FPGA MODELLING AND REAL-TIME EMBEDDED CONTROL DESIGN …s2is.org/Issues/v5/n3/papers/paper3.pdf ·...

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: [email protected]

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 swinging-

up 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.

INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 3, SEPTEMBER 2012

576

mailto:[email protected]�

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 Real-

Time 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.

Wael Benrejeb, Olfa Boubaker, FPGA Modelling and Real-time Embedded Control Design via Labview Software: Application for Swinging-up a Pendulum

577

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.

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.

Pendulum

Encoder

DC motor

Pivot point


578

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]:

-mulcosθ= mglsinθ θJ (1)

The energy of the system can be deduced as:

)1(cosθ5.0 2 −+= θmglJE P (2)

where:

JmlJ P += 2 (3)

Let Jmgl /ω0 = . The normalized energy is deduced as:

( )( ).1cosω/5.02

0 −+= θθmglE (4)

and the normalized state space system is described by:

( )

=

=

02

1

cos- sin ωθvθxθx

(5)

+


579

where [ ] [ ]TT θθxxx == 21 is the state vector and such that:

vgu = (6)

where u is the control law described by the following form:

( ) ( )( ) cossign - sign 0 θθEEku ng= (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]:

12π−

≈n

k (8)

III. 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.


580

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 field-

programmable 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.


581

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:

FNnθcom ×××

=4

360 (9)

where:

comθ : 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


582

Taking in account that ( ) 0min =comθ , the duty cycle is then computed as:

( )( )com

com

θθD

maxmean

= (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.


583

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)


584

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)


585

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


586

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


587

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.


588

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.

REFERENCES

[1] K. Hirota, T. Fukuda, “Soft computing in Mechatronics,” Springer-Verlag, New York, 1999.

[2] K. J. Åström, K. Furuta, “Swinging up a pendulum by energy control,” Automatica, vol. 36,

n°2, 2000, pp. 287-295.

[3] M.N.A. Zohari, M.Z.M. Tumari, M.S. Saealal, K.H. Ghazali, M.S. Ramli, “Practical sway

motion control for double pendulum-type overhead crane system,” International Journal on

Smart Sensing and Intelligent Systems, vol.5, n°2, 2012, pp. 362-381.

[4] K. Yoshida, “Swing-up control of an inverted pendulum by energy-based methods,” In Proc.

of the American Control Conference, San Diego, 1999, pp. 4045-4047.

[5] N. Muskinja, B. Tovornik, “Swinging up and stabilization of a real inverted pendulum,” IEEE

Transactions on Industrial Electronics, vol. 53, n°4, 2006, pp. 631-639.

[6] K.J. Aström, J. Aracil, F. Gordillo, “A family of smooth controllers for swinging up a

pendulum,” Automatica, vol. 44, n°7, 2008, pp. 1841-1848.

[7] J. H. Yang, S. Y. Shim, J. H. Seo, Y. S. Lee, “Swing-up control for an inverted pendulum

with restricted cart rail length,” International Journal of Control, Automation and Systems,

vol. 7, n°8, 2009, pp. 674-680.

[8] M. S. Park, D. Chwa, “Swing-up and stabilization control of inverted-pendulum systems via

coupled sliding-mode control method,” IEEE Transactions on Industrial Electronics, vol. 56,

n°9, 2009, 3541-3555.

[9] H.L. Li, B.C. Chang, C. Jagadish, H.G. Kwatny, “A DSP microprocessor hybrid control of

an inverted pendulum,” In Proc. IEEE International Conference on Control and Automation,

Christchurch, 2009, pp. 2317-2322.


589

[10] hrig, A. Bischoff, “Virtual laboratory for

real-time control of inverted pendulum/gantry crane,” In 11th Mediterranean Conference on

Control and Automation. Rhodes, 2003.

[11] M. Koga, H. Toriumi, M. Sampei, “An integrated software environment for the design

and real-time implementation of control systems,” Control Engineering Practice, vol. 6,

n°10, 1998, pp. 1287-1293.

[12] O. Boubaker, “National Instruments LabVIEW: Ultimate software for engineering

education,” in Proc. International Conference on Frontiers in Education: Computer Science

and Computer Engineering, Las Vegas, 2011.

http://cerc.wvu.edu/download/WORLDCOMP%2711/2011%20CD%20papers/FEC4450.pdf

[13] The National Instruments® LabVIEW™ Toolkit website (2010). [Online]. Available:

http://www.ni.com/labview/family/

[14] National Instruments®, LabVIEW™ FPGA Module User Manual, National Instruments®

Inc., Texas, 2004.

[15] National Instruments®, LabVIEW FPGA Module Release and Upgrade Notes (2010).

Available: http://www.ni.com/pdf/manuals/371572f.pdf

[16] National Instruments®, LabVIEW™ Real-Time Module User Manual, National

Instruments® Inc., Texas, 2003.

[17] National Instruments®, LabVIEW Real-Time Module Release and Upgrade Notes

(2010). Available: http://www.ni.com/pdf/manuals/371374g.pdf

[18] The National Instruments® LabVIEW™ Corporation website (2010). [Online].

Available: http://www.ni.com/labview/

[19] M. P. Singh, P. K. Tripathi, K.V Gangadharan, “FPGA based vibration control of a mass

varying two-degree of freedom system,” International Journal on Smart Sensing and

Intelligent Systems, vol.4, n°4, 2011, pp. 698-709.

[20] K. Dhanalakshmi, Aditya Avinash, M. Umapathy, M. Marimuthu, “Experimental study

on vibration control of shape memory alloy actuated flexible beam,” International Journal on

Smart Sensing and Intelligent Systems, vol. 3, n°2, 2010, pp. 156-175.

[21] National Instruments LabVIEW Embedded System Design website (2010). [Online].

Available: http://www.ni.com/embedded/


590

http://cerc.wvu.edu/download/WORLDCOMP%2711/2011%20CD%20papers/FEC4450.pdf�

http://www.ni.com/labview/family/�

http://www.ni.com/pdf/manuals/371572f.pdf�

http://www.ni.com/pdf/manuals/371374g.pdf�

http://www.ni.com/labview/�

http://www.ni.com/embedded/�

[22] W.T. Guoqiang, H.A Andrade, “A graphical programming and design environment for

FPGA-based hardware,” In Proc. IEEE International Conference on Field-Programmable

Technology, Beijing, 2010, pp. 337 - 340.

[23] R. Tekin, “MATLAB and LabVIEW in modeling, analysis and real time control of a

motion control system,” In Proc. 2010 8th IEEE International Conference on Control and

Automation, Ankara, 2010, pp. 2077 - 2081.

[24] M.C. Fang, S.M. Wang, “Rapid development of AUV system based on real-time and

FPGA frame,” in Proc. 2011 IEEE Symposium on Underwater Technology and 2011

Workshop on Scientific Use of Submarine Cables and Related Technologies, Tainan, 2011,

pp. 1-5.

[25] J. Truchard, “Bringing FPGA design to application domain experts,” in Proc. IEEE

International Conference on Field-Programmable Technology, 2010.

[26] Labcenter Electronics (2011). [Online]. Available:

http://www.labcenter.com/products/vsm_overview.cfm

[27] M.N. Satar, D. Abdul Ishak, “Application of Proteus VSM in modeling brushless DC

motor drives,” In Proc. 4th International Conference on Mechatronics, Kuala Lumpur, 2011,

pp. 1-7.

[28] H. Mehdi, O. Boubaker, “Rehabilitation of a human arm supported by a robotic

manipulator: A position/force cooperative control,” Journal of Computer Science, vol. 6,

2010, pp. 912-919.

[29] H. Mehdi, O. Boubaker, “Impedance controller tuned by particle swarm optimization for

robotic arms,” International Journal of Advanced Robotic Systems, vol. 8, 2011, pp. 93-103.

[30] A. Aloulou, O. Boubaker, “Control of a step walking combined to arms swinging for a

three dimensional humanoid prototype,” Journal of Computer Science, vol. 6, 2010, pp. 886-

895.


591

http://www.labcenter.com/products/vsm_overview.cfm�

FPGA MODELLING AND REAL-TIME EMBEDDED CONTROL DESIGN …s2is.org/Issues/v5/n3/papers/paper3.pdf ·...

Documents

Transcript of FPGA MODELLING AND REAL-TIME EMBEDDED CONTROL DESIGN …s2is.org/Issues/v5/n3/papers/paper3.pdf ·...