! 0 a# - co!i#er the !y!te) repre!ete# $y
The a!!ociate# !tate.tra!itio )atri9 i!+
For the iitial co#itio! x 1>8? x 0>8? 1- the re!po!e x >t ? "or the /ero.iput re!po!e i!+
A !i'le.iput- !i'le.output !y!te) ha! the !tate ,aria$le repre!etatio
The tra!"er "uctio o" the !y!te) T > s? Y > s?: U > s? i!+
The #i""eretial e
&here u>t ? i! the iput o" the "ir!t !y!te) a# x >t ? i! the output o" the !eco# !y!te)* The re!po!e x >t ? o" the !y!te) to a uit i)pul!e u>t ? i!+
$one of the above
Co!i#er the $loc% #ia'ra) $elo& "or Pro$le)! 5 throu'h 7+
The e""ect o" the iput R> s? a# the #i!tur$ace D> s? o the output Y > s? ca $e co!i#ere# i#epe#etly o" each other $ecau!e 2he system is casual. 2his is a linear system0 therefore &e can apply the principle of superposition. 2he disturbance D:s; occurs at high fre%uency0 &hile the input R:s; occurs at lo& fre%uency. 2he input R:s; does not influence the disturbance D:s;.
The !tate.!pace repre!etatio o" the clo!e#.loop !y!te) "ro) R> s? to Y > s? i!+
$one of the above
The !tea#y.!tate error #ue to a uit !tep #i!tur$ace D> s? 1: s i! >&ith R> s? 8?+
A !y!te) i! repre!ete# $y the tra!"er "uctio
A !tate ,aria$le repre!etatio i!+
1*
Consider a system &ith the mathematical model given by the differential e%uation/
A state variable representation of the system is/
Your :blank; A!&er+
For 4roblems and 0 consider the system represented by
0*
2he associated state-transition matri5 is/
Your A!&er+
Correct A!&er+
*
For the initial conditions x :B; = x :B; = 0 the response x :t ; for the 1eroinput response is/
Your A!&er+
Correct A!&er+
A single-input0 single-output system has the state variable representation
2*
2he transfer function of the system T :s; = Y :s;> U :s; is/
Your A!&er+
Correct A!&er+
2he differential e%uation model for t&o first-order systems in series is
3* &here u:t ; is the input of the first system and x :t ; is the output of the second system. 2he response x :t ; of the system to a unit impulse u:t ; is/
Your A!&er+
A first-order dynamic system is represented by the differential e%uation
4* y(t)=x(t) 2he corresponding transfer function is/
Your A!&er+
Correct A!&er+
Consider the block diagram belo& for 4roblems through G/
5*
2he effect of the input R:s; and the disturbance D:s; on the output Y :s; can be considered independently of each other because 2he input R:s; does not influence the disturbance D:s;. Your A!&er+ 2his is a linear system0 therefore &e can apply the Correct principle of superposition. A!&er+
6*
2he state-space representation of the closed-loop system from R:s; to Y :s; is/
Your A!&er+
Correct A!&er+
7*
2he steady-state error due to a unit step disturbance D:s; = >s is :&ith (:s; = B;/
Your A!&er+
A system is represented by the transfer function
18 * A state variable representation is/
Your A!&er+
Correct A!&er+
True or Fal!e This activity contains 5 questions.
The !tate.,aria$le! o" a !y!te) co)pri!e a !et o" ,aria$le! that #e!cri$e the "uture re!po!e o" the !y!te)- &he 'i,e the pre!et !tate- all "uture e9citatio iput!- a# the )athe)atical )o#el #e!cri$i' the #ya)ic!* 2rue False
The )atri9 e9poetial "uctio #e!cri$e! the u"orce# re!po!e o" the !y!te) a# i! calle# the !tate tra!itio )atri9* 2rue False
The output! o" a liear !y!te) ca $e relate# to the !tate ,aria$le! a# the iput !i'al! $y the !tate #i""eretial e
A ti)e.i,ariat cotrol !y!te) i! a !y!te) "or &hich oe or )ore o" the para)eter! o" the !y!te) )ay ,ary a! a "uctio o" ti)e* 2rue False
A !tate ,aria$le repre!etatio o" a !y!te) ca al&ay! $e &ritte i #ia'oal "or)* 2rue False
1 *
2he state-variables of a system comprise a set of variables that describe the future response of the system0 &hen given the present state0 all future e5citation inputs0 and the mathematical model describing the dynamics.
Your 2rue A!&er+
0 *
2he matri5 e5ponential function describes the unforced response of the system and is called the state transition matri5.
Your 2rue A!&er+
*
2he outputs of a linear system can be related to the state variables and the input signals by the state differential e%uation.
Your A!&er+ 2rue
Correct False A!&er+
2 *
A time-invariant control system is a system for &hich one or more of the parameters of the system may vary as a function of time.
Your A!&er+ 2rue
Correct False A!&er+
3 *
A state variable representation of a system can al&ays be &ritten in diagonal form.
Your A!&er+ 2rue
Correct False A!&er+
'atch the term &ith it3s definition
1*
Optio
1*1
Your A!&er +
A. "tate variable feedbac k
Correct A!&er+
*. "tate vector
1*0
1*
1*2
1*3
A !et o" u)$er! !uch that the %o&le#'e o" A. "tate the!e u)$er! a# the iput "uctio variable &ill-&ith the e
!. "tate of a system
A !y!te) "or &hich oe or )ore para)eter! )ay ,ary &ith ti)e*
". '. 2imeutput varying e%uation system
The )atri9 e9poetial "uctio that #e!cri$e! the u"orce# re!po!e o" the !y!te)*
A. "tate variable feedbac k
The !et o" ,aria$le! that #e!cri$e the !y!te)*
6. K. "tate 4hase variables variable canonica l form
#. Transition matrix,φ(t )
A. "tate variable feedbac k
(. "tate differential e%uation
1*5
The )athe)atical #o)ai that icorporate! the ti)e re!po!e a# the #e!criptio o" a !y!te) i ter)! o" ti)e t *
A. "tate variable feedbac k
F. 2ime domain
1*6
A appro9i)atio u!e# to o$tai the ti)e re!po!e o" a !y!te) $a!e# o the #i,i!io o" the ti)e ito !)all icre)et!- Bt *
A. "tate variable feedbac k
D. Discretetime appro5imatio n
The cotrol !i'al "or the proce!! i! a #irect "uctio o" all the !tate ,aria$le!*
A. "tate variable feedbac k
A. "tate variable feedback
A "u#a)etal or $a!ic "or) o" the !tate ,aria$le )o#el repre!etatio*
A. "tate variable feedbac k
4. Canonical form
A #ecouple# caoical "or) #i!playi' the #i!tict !y!te) pole! o the #ia'oal o" the !tate ,aria$le repre!etatio A )atri9*
A. "tate variable feedbac k
. Diagonal canonical form
A caoical "or) #e!cri$e# $y an "ee#$ac% loop! i,ol,i' the coe""iciet! o" the n.th or#er #eo)iator polyo)ial o" the tra!"er "uctio a# "ee#"or&ar# loop!
A. "tate variable feedbac k
+. nput feedfor&ard canonical form
1*4
1*7
1*1 8
1*1 1
1*1 0
o$taie# $y "ee#i' "or&ar# the iput !i'al* A $loc% #ia'oal caoical "or) "or !y!te)! that #o ot po!!e!! #i!tict !y!te) pole!*
A. "tate variable feedbac k
7. 7ordan canonical form
1*1 2
A i)portat )atri9 "uctio- #e"ie# a! eAt I At >At?0:0 - that play! a role i the !olutio o" liear co!tat coe""iciet #i""eretial e
A. "tate variable feedbac k
. 'atri5 e5ponential function
1*1 3
The al'e$raic e
A. "tate variable feedbac k
". utput e%uation
A caoical "or) #e!cri$e# $y n "ee#$ac% loop! i,ol,i' the an coe""iciet! o" the n.th or#er #eo)iator polyo)ial o" the tra!"er "uctio a# m "ee#"or&ar# loop! i,ol,i' the bm coe""iciet! o" the m.th or#er u)erator polyo)ial o" the t ra!"er "uctio*
A. "tate variable feedbac k
6. 4hase variable canonical form
The !tate ,aria$le! a!!ociate# &ith the pha!e ,aria$le caoical "or)*
A. "tate variable feedbac k
$. 4hase variables
The !tate ,aria$le! repre!eti' the phy!ical ,aria$le! o" the !y!te)*
A. "tate variable feedbac k
). 4hysical variables
A ti)e.#o)ai )o#el co)pri!e# o" the !tate #i""eretial e
A. "tate variable feedbac k
C. "tatespace representatio n
1*1
1*1 4
1*1 5
1*1 6
1*1 7
Chapter 4 Multiple Choice This activity contains 10 questions.
The plat o" a uity "ee#$ac% clo!e#.loop !y!te) i!
The !e!iti,ity o" the clo!e#.loop !y!te) to !)all cha'e! i
i!+
Co!i#er the "ollo&i' t&o !y!te)!+
The!e !y!te)! ha,e the !a)e tra!"er "uctio &he K 1 K 0 188* @hich !y!te) i! )o!t !e!iti,e to ,ariatio! i the para)eter K 1( Co)pute the !e!iti,ity u!i' the o)ial ,alue! K 1 K 0 188*
#oth systems are e%ually sensitive to changes in K .
Co!i#er the clo!e#.loop tra!"er "uctio
&here A1- A0- A-a# A2 are co!tat!* Co)pute the !e!iti,ity o" the !y!te) to ,ariatio! i the para)eter k *
Co!i#er the $loc% #ia'ra) o" a !u$)er!i$le ,ehicle "or Pro$le)! 25+
The clo!e#.loop tra!"er "uctio o" the !u$)er!i$le ,ehicle i!+
The !tea#y.!tate trac%i' error to a uit !tep iput R(s) i!
Co!i#er the $loc% #ia'ra) o" a )achie.tool cotrol !y!te) "or Pro$le)! 67+
Co)pute the )ii)al ,alue o" K !o that the !tea#y.!tate error #ue to a uit !tep #i!tur$ace i! le!! tha 18G*
K=b
The plant of a unity feedback closed-loop system is
The sensitivity of the closed-loop system to small changes in is: Your A!&er+
Correct A!&er+ 1.
Consider the follo&ing t&o systems/
0*
2hese systems have the same transfer function &hen K = K = BB. Which system is most sensitive to variations in the parameter K , Compute the sensitivity using the nominal values K = K = BB.
Your A!&er +
Correct A!&er +
Consider the closed-loop transfer function
* &here 0 0 0and ? are constants. Compute the sensitivity of the system to variations in the parameter ! .
Your A!&er +
Correct A!&er +
2*
Consider the block diagram of a submersible vehicle for 4roblems ?H /
2he closed-loop transfer function of the submersible vehicle is/
Your A!&er +
Correct A!&er +
3*
Your A!&er +
Correct A!&er +
4*
Your A!&er +
Correct A!&er +
2he steady-state tracking error to a unit step input R(s) is
5* Your A!&er +
Correct A!&er +
6*
Consider the block diagram of a machine-tool control system for 4roblems IHG/
Your A!& er+
7*
Compute the minimal value of K so that the steady-state error due to a unit step disturbance is less than BJ.
Your A!& er+
18*
Your A!&er +
Correct A!&er +
1*
ne of the most important characteristics of control systems is their transient response.
Your 2rue A!&er+
0*
2he system sensitivity is the ratio of the change in the system transfer function to the change of a process transfer function for a small incremental change.
Your 2rue A!&er+
A primary advantage of a open-loop control system is its ability to
*
reduce the system’s sensitivity.
Your False A!&er+
A disturbance is a desired input signal that affects the system’s output signal.
2*
Your False A!&er+
An advantage of using feedback is a decreased sensitivity of the system to variations in the parameters of the process.
3*
Your False A!&er+
Correct 2rue A!&er+
1.
Match the term with it's definition Optio
1*1
1*0
1*
1*2
A u&ate# iput !i'al that a""ect! the !y!te) ! output !i'al*
The #i""erece $et&ee the #e!ire# output-R >! ?-a# the actual output-Y >! ?
A !y!te) &ithout "ee#$ac% that #irectly 'eerate! the output i re!po!e to a iput !i'al*
The error &he the ti)e perio# i! lar'e a# the tra!iet re!po!e ha! #ecaye#-lea,i' the cotiuou! re!po!e*
1*3
The ratio o" the cha'e i the !y!te) tra!"er "uctio to the cha'e o" a proce!! tra!"er "uctio >or para)eter? "or a !)all icre)etal cha'e* The re!po!e o" a !y!te) a! a "uctio o" ti)e*
1*4
1*5
A !y!te) &ith a )ea!ure)et o" the output !i'al a# a co)pari!o &ith the #e!ire# output to 'eerate a error !i'al that i! applie# to the actuator*
1*6
A )ea!ure o" the !tructure- itricatee!!- or $eha,ior o" a !y!te) that characteri/e! the r elatio!hip! a# iteractio! $et&ee ,ariou! co)poet!*
1*7
The part!- !u$!y!te)!- or !u$a!!e)$lie! that co)pri!e a total !y!te)*
1*18
A attri$ute o" a !y!te) that #e!cri$e! a te#ecy o" the !y!te) to #epart "ro) the e
1*11
A re#uctio i the a)plitu#e o" the ratio o" the output !i'al to the iput !i'al throu'h a !y!te)- u!ually )ea!ure# i #eci$el!*
The percet o,er!hoot o" the output to a uit !tep iput i! appro9i)ately+ "# = GJ "# = BJ "# = J $o overshoot
Co!i#er the $loc% #ia'ra) o" a le,itatio cotrol !y!te) o" a ,ehicle i Pro$le)! a# 2+
Fi# the ,alue o" K !o that the !y!te) pro,i#e! a opti)u) ITAE re!po!e "or a !tep iput* K = .@ K = .B K = B?. K = .B
Co)pute the e9pecte# percet o,er!hoot to a uit !tep iput* $o overshoot e5pected "# = B.IJ
"# = ?.@J "# = .?J
A !y!te) ha! the clo!e#.loop tra!"er "uctio T(s) 'i,e $y
=!i' the otio o" dominant poles, e!ti)ate the e9pecte# percet o,er!hoot*
$o overshoot e5pected
#oth specifications can be satisfied. nly the second specification "# LBJ can be satisfied. nly the first specification T $ L.B can be satisfied. $either specification can be satisfied.
Co!i#er the )achie.tool cotrol !y!te)
&here
a# &here the o)ial ,alue o" K 18* =!i' a 0G criterio- co)pute the !ettli' ti)e- T s - "or a uit !tep #i!tur$ace* T s = B.Bs T s = B.Gs T s = .Bs T s = ?.Is
K =GG K =@G K =?G $one of the above
I Pro$le)! 7 a# 18- co!i#er a !atellite cotrol !y!te) to )aitai the attitu#e orietatio*
A !eco#.or#er appro9i)ate )o#el o" the ope.loop cotrol !y!te) i!+
=!i' the !eco#.or#er !y!te) appro9i)atio >!ee Pro$le) 7?- e!ti)ate the 'ai K !o that the percet o,er!hoot i! appro9i)ately 13G* K = BB K = BBB K = B $one of the above 1 .
Consider the following closed-loop control system for roblems 1 and !:
The steady-state error to a unit step input is: Your A!&er+
Correct A!&er+
2he percent overshoot of the output to a unit step input is appro5imately/
0*
"# = GJ Your A!&er+
*
Consider the block diagram of a levitation control system of a vehicle in 4roblems and ?/
Find the value of K so that the system provides an optimum 2A) response for a step input. K = .B Your A!&er+
Compute the e5pected percent overshoot to a unit step input.
2*
$o overshoot e5pected Your A!&er+ "# = ?.@J Correct A!&er+
A system has the closed-loop transfer function T(s) given by
3*
8sing the notion of %ominant $o&es' estimate the e5pected percent overshoot.
Your A!&er+
Consider the unity feedback control system
4*
#oth specifications can be satisfied. Your A!&er+
Consider the machine-tool control system
5*
&here
and &here the nominal value of K =B. 8sing a J criterion0 compute the settling time0 T s 0 for a unit step disturbance.
T s = B.Gs Your A!&er+
A plant has the open-loop transfer function given by
6*
and is controlled by a proportional controller K 0 as sho&n in the block diagram/
2he value of K that yields a steady-state error e%ual to B.B for a unit step input is/ K =@G Your A!&er+ K =GG Correct A!&er+
7*
n 4roblems G and B0 consider a satellite control system to maintain the attitude orientation.
A second-order appro5imate model of the open-loop control system is/
Your A!&er+
Correct A!&er+
18*
8sing the second-order system appro5imation :see 4roblem G;0 estimate the gain K so that the percent overshoot is appro5imately J. K = BBB Your A!&er+
K = BB Correct A!&er+
True or Fal!e This activity contains 5 questions.
I 'eeral- a thir# or#er !y!te) ca $e appro9i)ate# $y a !eco#. or#er !y!te) #o)iat root! i" the real part o" the #o)iat root! i! le!! tha 1:18 o" the real part o" the thir# root* 2rue False
The u)$er o" /ero! o" the "or&ar# path tra!"er "uctio at the ori'i i! calle# the type u)$er* 2rue False
The ri!e ti)e- i! #e"ie# a! the ti)e re
For a !eco#.or#er !y!te) &ith o /ero!- the percet o,er!hoot to a uit !tep i! a "uctio o" the #a)pi' ratio*
2rue False
A type 1 !y!te) ha! a /ero !tea#y. !tate trac%i' error to a ra)p iput* 2rue False
"n general# a third order s ystem can be appro$imated by a second-order system dominant roots if the real part of the dominant roots is less than 1%1& of the real part of the third root. Your A!&er+ False
Correct A!&er+ 2rue 1.
0*
2he number of 1eros of the for&ard path transfer function at the origin is called the type number.
Your A!&er+ False
*
2he rise time0 is defined as the time re%uired for the system to settle &ithin a certain percentage of the input amplitude.
Your A!&er+ 2rue
Correct A!&er+ False
For a second-order system &ith no 1eros0 the percent overshoot to a unit step is a function of the damping ratio.
2*
Your A!&er+ 2rue
A type system has a 1ero steadystate tracking error to a ramp input.
3*
Your A!&er+ 2rue
Correct A!&er+ False 'atch the term &ith it3s definition
1*
Optio
1*1
1*0
1*
1*4
Correct A!&er+
The ti)e "or a !y!te) to re!po# to a !tep iput a# ri!e to a pea% re!po!e*
A. 8nit impulse
. 4eak time
The root! o" the characteri!tic e
A. 8nit impulse
7. Dominant roots
The u)$er o" pole! o" the tra!"er "uctio-! (s )- at the ori'i*
A. 8nit impulse
D. 2ype number
A. 8nit impulse
*. 9elocity error constant
A. 8nit impulse
K. 2est input signal
1*2
1*3
Your A!&er+
A iput !i'al u!e# a! a !ta#ar# te!t o" a !y!te) ! a$ility to re!po# a#e
The ti)e re
C. "ettling time
A !et o" pre!cri$e# per"or)ace criteria*
A. 8nit impulse
$. Design specifications
A !y!te) &ho!e para)eter! are a#;u!te# !o that the per"or)ace i#e9 reache! a e9tre)u) ,alue*
A. 8nit impulse
4. ptimum control system
A
A. 8nit impulse
. 4erformance inde5
A. 8nit impulse
#. (ise time
1*18
The ti)e "or a !y!te) to re!po# to a !tep iput a# attai a re!po!e e
1*11
The a)out $y &hich the !y!te) output re!po!e procee#! $eyo# the #e!ire# re!po!e*
A. 8nit impulse
). 4ercent overshoot
A. 8nit impulse
+. Acceleration error
1*5
1*6
1*7
The co!tat e,aluate# a!
1*10
*
constant0 A. 8nit impulse
F. 4osition error constant0
The co!tituet o" the !y!te) re!po!e that e9i!t! a lo' ti)e "ollo&i' ay !i'al iitiatio*
A. 8nit impulse
!. "teadystate response
The co!tituet o" the !y!te) re!po!e that #i!appear! &ith ti)e*
A. 8nit impulse
'. 2ransient response
A te!t iput co!i!ti' o" a i)pul!e o" i"iite a)plitu#e a# /ero &i#th- a# ha,i' a area o" uity*
A. 8nit impulse
A. 8nit impulse
The co!tat e,aluate# a!
1*1
1*12
1*13
1*14
Multiple Choice This activity contains 10 questions.
A !y!te) ha! the characteri!tic e
*
The ra'e o" K "or a !ta$le !y!te) i!+ K LB.?@ K MB.?@ B LK LB.?@ 8nstable for all K
=tili/i' the Routh.Hur&it/ criterio- #eter)ie &hether the "ollo&i' poly.o)ial! are !ta$le or u!ta$le+
$:s; is stable0 $:s; is unstable $:s; is stable0 $:s; is stable $:s; is unstable0 $:s; is unstable $:s; is unstable0 $:s; is stable
"table for K = .B and stable for K = 8nstable for K = .B and unstable for K = "table for K = .B and unstable for K = 8nstable for K = .B and stable for K =
Co!i#er a uity e'ati,e "ee#$ac% !y!te)
K =B K = 2he system is unstable for all K . 2he system is stable for all K .
A !y!te) i! repre!ete# $y 9e9clJ A9- &here
The ,alue! o" % "or a !ta$le !y!te) are K => K L> K M> 2he system is stable for all ! .
=!i' the Routh array to a!!i!t i co)putei' the root! o" the polyo)ial
Co!i#er the lateral po!itio cotrol !y!te) "or a la#i' o aircra"t carrier*
The ra'e o" K "or !ta$ility i! BB. LK L@B.@I B.B@ LK L.GI K L@B.@I 2he system is unstable for all K MB
I Pro$le)! 6 a# 7- co!i#er a che)ical proce!! repre!ete# i a !tate.!pace "or)
The characteri!tic e
q:s; = s - s N B q:s; = sNs - Bs - @ q:s; = s- s N Bs - q:s; = sNs - Bs N
=!i' the Routh.Hur&it/ criterio- #eter)ie &hether the !y!te) i! !ta$le- u!ta$le- o" )ar'ially !ta$le* marginally stabled stable unstable
A !y!te) ha! the "ollo&i' $loc% #ia'ra) repre!etatio
&here K i! al&ay! po!iti,e* The li)iti' 'ai "or a !ta$le !y!te) i!+ K L B K L II K L BB "table for all K MB
A system has the characteristic e%uation
1* 2he range of K for a stable system is/ K MB.?@ Your A!&er+
0*
8tili1ing the (outh-!ur&it1 criterion0 determine &hether the follo&ing poly-nomials are stable or unstable/
$:s; is stable0 $:s; is stable Your A!&er+ $:s; is stable0 $:s; is unstable Correct A!&er+
Consider the feedback control system block diagram
*
nvestigate closed-loop stability for
8nstable for K = .B and unstable for K = Your A!&er+ 8nstable for K = .B and stable for K = Correct
A!&er+
Consider a unity negative feedback system
2*
2he system is unstable for all K . Your A!&er+ K = Correct A!&er+
A system is represented by O5e5clP =A50 &here
3*
2he values of k for a stable system are K M> Your A!&er+
4*
8sing the (outh array to assist in compute=ing the roots of the polynomial
Your A!&er+
Correct A!&er+
5*
Consider the lateral position control system for a landing on aircraft carrier.
2he range of K for stability is B.B@ LK L.GI Your A!&er+ K L@B.@I Correct A!&er+
6*
n 4roblems I and G0 consider a chemical process represented in a statespace form
2he characteristic e%uation is/ q:s; = s- s N Bs - Your A!&er+ q:s; = sNs - Bs N Correct A!&er+
7*
8sing the (outh-!ur&it1 criterion0 determine &hether the system is stable0 unstable0 of marginally stable. unstable Your A!&er+ stable Correct A!&er+
A system has the follo&ing block diagram representation
18 *
&here K is al&ays positive. 2he limiting gain for a stable system is/ K L B Your A!&er+
stable system is a dynamic system with a bounded output response for any input. Your A!&er+ 2rue
1. Correct False A!&er+
A marginally stable system has poles on the -a5is.
0* Your 2rue A!&er+
A system is stable if all poles lie in the right half-plane.
* Your False A!&er+
2*
2he (outh-!ur&it1 criterion is a necessary and sufficient criterion for determining the stability of linear systems.
Your 2rue A!&er+
(elative stability characteri1es the degree of stability.
3* Your 2rue A!&er+
1* 'atch the term &ith it3s definition Optio
Correct A!&er+
A per"or)ace )ea!ure o" a !y!te)*
A. (outh!ur&it1 criterion
). "tability
A #ya)ic !y!te) &ith a $ou#e# !y!te) re!po!e to a $ou#e# iput*
#. Au5illary polynomial
D. "table system
1*1
1*0
Your A!&er+
1*
The property that i! )ea!ure# $y the relati,e real part o" each root or pair o" root! o" the characteri!itic e
1*2
A criterio "or #eter)ii' the !ta$ility o" D. "table a !y!te) $y e9a)ii' the characteri!tic system e
A. (outh!ur&it1 criterion
The e
). "tability
#. Au5illary polynomial
1*4
A !y!te) #e!criptio that re,eal! &hether a !y!te) i! !ta$le or ot !ta$le &ithout co!i#eratio o" other !y!te) attri$ute! !uch a! #e'ree o" !ta$ility*
F. (elative stability
*. Absolute stability
1*5
A !y!te) po!!e!!e! thi! type o" !ta$ility i" the /ero iput re!po!e re)ai! $ou#e# a! *
*. Absolute stability
C. 'arginally stable
1*3
C. 'arginally stable
F. (elative stability
Co!i#er a cotrol !y!te) "or a auto)o$ile !u!pe!io te!ter
K = G. K = .? K = ?. K = .
I Pro$le)! 0 a# - co!i#er the uity "ee#$ac% !y!te)
0* The appro9i)ate a'le! o" #eparture o" the root.locu! "ro) the co)ple9 pole! are
$one of the above
The root.locu! o" thi! !y!te) 'i,e $y &hich o" the "ollo&i'
K = B K = BBB K = K = B
Co!i#er the uity "ee#$ac% cotrol !y!te)
=!i' the root.locu! )etho#- #eter)ie that )a9i)u) ,alue o" " "or clo!e#.loop !ta$ility* * =.I * =. 8nstable for all * MB "table for all * MB
K = .I K = . K = ?.IG "table for all K M B
Suppo!e that a !i)ple proportioal cotroller i! utili/e#- that i!! #( s) = K Deter)ie the )a9i)u) cotroller 'ai K "or clo!e#.loop !ta$ility* K = ?.?G K = B.B K = .?G 8nstable for all K M B
Co!i#er the uity "ee#$ac% !y!te)
Deter)ie the $rea%&ay poit o the real a9i! a# the re!pecti,e 'aiK* s =.? K =I. s =-. K =?.G s =-.I K =I. $one of the above
The #eparture a'le! "ro) the co)ple9 pole! a# the arri,al a'le! at the co)ple9 /ero! are+
$one of the above
Consider a control system for an automobile suspension tester
1*
K = ?. Your A!&er+
n 4roblems and 0 consider the unity feedback system
0*
0* 2he appro5imate angles of departure of the root-locus from the comple5
poles are $one of the above Your A!&er+
Correct A!&er+
2he root-locus of this system given by &hich of the follo&ing
* Your A!&er+
Correct A!&er+
2*
K = = BBB Your A!&er+ K = = B Correct A!&er+
Consider the unity feedback control system
3*
8sing the root-locus method0 determine that ma5imum value of * of * for for closedloop stability. * =. =. Your A!&er+
4*
Determine the ma5imum value of the gain K for closed-loop stability. stability. K = = . Your A!&er+ K = = .I Correct A!&er+
5*
"uppose that a simple proportional controller is utili1ed0 that is0 +c (s) (s) = K
Determine the ma5imum controller gain K for closed-loop stability. = B.B K = Your A!&er+ K = = ?.?G Correct A!&er+
Consider the unity feedback system
6*
Determine the break&ay point on the real a5is and the respective gain0 K. =I. s =-.I K =I. Your A!&er+
n 4roblems G and B0 consider the feedback system
7*
2he root-locus is &hich of the follo&ing/
Your A!&er+
18*
2he departure angles from the comple5 poles and the arrival angles at the comple5 1eros are/
Your A!&er+
Correct A!&er+
The root-locus is the path the roots of the characteristic e(uation )given by 1 * +,)s & trace out on the s-plane as the system parameter + varies.
1.
Your A!&er+ False
Correct A!&er+ 2rue
0*
n the root locus plot0 the number of separate loci is e%ual to the number of poles of +(s).
Your A!&er+ 2rue
2he root-locus al&ays starts at the 1eros and ends at the poles of +(s).
* Your A!&er+ False
2*
2he root locus provides the control system designer &ith a measure of the sensitivity of the poles of the system to variations of a parameter of interest.
Your A!&er+ 2rue
3*
2he root locus provides valuable insight into the response of a system to various test inputs.
Your A!&er+ False
Correct A!&er+ 2rue
1.
Match the term with it's definition Optio
Your A!&er+
Correct A!&er+
1*1
A )etho# o" !electi' oe or t&o para)eter! u!i' the root locu! )etho#*
A. Asymptote centroid
'. 4arameter design
1*0
The !e!iti,ity o" the root! a! a para)eter cha'e! "ro) it! or)al ,alue*
#. 4 controller
7. (oot sensitivity
C. (oot contours
. (oot locus
1*
The locu! or path o" the root! trace# out o the s.plae a! a para)eter i! cha'e#*
1*2
The root locu! lyi' i a !ectio o" the real a9i! to the le"t o" a o## u)$er o" pole! a# /ero!*
D. #reaka&ay point
(. (oot locus segments on the real a5is
1*3
The )etho# "or #eter)ii' the locu! o" root! o" the characteri!tic
). $umber of separate loci
. (oot locus method
F. Angle of departure
A. Asymptote centroid
The poit o the real a9i! &here the locu! #epart! "ro) the real a9i! o" the s.plae*
*. Dominant roots
D. #reaka&ay point
A path or tra;ectory that i! trace# out a! a para)eter i! cha'e#*
!. Angle of departure
$. +ocus
The a'le at &hich a locu! lea,e! a co)ple9 pole i the ! .plae*
7. (oot sensitivity
F. Angle of departure
E
. (oot locus
). $umber of separate loci
e
,arie!
The ceter o" the liear a!y)ptote!-
1*4
1*5
1*6
1*7
1*18
*
