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9 PARAMETER ESTIMATION To simulate a Delta-3 robot in Simulink one needs to choose parameters so the model becomes as close as possible to the real robot. Therefore it is good to divide the parameters into different parts for the different equipment used to control the robot. P1, P2, P3 and P4 contain the parameters used in the different parts shown in Figure 9.1. Figure 9.1, P1, P2, P3 and P4 are the parameterization for the different blocks. Where “d” is the robot dynamics. The parameters in P1 are given from the robot manufacture and are depending on the robots physically structure such as the upper arms, forearms, base plate and the travelling plate. These parameters are needed to be able to calculate the inverse and forward kinematics for the robot. The parameters in P2 are given from the drive unit MC-4 which ELAU GmbH use to control their motors. The configurations of these parameters are the same as the configuration in the real MC-4s which are used at the real robot. P3 contains values given from the real robot structure such as the weight of the different parts of the robot. P3 also contains the parameters given in P1 and the torques given to the motors. The parameters in P3 are used in chapter 4.8.3 to be able to obtain the coupling effect between the arms which is given in Eq. 4.31. The parameters in P4 are given from the motor model which is used to simulate the motors which ELAU GmbH is using. The parameters are given from the data sheets from the motor which is used on the real robot. The parameters in P4 are also estimated with the Matlab function lsqnonlin to try to obtain better dynamics in the Simulink motor model. lsqnonlin is used to solve nonlinear least-squares curve fitting problems. In this case the curve fitting problem is between the Simulink model output and the real robots output. Matlab tries to estimate the parameters which the user has given as initial value so the curve fitting problem becomes minimized. But this function in Matlab can’t find any better values for the parameters in P4 to be able to include more of the dynamics from the real motor. The Matlab function only returns the same values as the initial value. This could depend on that the nonlinear least-square curve fitting problem already is in a minimum. And when Matlab tries to change the parameters it only finds values which makes the non-linear curve fitting problem bigger instead of smaller. Table 9-1 shows an overview of the parameters which are included in the different parameterization parameters P1 (Kinematics), P2 (drive unit MC4), P3 (dynamic for real robot) and P4 (Motor parameters). ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 38
For explanation of the parameters in Table 9-1 see section 1.3.2 Variables and parameters. Parametrization P1 (Kinematics) P2 (MC-4) P3 (Dynamics) P4 (Motor) la lb RA RB αA αB αC KPpos KPvel KIvel KPcurr KIcurr FFcurr Fvel FcurrRef Fcurr CO CT ______________________________________________________________________________ Public Report ELAU GmbH, Marktheidenfeld 39 la lb RA RB αA αB αC mb mfb mn mpayload mc rGb τ kr ipeak inom RPMmax Km Im IBrake R L zp Fv Fs GRin GRout Table 9-1, the variables P1, P3 and P4 which contains the parameters as shown in the table can be found in Eq. 4.1, Eq. 4.2 , Eq. 4.27, Eq. 4.31. The parameters in P2 can be found in the simulink model. Figure 9.2, configuration window for parameters in P2 in the Simulink model. ILoad τload CE Figure 9.3, configuration window for parameters in P4 in the Simulink model.
Page 1: ISSN 0280-5316 ISRN LUTFD2/TFRT--58
Page 5: Acknowledgements This Master thesis
Page 8 and 9: 7 Control approach - ELAU GmbH ....
Page 10 and 11: α1 frame rotation angle for arm at
Page 12 and 13: 2 BACKGROUND 2.1 ROBOTICS The word
Page 14 and 15: 2.2.2 SOFTWARE - ELAU GMBH EPAS-4 i
Page 16 and 17: 3 KINEMATICS - SERIAL ROBOT In the
Page 18 and 19: 3.2 INVERSE KINEMATICS When the for
Page 20 and 21: 4 KINEMATICS & KINETICS - DELTA-3 R
Page 22 and 23: 4.3 Forward Kinematics The forward
Page 24 and 25: Figure 4.5, inverse kinematics tran
Page 26 and 27: where & ⎡x& n ⎤ ⎡− lA sin(
Page 28 and 29: 4.7 ACTUATOR DYNAMICS In most exist
Page 30 and 31: The inertia contribution of each up
Page 32 and 33: According to d’Alembert’s princ
Page 34 and 35: 5 TRAJECTORY A trajectory is a path
Page 36 and 37: 6 TRAJECTORY - ELAU GMBH C600 is th
Page 38 and 39: 6.2 CIRCULAR INTERPOLATION In the E
Page 40 and 41: 7.1 MC-4 DRIVE The MC-4 drive is a
Page 42 and 43: Figure 8.2, Simulink model with mot
Page 46 and 47: 10 EXPERIMENTS For the experiments
Page 48 and 49: Figure 11.2, shows the motion of th
Page 50 and 51: Figure 11.6, shows the current I ef
Page 52 and 53: 11.1.2 SIMULINK EXPERIMENT 2 Figure
Page 54 and 55: Figure 11.13, shows the acceleratio
Page 56 and 57: measured actual value from the real
Page 58 and 59: and are shown over the time in seco
Page 60 and 61: Figure 11.23 shows the x, y and z c
Page 62 and 63: Figure 11.27, the blue line shows t
Page 64 and 65: Figure 11.31, the blue line shows t
Page 66 and 67: In Figure 11.36 the blue line repre
Page 68 and 69: 11.2.3 JACOBIAN EXPERIMENT 3 Figure
Page 70 and 71: In Figure 11.44 the blue line repre
Page 72 and 73: 12 CONCLUSIONS In section 11.1 one

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