Page 67 - IJOCTA-15-3

FPGA design and implementation of fuzzy learning control: Application on DC motor position control
By applying the Laplace transform to the 4.1. Fixed point data type
above equations, we obtain :
FPGA circuits generally support the following
two types of data: fixed-point data and floating-
(Js + b) sθ (s) = KI (s) (10)
point data. However, designs based on the
fixed-point data type consume fewer hardware re-
(Js + b) I (s) = V (s) − Ksθ (s) (11) sources and less power, with shorter computation
From Equation (10) , the current formula is times. 34
given by: However, most complex algorithms have non-
linear functions that are not supported by the
(Js + b) sθ (s) fixed-point data type. These functions must,
I (s) = (12)
K therefore, be approximated by other linear func-
From Equations (11) and (12), and consider- tions, which negatively affects the accuracy of the
ing that the output of the system is the angular computations. In this work, the design methodol-
position of the motor shaft θ (s), and the input of ogy adopted is based on MATLAB-Simulink soft-
the system is the voltage of the armature V (s), ware.
the transfer function of the DC motor is : The fixed-point representation on MATLAB-
Simulink used in this work is as follows:
θ (s) K fixdt(s, l, d). fixdt creates a numerical type on
= (13)
2
V (s) s [(Ls + R) (Js + b) + K ] Simulink describing a fixed point. s represents
the sign bit, l the length of the binary word and
Where :
d the length of its fractional part.
J : Moment of inertia of the rotor
R : Electric resistance For example, fixdt(1, 16, 8): Here, 16 repre-
L : Electric inductance sents the length of the signal in bits, 1 is the sign
bit (signed in this case), and 8 is the length of the
b : Motor viscous friction constant
fractional part in bits. Details of the fixed-point
However, in our case, the numerical values of the
representation in MATLAB-Simulink are given in
above constants are not available, so the calcula-
Table 2.
tion of the model of the DC motor must be done
experimentally using the Zedboard FPGA.
Table 2. Fixed-point repr´esentation in Simulink
The DC motor is considered as a black box.
Its identification consists of applying a voltage V Datatypemode Fixed − point :
and obtaining the angular position θ of the motor. binarypointscaling
Based on these measurements, the MATLAB sys- Signedness Signed
tem identification toolbox 33 is used to calculate
Wordlength 16
the parameters of the motor model.
Fractionlength 8
During the identification process, it is discov-
ered that the DC motor does not start within a The control algorithm is developed in the
range of voltage values. Knowing that the motor Simulink environment as a double-precision
supply voltage is 12V, the dead zone of this motor floating-point model using blocks supported by
is [-2.4V 2.4V]. The model obtained by the Sys- the HDL Coder and then converted to a fixed-
tem Identification Toolbox is represented by the point model using the Fixed-Point Tool. This
following discrete transfer function, with a sam- tool calculates the correct integer and fractional
pling time of T e =0.001 s. parts of each input/output block from the devel-
oped floating-point model, respecting the rules
θ(z) b 0 of fixed-point arithmetic and optimizing binary
G(z) = = word lengths.
2
V (z) a 2 z + a 1 z + a 0
(14)
16.4
= 4.2. FPGA in the loop simulation
2
z + 0.6615z + 0.00041255
Before applying it to the motor control, the
proposed algorithm must be simulated on the
4. FPGA implementation
MATLAB-Simulink environment with the system
Before applying the controller to the experimental in order to test its behavior during various robust-
device, we must first test its behavior on the Zed- ness tests. The proposed controller is developed
board Zynq-7000 FPGA using the FPGA-in-the- on Simulink with the blocks of HDL Coder and
loop (FIL) simulation technique in the Simulink converted into a model with a fixed-point data
environment of MATLAB. type, then its VHDL code is generated, which is
439