Mechatronic approach for design and control of a hydraulic 3-DOF parallel robot.

Hancu, Olimpiu ; Maties, Vistrian ; Balan, Radu 等

Abstract: Modern machine tools based on parallel kinematic architecture provide excellent performance in terms of stiffness/weight ratio. Also, hydraulic actuators are widely used in industrial applications due to several advantages like large force and torque, high power to weight ratio, rapid response. The current paper presents the mechatronic design of a translational 3-DOF parallel robot which uses three hydraulic actuators to control the motion of the end-effector. The mechatronic approach in the design of products allows optimal design and also a global analysis of the system in terms of precision and efficiency. A dSPACE platform and a digital control board based on Atmel ATmega8535 microcontroller are used to compare the behavior of system under PD and state feedback control. Both simulation and experimental results are provided to show the effectiveness of the models and control methods.

Key words: mechatronics, servo hydraulic, simulation, motion control.

1. INTRODUCTION

The mechatronic approaches in the design of products and processes involve integrated methods for a global analysis of the whole system in terms of precision, efficiency, costs, maintenance (Khan et al., 2005). These will conduct to an increased functionality and flexibility, to an optimized design of systems. Software environments concur to compute, to solve and analyze, to simulate and test models, equations, control strategies, electronic boards. An integrated design method of a 3-DOF hydraulic parallel robot is detailed in this paper and experimental results are provided to validate the approach.

2. THE PARALLEL STRUCTURE

The parallel structure (Fig.1) with 3 prismatic and 6 universal joints in 3-PUU configuration, with 3 inextensible shafts allows only three degree of freedom along the Ox, Oy, Oz axes (Gregorio & Parenti, 1999). Based on the assumption of pure translational motion of the end-effector, we can write the equations for the inverse kinematics of the robot, using geometrical approach:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

If we consider [e.sub.i] = [a.sub.i] - [b.sub.i] (2)

and [w.sub.i] = L - [d.sub.i] (3)

the joint coordinate of the i-th linear actuator as a function of the cartesian position of the end-effector is:

[d.sub.i] = [p.sub.z] [+ or -] [square root of ([l.sup.2.sub.i] + 2[e.sub.ix][p.sub.x] + 2[e.sub.iy][p.sub.y] - [e.sup.2.sub.i] - [p.sup.2.sub.x] - [p.sup.2.sub.y])] (4)

Two solutions exist, according to the possibility of a symmetric mounting of rods. So, the reference coordinates of linear actuators can be computed with (5) for a position of the end-effector in cartesian space.

[w.sub.i] = L - [p.sub.z] - [square root of ([l.sup.2.sub.i] + 2[e.sub.ix][p.sub.x] + 2[e.sub.iy][p.sub.y] - [e.sup.2.sub.i] - [p.sup.2.sub.x] - [p.sup.2.sub.y])] (5)

The last relation will be used to compute the reference signals of the hydraulic actuators for an input curve.

[FIGURE 1 OMITTED]

3. HYDRAULIC SYSTEM

We will use three linear hydraulic motors to actuate the parallel structure. The hydraulic system is made up of three servovalves MOOG DDV633, a pump unit with constant flow rate, a pressure relieve valve, three linear motors and sensors in order to determine the state parameters of the system. Figure 2 describes the structure of the hydraulic system.

[FIGURE 2 OMITTED]

The mathematical model (6) of the hydraulic servo system, (Yao et al., 2000), includes the nonlinearities of friction forces, valves dynamics, oil compressibility and load influence. The details regarding the design of the hydraulic servo system, the value and parameters significance are detailed in Hancu et al., 2006, a.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

4. SYSTEM INTEGRATION

The mechatronic approach in the design of products and processes involves integration of the components of global system into an environment that allows a global analysis of the system in terms of precision, efficiency, costs, maintenance.

In this paper a virtual dynamic analysis was developed under Matlab and Nastran. In order to simplify the design process, the inverse dynamics of mechanical structure was realized using Visual Nastran and then the model was integrated to Matlab (Fig.3.). The robot dynamics is transmitted to linear actuators by means of force feedbacks that modify the load of the actuators. A path generator function is used to generate a parametric curve in the cartesian space. The reference signals of the actuators are computed using relation (5).

[FIGURE 3 OMITTED]

5. CONTROL STRATEGIES. IMPLEMENTATION

The parallel structure is controlled by means of three identical controllers which are assigned to linear actuators. The behavior of global model/system will be simulated for two control strategies. The first approach is developed base on a PD controller that assigns a set of constants for the advance strokes and other set of constants for the return strokes of the hydraulic actuators. In this way the asymmetrical shapes of the actuators chambers are compensated. The second strategy is based on the optimal state feedback where the state variables are displacement y, velocity y' and acceleration y". The linear displacements are measured by sensors and then through differentiating, the velocities and accelerations were computed. In order to compute the control laws, the valves nonlinearities were linearized around the null position of valve, but the tests were done for the nonlinear model of system (Fig.4).

[FIGURE 4 OMITTED]

As a first step of a real implementation, dynamics and positioning accuracy of a single hydraulic cylinder were investigated using a dSpace DS1104 board and a digital platform based on AVR ATMega 8535 microcontroller (Hancu et al., 2006, b). The experimental results confirm the theoretical analysis. Comparisons were made between control strategies for these two digital implementations.

6. CONCLUSION

This integrated approach allows the investigation of dynamics for complex systems in terms of precision and efficiency. Two control strategies were used to test the global model which includes the nonlinearities of hydraulic system. The simulation and experimental results show the effectiveness of approach. Future researches will be addressed to improve the control strategy by extending the model linearization and by online identification of model.

7. REFERENCES

Gregorio, R. Di. & Parenti-Castelli, V. (1999). Mobility analyses of the 3-UPU parallel mechanism assembled for a pure translational motion, IEEE-ASME International Conference on Advansed Intelligent Mechatronics, Atlanta

Hancu, O.; Vistrian, M. & Balan, R. (2006, a). Modeling, simulation and control a hydraulic servo system. PAMM * Proc. Appl. Math. Mech., Volume 6, Issue 1, December 2006, Pages: 811-812, PAMM / DOI 10.1002/pamm.200610385, Copyright [C] 2006 WILE-YVCH Verlag GmbH & Co. KGaA, Weinheim

Hancu, O.; Maties, V. & Balan, R. (2006, b). Design and Experimental Test of a Hydraulic Servo System, COMEFIM 8--The 8th International Conference on Mechatronics and Precision Engineering, Acta Technica Napocensis, vol II, pp.307-312, 2006, Cluj-Napoca

Khan, H.; Abou, S. C. & Sepehri, N. (2005). Nonlinear observer-based fault detection technique for electro-hydraulic servo-positioning system, Mechatronics, Vol. 15, No. 9, November 2005, ISSN 0957-4158

Yao, B.; Bu, F.; Reedy, J. & Chiu, G. T.-C. (2000). Adaptive Robust Motion Control of Single-Rod Hydraulic Actuators: Theory and Experiments, IEEE/ASME Transactions on Mechatronics, vol. 5, no. 1, pp. 79-91, march 2000.