Fig 9 simulation results in the case of posture1 a

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Fig. 9. Simulation results in the case of Posture1. (a) Without model-based control. (b) With model-based control. Fig. 10. Simulation results in the case of Posture2. phase is –1000 min -1 /28 ms. The value of K b is set to -0.7. Fig. 9 indicates that the proposed model-based control suppresses the residual vibration of the end- effector in view of the vibration acceleration. The settling time, namely the time interval between and , is reduced down to about 1/2 (from 432 to 193 ms) without the time-delay of the load’s response. Further, Fig. 10 indicates that the settling time is re- duced down to about 1/2 (from 289 to 151 ms). 4. EXPERIMENTAL RESULTS AND CON- SIDERATIONS 4.1. Experimental set-up Fig. 11 shows a schematic diagram of the experi- mental set-up. Physical parameters of the experimen- tal set-up are shown in Table 1. A harmonic drive gear reducer whose reduction ratio is 1/100 is con- nected to a motor, and a driven machine part is con- nected to this reducer’s output shaft. The inertia ra- tios of the driven machine part to the driving machine part are about 8.4 for Posture1 and 3.3 for Posture2, respectively. The first natural frequency of the system varies from 7 Hz to 12 Hz depending on the posture of the robot arm as shown in Fig. 5. With respect to the servo control system of the waist axis, an AC servo motor and a driver are em- ployed. Their servo parameters are equivalently con- verted into those of the DC servo system as shown in Table 1. 4.2. Construction of control system The velocity control system of the main control loop consists of the software servo system. The ve- locity command is generated from the personal com- puter. Fig. 11. Schematic diagram of the experimental set-up.
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