INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
FPGA MODELLING AND REAL-TIME EMBEDDED CONTROL
DESIGN VIA LABVIEW SOFTWARE: APPLICATION FOR
SWINGING-UP A PENDULUM
Wael Benrejeb, Olfa Boubaker
National Institute of Applied Sciences and Technology
Centre Urbain Nord BP 676, 1080 Tunis Cedex, Tunisia
Emails: olfa.boubaker@insat.rnu.tn
Submitted: May 15, 2012
Accepted: July 20, 2012
Published: Sep. 1, 2012
Abstract- In this paper, Real-Time embedded control is designed via LabVIEW software for swingingup a pendulum from its pending position to its upright position. Since the pendulum system has a
typical nonlinear instable model, the control problem is achieved using the Astrom-Furuta energy
control strategy. To overcome the complexities for the design and the real-Time implementation of the
controller of the nonlinear system, FPGA and Real-Time Modules of LabVIEW software are used. A
validation test is finally achieved using Proteus software via its Virtual Simulation Models (VSM).
Simulation results show the capabilities of LabVIEW FPGA and Real-Time modules to customize
control applications with flexible time control without VHDL coding or board design.
Index terms: Field programmable gate arrays, Programmable control, Software design, Inverted pendulum.
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Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
I.
INTRODUCTION
For at least fifty years, the pendulum has been the most popular benchmark, among others, for
teaching and researches in Control Theory and Mechatronics [1]. Different versions of the
pendulum benchmark exist offering a variety of interesting control challenges. The most familiar
types are the rotational single-arm pendulum [2], the double arm pendulum [3] and the cart
inverted pendulum [4]. The principal control task considered in many research works is the
swinging up from the stable equilibrium point to the unstable equilibrium [2, 4, 5, 6, 7, 8].
Though the structure of the inverted pendulum seems to be quite simple, the upswing control is
much more difficult than it appears since the pendulum is a typically non linear system and many
conventional techniques control are ineffective. Several real experimental models of the
pendulum benchmark are performed [5, 9]. In the most cases, integrated software’s are used to
support the design and the real-time implementation of controllers [10, 11].
On the other side, National Instruments® (NI) LabVIEW™ is considered, nowadays, as the most
professional integrated software/Hardware platform [12]. Furthermore, more than 25 LabVIEW
modules and toolkits are added to this software for specific applications [13]. In this framework,
FPGA Module [14, 15] allow development of FPGA programs on NI reconfigurable Input/output
RIO hardware targets for custom applications and control algorithms with loop rates up to 40
MHz without VHDL coding or board design. It executes multiple tasks simultaneously. In the
same context, Real-Time Module [16, 17] allows designing, prototyping and deploying of RealTime Controllers. Furthermore, to shorten time of designing and deploying it is also possible to
take the advantage of the NI embedded platforms [18, 19]. Using LabVIEW graphical
programming, we can then develop customized control applications on a desktop machine [20],
and then download and execute the program to run on an independent NI hardware target.
In this paper, FPGA based real time control of an inverted pendulum using LabVIEW Software is
investigated. The control objective is to swing up the pendulum from its instable equilibrium
position to its stable position using the well known Astrom-Furuta Swing-up control strategy.
FPGA and Real-Time modules of LabVIEW software will be used to design the nonlinear model
of the inverted pendulum and to implement its switching control law.
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INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
II.
PROBLEM FORMULATION
Consider the pendulum system shown by Fig. 1. The control problem considered is the swinging
up the pendulum from the pending position to the upright position. The swing up of the
pendulum is archived by a DC motor.
Encoder
DC motor
Pivot point
Pendulum
Fig.1. Pendulum system
To find out the position and speed of the DC motor we will choose a square encoder with two
outputs track to indicate the position and direction of rotation. The two square wave outputs (A
and B) have the same number of pulses per revolution and are in quadrature relation to each
other: A leads B by 90° for clockwise rotation and B leads A by 90º for counter-clockwise
rotation. The pulse outputs indicate amount of shaft rotation, and the A / B phase difference
indicates direction of rotation.
Let now denote, the angle between the vertical and the pendulum by θ (see Fig.2), which is
positive in the clock-wise direction. m, J and l are the mass of the pendulum, the moment of
inertia with respect to the pivot point and the distance from the pivot to the center of mass,
respectively.
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Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
+
Fig.2. Inverted pendulum swing-up problem
The acceleration of gravity is g and the acceleration of the pivot is u = ng. Under some
predefined assumptions, the equations of motion of the pendulum are described by [2]:
Jθ= mglsinθ -mulcosθ
(1)
The energy of the system can be deduced as:
E = 0.5 J P θ 2 + mgl (cos θ − 1)
(2)
where:
J P = ml 2 + J
(3)
Let ω 0 = mgl / J . The normalized energy is deduced as:
(
(
E = mgl 0.5 θ / ω 0
)
2
)
+ cos θ − 1 .
(4)
and the normalized state space system is described by:

 x1 = θ


 x 2 = (sin θ - v cos θ )ω0
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(5)
INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
where x = [x1
[
]
T
T
x 2 ] = θ θ is the state vector and such that:
u = vg
(6)
where u is the control law described by the following form:
(
(
u = sign ng k (E - E 0 )sign θ cosθ
))
(7)
signng denotes a function which saturates at ng and E0 the desired energy allowing the pendulum
to reach the upright position. This strategy is essentially a bang-bang strategy for large errors and
a proportional control for small errors. For small values of n the relation between n and k is
approximately given by [2]:
k≈
III.
π
2n − 1
(8)
PROBLEM SOLUTION
A. NI LabVIEW Reconfigurable Platform
The NI LabVIEW technology of reconfigurable platform is based on four main parts (see Fig.3):
-
A Real-Time processor,
-
A reconfigurable FPGA
-
An Input / Output module
-
A graphical development software.
Combined, these four components provide the ability to quickly create a specific material for
high performance and flexible time control.
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Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
Fig.3. Typical LabVIEW development platform [21]
Based on cost and technological constrains, we choose the Single-Board RIO 9632 for our
application (see Fig.4). This device offer 32 Analogical Inputs, 4 Analogical outputs, 400 MHz
for the processor Speed, 128 MB Memory (DRAM), 2M FPGA Size (Gates), an RS232 serial
port for connection to peripherals and devices and more options.
Fig.4. NI Single-Board RIO technology [21]
B. LabVIEW Graphical Software Code
For rapid modeling and control prototyping, we use NI LabVIEW FPGA and Real-Time Modules
[19, 21, 22, 23, 24]. FPGA module offer the advantage of graphical development for fieldprogrammable gate array (FPGA) chips on NI reconfigurable hardware with loop rates up to 40
MHz and without VHDL coding or board design.
Furthermore, multiple tasks can be
simultaneously and deterministically executed and we can implement custom timing and
triggering logic with 25 ns resolution.
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INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
LabVIEW Real-Time Module offers the possibility to design and deploy embedded Real-Time
Controllers. To design and deploy the swing up control of the inverted pendulum, the following
tasks are elaborated:
- Acquisition of the signals A & B from the encoder and generation of pulse width modulation
(PWM) control signal to the DC motor via the FPGA Module.
- Design of the real-Time embedded control law (7) via Real-Time Module.
The FPGA and Real-Time control application is first developed on a desktop machine using a
LabVIEW graphical program, and then downloaded and executed to run on the independent
Single-Board RIO 9632 hardware.
Acquisition of the signals A and B from the encoder is achieved using the FPGA Module of
LabVIEW software via the LabVIEW structure shown in Fig.5.a. In the previous code, an XOR
Gate between the present values and previous values of channels A and B was considered to
detect the change in the state. When the previous state of Channel A is the same as the current
state of the channel B then the position is incremented, otherwise it is decremented (see Fig.6). A
speedometer is also designed in this code (see tick/count variable). The PWM signal is generated
and applied to the DC motor to swing up the pendulum via the FPGA module using the
LabVIEW code shown in Fig.5.b. The two loops shown in Fig.5 are High-Speed and Parallel
Loops.
To avoid using arithmetic operators in the FPGA module that can weigh the processing time, the
design of the controller is achieved via Real-Time Module as follows: First, a program of speed
computation is designed using the following relationship for the computed angular speed:
n × 360
θcom =
4× N × F
where:
θcom : Computed angular velocity by the Real-Time Module
n : tick / count number delivered by the FPGA code
N : Number of pulses per revolution
F : FPGA frequency
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(9)
Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
( )
Taking in account that min θcom = 0 , the duty cycle is then computed as:
D=
( )
( )
mean θcom
max θcom
(10)
In the last LabVIEW project, five shared variables are used: the computed angular position, the
computed angular speed, the PWM duty cycle, the normalized energy and the control law.
(a)
(b)
Fig.5. High-Speed, Parallel Loops in LabVIEW FPGA Module. (a) LabVIEW loop for
acquisition of signals A & B from the encoder; (b) LabVIEW loop for generating PWM signal.
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INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
Fig.6.Incrementing and decrementing the angular position signal.
Fig.7. Computation of angular position and velocity via Real-Time toolkit.
The ordinary differential system (ODE) (5) is then designed using the LabVIEW Math Script
Node Virtual Instrument (VI) as represented in Fig.8.
Fig.8. Math Script Node VI of the system (5)
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Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
The normalized Energy (4) and the control law (7) needed to solve the ODE system (5) are
computed as shown by Fig.9. The ode system (5) is then solved using the ODE VI given in
Fig.10 .The derivatives of the state variables are then deduced and used to compute the PWM
signal exploited by FPGA code in Fig. 5.b.
Fig.9. Computation of the normalized energy (4) and the control law (7)
Fig.10. Solving the ordinary differential system (5)
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INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
C. Test Validation via Proteus VSM
In this section we present a test validation of the designed Real-Time control without using the
NI Single-Board RIO 9632 device. We take advantage of the new version of Proteus software 7.7
with its Virtual Simulation Modelling (VSM) [25] as a Real-Time simulation tool for modelling
the performance of PMW controller. The usage of Proteus VSM enables us shorter product
development time and thus reducing development cost [26]. The Proteus VSM computed aided
design (CAD) model is shown in Fig.11 where the microcontroller PIC 18F2550, the square
encoder and the standard RS-232 are used to convert the angular speed generated by the
LabVIEW FPGA Module into a PWM signal in order to rotate the shaft of the DC motor. Result
of the test validation are derived for parameter k = 1. Fig. 12 shows transmitted and received
signals via Proteus animation VSM interface whereas Fig.13 shows the encoder signal received
by a LabVIEW User Interface via an RS232 standard. As we can see, VISA drivers running on
the Real Time processor is used to communicate with the RS-232 port. The waveform graph
shown by this User Interface show clearly that the encoder signal that will be exploited by
FPGA/Real Time toolkits to compute the control law is well received. Furthermore, the profile
of the encoder signal is correct in amplitude and time and corresponds exactly to the signal send
by Proteus VSM interface.
Fig.11. Design of test verification circuit via Proteus VSM
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Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
Fig.12. Received and transmitted signals via Proteus animation VSM interface.
Fig.13. Encoder signal send by Proteus VSM and received by a LabVIEW User Interface via an
RS232 standard
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INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012
The control law (7), shown in Fig.14 is different from that applied in simulation results in [2] since
we have replaced the saturation function by the sign function. In this figure, we can clearly see the
chattering effect in the control variable profile. On the other hand, we can remark that the velocity
variable shown in Fig. 15 makes three switching to cancel. So, we can deduce that the control law
swings the pendulum to its upright position after three switches. We can also observe that the control
law continues to switch which can prove that the pendulum not falls down but it is maintained at its
upright position with almost zero velocity.
Fig.14. Control law
Fig.15. Angular velocity
VI. CONCLUSIONS
In this paper, Real-Time embedded control is designed via FPGA and Real-Time Modules of
LabVIEW software for swinging-up the inverted pendulum via an inherent non linear control
strategy. A validation test is achieved using Proteus software via its Virtual Simulation Models.
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Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software:
Application for Swinging-up a Pendulum
Simulation results show the capabilities of the proposed approach to customize the complex
control application with flexible time control without VHDL coding or board design. In future
works, complex nonlinear controllers [28, 29, 30] will be designed for robotic applications via
LabVIEW software using the same implementation strategy presented in this paper.
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Application for Swinging-up a Pendulum
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