**5. Conclusion**

0 1

Legs (mm)

200 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Position

Different situations in trajectory control are considered in this section. These are shown in Figure 36-38. As can be seen from the figures legs followed the desired trajectories

> 0 0.02

> 0 0.05 0.1

> 0 0.02

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> -0.02

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> -0.05

<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> -0.02

Time (sec)

Errors of the Legs (mm)

0 0.05



<sup>0</sup> <sup>2</sup> <sup>4</sup> <sup>6</sup> <sup>8</sup> -0.05

0 2 4 6 8

0 2 4 6

Time (sec)

rot x others


**4.5.2 Trajectory control** 

synchronous.

Legs (mm)

References (degree)

Fig. 35. Phase diagram of the SMC position control

0 1 2 3 4 5 6 7 8

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> <sup>7</sup> <sup>8</sup> -10

Time (sec)

Fig. 36. (a) Rotation in *x* direction (b) Errors of the legs

(a) (b)

0

2

4

Velocity

6

8

10

12

In this study, a high precision 6 DOF Stewart platform is controlled by a PID and sliding mode controller. These controllers were embedded in a Dspace DS1103 real time controller which is programmable in the Simulink environment. Design details and development stages of the PID and SMC are given from subsystems to main model in Simulink. This study can be a good example to show how a real time controller can be developed using Matlab/Simulink and Dspace DS1103. In order to test the performance of the controllers, several position and trajectory tracking experiments were conducted. Step inputs are used for position control and Kane transition function is used to generate trajectory. In the position experiments using both controllers, there is no steady state error and moving plate of the SP is positioned to the desired target with an error less than 0.5 *µm*. Sliding mode controller is better performance in terms of overshoot than PID but PID has faster response due to high gain. In the tracking experiments, PID and SMC have similar responses under no load. If nonlinear external forces are applied to moving platform, control performance of the SMC will be better than PID.
