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IV. Fuzzy Controller
si 1  s
 Ai ( s) 
2
and
 A ( s)  1   A ( s)
i 1
i
• (b) Compute the membership degree of s and ds. Fig. 4
shows that the only two linguistic values are excited
(resulting in a non-zero membership) in any input value,
and the membership degree can be derived by
• Where si 1   6  2 * (i  1) Similar results can be obtained in
computing the membership degree  B (ds)
j
• (c) Select the initial fuzzy control rules by referring to the
dynamic response characteristics, such as,
IF s is A i and s is B j THEN u f is c j,i
IV. Fuzzy Controller
• where i and j = 0~6, Ai and Bj are fuzzy number, and cj,i is
real number. The graph of fuzzification and fuzzy rule table
is shown in Fig. 4.
• (d) Construct the fuzzy system uf (s,ds) by using the
singleton fuzzifier, product-inference rule, and central
average defuzzifier method. Although there are total 49
fuzzy rules in Fig. 4 will be inferred, actually only 4 fuzzy
rules can be effectively excited to generate a non-zero
output. Therefore, the (16) can be replaced by the following
i 1 j 1
expression:
u f ( s, ds ) 
 c
n i m  j
m,n
[  An ( s ) *  Bm (ds )]
i 1 j 1

n i m  j
An
( s ) *  Bm (ds )
i 1 j 1
   c m ,n * d n ,m
n i m  j
IV. Fuzzy Controller
• where d n ,m   A ( s) *  B (ds) . And cm ,n those are
consequent parameters. In addition, by using (15), it is
straight forward to obtain in (17).
n
i 1 j 1
 d
n i m  j
n ,m
m
1
Fig. 4 The symmetrical triangular membership function of s and ds,
fuzzy rule table, fuzzy inference and fuzzification
V. Design of Fuzzy Sliding Mode
Controller
• In this section, a fuzzy sliding surface is introduced to
develop a sliding mode controller which the expression
−k*sat (s /) is replaced by an inference fuzzy system for
eliminate the chattering phenomenon. The designed fuzzy
logic controller has two inputs and an output. The inputs
are sliding surface (s) and the change of the sliding surface
(or ds) in a sample time, and output is the uf. The control
law in (10) is computed with explanation in section III. The
configuration of the overall control system is shown in Fig.5
V. Design of Fuzzy Sliding Mode
Controller
Fig. 5 Diagram of FSMC for DC motor drive system
u  u c  u eq
• Condition for s =0:
• Where η is a positive constant that guarantees the
system trajectories hit the sliding surface in finite time.
Using a sign function often causes chattering in practice.
One solution is to introduce a boundary layer around the
switch surface(7)
• Whereuc  k * sat ( s /  ) and constant factor φ defines the
thickness of the boundary layer. The sat(s/φ) is a
saturation function which is defined as:
N1
Figure 6. State diagram of a FSM for describing the fuzzy sliding mode controller in speed loop.
V. Design of Fuzzy Sliding Mode
Controller
Figure 7. Internal circuit of the proposed FPGA-based motion
control IC for DC motor drive.
speed (rpm)
Results by implementing in
Hardware
800
600
400
200
0
0
100
200
300
Time (ms)
400
500
600
-100
0
100
200
300
Time (ms)
400
500
600
error
100
50
0
-50
speed (rpm)
Fig. 8 Step response with speed changing from 200rpm to 800rpm.
1200
900
500
200
0
100
200
100
200
300
Time (ms)
400
500
600
400
500
600
error
200
100
0
-100
-200
0
300
Time (ms)
Fig. 9 Step response with speed changing from 200rpm to 1200rpm.
Results by implementing in
Hardware
speed (rpm)
1500
1000
500
200
0
0
50
100
150
0
50
100
150
200
Time (ms)
250
300
350
400
250
300
350
400
200
error
100
0
-100
-200
200
Time (ms)
speed (rpm)
Fig. 10 Step response with speed changing from 200rpm to 1500rpm.
2000
1500
800
300
0
0
50
100
150
200
250
300
350
400
450
300
350
400
450
Time (ms)
200
error
100
0
-100
-200
0
50
100
150
200
250
Time (ms)
Fig. 11 Step response with speed changing from 300rpm to 2000rpm.