Stefan'Leitner' ECE'422'/'HW5' April'1,'2015'

'

' 1'

Problem'12.9b,c,d)''

'Matlab&Code:&'

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'

%'

%'''ECE'422'/'HW4'%'''Stefan'Leitner'

%'''000413506'%'''12.9b,c'

%'

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'

'clear'all;'

close'all;'

'num=0.8;'

den=[0.025'0.575'1.55'1];'

figure(1),'rlocus(num,'den)''

%'Step'Response'numc='32;'

denc=[0.025'0.575'1.55'33];'

figure(2),'step(numc,'denc)''

'

'

Stefan'Leitner' ECE'422'/'HW5' April'1,'2015'

'

' 2'

''

''

−70 −60 −50 −40 −30 −20 −10 0 10 20 30−60

−40

−20

0

20

40

60

Root Locus

Real Axis (seconds−1)

Imag

inar

y Ax

is (s

econ

ds−1

)

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Step Response

Time (seconds)

Ampl

itude

Stefan'Leitner' ECE'422'/'HW5' April'1,'2015'

'

' 3'

Simulink&Block&Diagram:&'

''

Step&Response:&''

'''

''

'

''

'

''

''

'

''

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Stefan'Leitner' ECE'422'/'HW5' April'1,'2015'

'

' 4'

Problem'12.10a,b)''

'Matlab&Code:&'

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'

%'

%'''ECE'422'/'HW4'%'''Stefan'Leitner'

%'''000413506'%'''12.10a'

%'

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'

's'='tf('s');'

H'='32/(32'+'4*(1+s)/(1+0.04*s)'+'(1+0.05*s)*(1+0.5*s)*(1+s))'%'to'determine'the'

coefficients'of'the'new'TF''

''

numc='[1.28'32];'denc=[0.001'0.048'0.637'6.87'37];'

figure(2),'step(numc,'denc)''

''''''''''''''' ''

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

Step Response

Time (seconds)

Ampl

itude

Stefan'Leitner' ECE'422'/'HW5' April'1,'2015'

'

' 5'

Simulink&Block&Diagram:&

'&&&&&Step&Response:&'

'''

'

''

'

''

Stefan'Leitner' ECE'422'/'HW5' April'1,'2015'

'

' 6'

Problem'12.11)''

'Simulink&Block&Diagram:&'

''Step&Response:&'

''

'

''

As'required,'the'proportional'part'was'set'to'2'and'varied'were'the'integral/'and'the'derivative/part'in'order'to'achieve'a'minimum'overshoot'and'a'very'small'settling'time.'