page 97

6. For all the components we can now draw a ‘block diagram’

vdesired	verror		K			θ gas	F	1	vactual
		K + ----			+ K s		10	------
	+	c		i	d			Ms
			s
	-
				• A ‘negative feedback loop
					that is the fundamental part of this
					‘closed loop control system’

7.1.3 Manipulating Block Diagrams

r

G( s)

c

+

G( s)

-

r

c

--------------------------------

is equal to

1 + G( s)

H( s)

H( s)

NEGATIVE FEEDBACK

r

G( s)

c

+

G( s)

+

r

c

--------------------------------

is equal to

1 – G( s) H( s)

H( s)

POSITIVE FEEDBACK

page 98

			c		c			r
r		G( s)		is equal to			1
							-----------
							G( s)

r

G( s)

c

r

c

G( s)

is equal to

G( s)

c

c

r

G( s)

H( s)

b

r

G( s) H( s)

b

is equal to

r

G( s)

c

r

c

G( s)

is equal to

1

-----------

G( s)

r

r

r

e

r

G( s)

e

G( s)

b

is equal to

b

c

1

-----------

G( s)

page 99

r

c

r

G( s)

c

G( s)

is equal to

c

G( s)

c

c

e.g. The block diagram of the car speed control system

vdesired

verror

Ki

+ K

s

θ gas

10

F

1

vactual

+

K

c

+ ----

d

-------

-

s

Ms

v

desired

v

error

Ki

θ

gas

10

v

actual

+ K

s

------

+

K

c

+ ----

d

Ms

-

s

vdesired verror

+

-

= G(s)

	K		Ki		10
		c	+ ----	+ K s	------
			s	d
					Ms

H(s) = 1

					Kc	Ki			10
v						+ ----	+ Kds		-------
		desired				s			Ms
				----------------------------------------------------------------------
					Kc	Ki			10	( 1)
				1 +		+ ----	+ Kds		-------
						s			Ms

vactual

vactual

vdesired

vdesired

page 100

		Kc	Ki
			+ ----s	+ Kds
	----------------------------------------------------
	Ms			Ki
	-------10	+	Kc + ----s		+ Kds

			s2( K ) + s( K ) +			( K )
				d	c	i
	-----------------------------------------------------------------
	s	2	M	+ K	+ s( K )	+ ( K )
			-----
			10	d	c	i

v						s2( K )		+ s( K )	+ ( K )
	actual
		=					d	c		i
-----------------
				-----------------------------------------------------------------
vdesired				s	2	M	+ K	+ s( K )		+ ( K )
						-----
						10		d	c	i

vactual

vactual

7.1.3.1 - Commercial PID Tuners

•WARNING: Don’t assume results from these systems are perfect, proper engineering methods must be used to avoid failures in critical systems.

•EXPERTUNE

•address G.E.S.

4734 Soneearhray Dr. Hubertus, WI 53033 tel: [phone]

•approx. $1500 (U.S.)

•will automatically adjust gain and time constant

•LT/TUNE

•address

Control Soft Inc. 4122 Wyncote Rd. Cleveland, OH 44121 tel: [phone]