1. REAL TIME IMPLEMENTATION OF FUZZY SLIDING MODE CONTROLLER FOR ROBOT ARM ACTUATED BY PNEUMATIC MUSCLES.
CDTA
S2RA, CDTA,
July , 2011
A.REZOUG, M. HAMERALIN and M. TADJINE Division robotique et productique. Centre de Développement des Technologies Avancées Cité 20 août, B. P. 17, Baba Hassen, Algiers, Algeria
We divided this part in two steps. In the first one, we design the conventional sliding mode control, while the second proposes the fuzzy sliding mode control approach to control 1-link of the robot actuated by (PAM)
A. Sliding mode control design
A Sliding Mode Control is a Variable Structure Control (VSC). Basically, VSC includes several different continuous functions that map plant state to a control surface. The switching among these functions is determined by plant state which is represented by a switching function [7].
Considering the system to be controlled described by state-space equation:
The sliding mode control comports two terms which are equivalent control term and switching control as:
Where ueq is the equivalent part of the sliding mode control, i.e. the necessary known part of the control system.
 us described the discontinues control is given by :
with :
The inputs (s and ), the output of control law (ufuzzy) and fuzzy variables are defined with twenty-one linguistic rules. The membership functions of the fuzzy variables are chosen to be fully overlapped, triangular, trapezoidal and symmetric. The design of the fuzzy sliding mode controller need there steps (fuzzification, inference and defuzzification) :
Fuzzification : (1) The fuzzy sets of first input (s) are defined as P s(Positive), Zs (Zero), and Ns (Negative).
(2) The fuzzy sets of second input ( ) are defined as P (Positive), Z (Zero), and N ((Negative).
(3) The fuzzy sets of the output are defined as PB (Positive big), PM (positive Middle), Z (Zero), NM (Negative Middle), and NB (negative big).
Figure. 5: distribution of the fuzzy labels through the deferent discourse universe of the inputs /output of the fuzzy controller.
Inference engine : the diagonal table of rules is presented as fellow, which are able to guarantee the stability of the robot.
In our case of control, we choose to not use the equivalent control calculated from the model of the robot. We uses only the discontinuous part of control. this choose is imposed by the parameters variation of the not possible to its estimation exactly. The equivalent control part will be compensated by the fuzzy controller will be presented. 
1-Introduction
3- fuzzy sliding mode control design
In (1950s) [11] [12], Dr. Joseph .L McKibben has remarked the human capacity to adapt an external load while producing adequate forces in real environment using his soft multiple natural muscles. Thus, he proposed the pneumatic artificial muscles (PAM) for artificial limb of the handicapped [13].
pneumatic artificial muscles PAM are a class of devices or mechanisms that convert pneumatic power into useful mechanical work or motion. PAMs are contractile devices and can consequently generate unidirectional motion. Just as with skeletal muscles, two actuators are needed to be coupled in order to generate a bidirectional motion, one for each direction, then two antagonistic coupled with PAM are need to actuate a revolute joint as shown in Figure 2. The mechanical motion produced by a variation of the joint variables can be obtained by modifying the pressure ΔP in each muscle. The motion principle is shown in Figure 1. We have chosen these actuators for the reason that is suitable for domestic’s application environments.
B. Fuzzy sliding mode control design
This paper presents the real time implementation of the fuzzy sliding mode to control of 1-link robot arm actuated by pneumatic artificial muscles, when we can avoid the nonlinear modelling problem and garnered the stability and the robustness of our system. In addition, the chattering effect can be reduced.
Figure 1: 1-link arm robot actuated by the muscles.
2-The robot manipulator with pneumatic artificial muscles
The following figures shows the used robot and an example of the FESTO pneumatic muscles :
Joint 2
Joint 1
Distributors
Air Source
Valve
Stem S NM Z PM N PB P NB
Deffuzzification: we used the centre of area method to obtain the crisp value should be send to the actuators of the robot .
Figure.3. FESTO artificial muscles.
Figure 2: 2-DOF robot arm actuated by the muscles.
4- results and discussion
The (PAMs) consequently (PAMs) based robots have many desirable characteristics, such as high power-to-weight ratios, high power-to-volume ratios, and inherent compliance
Experimental results are used to examine the feasibility and the validity of the proposed fuzzy sliding mode controller. The experimental are accomplished by the implementation in C language on the Pentium 4 PC, the low control is transformed to the actuators of robot through the MPC555 control card by using of CAN communications bus, In order to handle efficiently such a distributed architecture, we used the SynDEx software [9] which Linux/RTAI, which is developed in collaboration with INRIA. The regulation mode is adopted to test the capability of the proposed controller to maintain the imposed performances and the robustness. We aim to that our 1-link robot attend the desired angular position of 14 degree, with the initial position of zero degree, with the minimum of static and dynamic errors:
In the opposite, there exist many difficult in the control of robot arm actuated by (PAM), we can give : the phenomenon of hysteresis generated at the time of inflated/deflated, the pressure in the each muscles is not identical the antagonistic muscles is affected by the temperature and volume variations in each muscles. The flow of each distributors is supposed to be identical, but really they can have a little difference from one to other, delay induced by the length of air conductor between the distributor and the muscle. The characteristics of a muscle change slightly when the number of operating cycle increases, these phenomena’s will change the characteristics of the system behaviour, i.e. the parameters of the system are not exactly known the modelling errors and parameters uncertainties of the model may be appeared.
In order to cure to this problems we adapt the fuzzy sliding mode control. This paper presents the real time implementation of the fuzzy sliding mode to control of 1-link robot arm actuated by pneumatic artificial muscles when we can avoid the nonlinear modelling problems and garnered the stability and the robustness of our system.
2-The robot manipulator identification
The dynamic behaviour of the system-muscles, valves and the joint were characterized by open-loop SBPA input response tests. A PRBS signal is a popular input signal for system identification because it is persistently exciting to the order of the period of the signal. A maximum length PRBS signal has a correlation function that resembles a white noise correlation function [2]. This property does not hold for non-maximum length sequences. Thus the PRBS signal used in identification processes should be a maximum length PRBS signal. Small steps command signal were injected to result joint angular displacement values. The robot dynamics can be described by the second-order linear differential equation ; this led to the following model:
then deduced transfer function was given by the following equation
Figure 6 : angular position response.
Figure 7: control signal.
Figure 8: surface.
we observe from the position response curvature that the joint tracked adequately the imposed reference angle, with the existence of satisfactory static and dynamic errors. We can see from the figures of the control signal like that of sliding surface the smoothes signals, and then the chattering effect is attenuated.
5-Conclusion
This paper presents the real time implementation of the fuzzy sliding mode controller (FSMC) for the robot arms actuated by pneumatic artificial muscles. From this work and through the experimental results, we demonstrated that the effectiveness of (FSMC) combination to control this type of robot with avoidance of the modeling problems, and garneted the stability and robustness of the closed loop system and the attenuation of the chattering effect.
Reference
[1] H. P. H. Ann, K. K. Ahn, & J. I. Yoon, Identification of the 2-Axes Pneumatic Artificial Muscle (PAM) Robot Arm Using Double NARX Fuzzy Model and Genetic Algorithm. Proc. Int. Conf. on Smart Manufacturing Application, Gyeonggi-do, KR, 2008, 84 – 89.
[2] B. Vanderborght, B. Verrelst, R. V. Ham, J. Vermeulen, & D. Lefeber, Dynamic Control of a Bipedal Walking Robot actuated with Pneumatic Artificial Muscle. Proc. IEEE Int. Conf. on Robotics and Automation, Barcelona, SP, 2005, 1-6.
[3] D.G. Caldwell, M. Cerda, G.A., & C.J Bowler, Investigation of Bipedal Robot Locomotion using Pneumatic Muscle Actuators. Proc. IEEE Int. Conf. on Robotics and Automation, Albuquerque, NM, 1997,
[4] M. Chettouh, R. Guernane, & M. Hamerlain, A Robot arm driven by artificial fluidic muscles. Proc. Of ICSIT/IEEE conf , Alger, DZ, 2005.
[5] Caldwell, D. G., Tsagarakis, N, & Medrano-Cerda, Development of a Pneumatic Muscle Actuator driven Manipulator Rig for Nuclear Waste Retrieval Operations. Proc. IEEE Int. Conf. on Robotics and Automation, Detroit, Michigan, USA, 1999,
[6] M.Hamerlain, Commande hiérarchisée a modèle de référence et à structure variable un robot manipulateur à muscle artificiels (thèse de doctorat université de Toulouse III, 1993).
[7] S. Tian, G. Ding, D. Yan, L. Lin, & Meng Shi, Nonlinear Controlling of Artificial Muscle System with Neural Networks. Proc. IEEE Int. Conf. on Robotics and Biomimetics, CN, 2004,
[8] E.H. Mamdani, Application of fuzzy algorithms for control of simple dynamic plant, IEEE Transaction. 12(121), 1974,
[9] Slotine, J.J.E & W. Li. Applied Nonlinear Control, (Englewood Cliffs, NJ: Printice Hall, 1991).
[10] L. Zhang, J. Xie, & D. aohua Lu, Adaptive Robust Control of One-link Joint Actuated by Pneumatic Artificial Muscles. Proc. 1st Int. Conf. on Bioinformatics and Biomedical Engineering, CN. 2007,
[11] M. Mihajlov, V. Nikolić, & D. Antić, Position control of an electro-hydraulic Servo system using sliding mode control Enhanced by fuzzy pi controller. Journal of Mechanical Engineering, 9(1), 2002, 1217– 1230.
Figure.4. Identification of the articulation one .
The graph for the model validation is illustrated in Figure (4) such that bleu line presents the approximated model responses and the black lines are the real system output. It is very important to say that the obtained linear model is not representative of the real robot. But, this linearization is used in transitory step for objective to apply the sliding mode control (SMC). The SMC technique is very knowledge by its robustness compared to systems poorly modeled and/or has parameter variations, and/or external disturbances. .