M Shown in Fig. P4.3-8 is the block diagram of one joint of a robot arm....
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M Shown in Fig. P4.3-8 is the block diagram of one joint of a robot arm. This system is described in Problem 1.5-4. The signal M(s) is the sampler input, E (s) is the servomotor input voltage, m(s) is the motor shaft angle, and the output (s) is the angle of the arm. (a) Suppose that the sampling-and-data-reconstruction process is implemented with an analog-to-dig- ital converter (A/D) and a digital-to-analog converter. Redraw Fig. P4.3-8 showing the A/D and the D/A. (b) Suppose that the units of ea(t) are volts, and of Om(t) are rpm. The servomotor is rated at 24 V (the volt- age ea(t) should be less than or equal to 24 V in magnitude). Commercially available D/As are usually rated with output voltage ranges of ±5 V, ± 10 V, 0 to 5 V, 0 to 10 V, or 0 to 20 V. If the gain of the power amplifier is 2.4, what should be the rated voltage of the D/A? Why? (c) Derive the analog transfer function a(s)/Ea(s). (d) With K = 2.4 and T = 0.1 s, derive the pulse transfer function(z)/M(z). (e) Derive the steady-state output for m(t) constant. Justify this value from the motor characteristics. (f) Verify the results of part (d) by computer. T 1-g-Ts S Power amplifier K FIG. P4.3-8 Model of robot arm joint. Ea Servomotor 200 0.5 s +1 m S 0, 'm Gears 1 100 M Shown in Fig. P4.3-8 is the block diagram of one joint of a robot arm. This system is described in Problem 1.5-4. The signal M(s) is the sampler input, E (s) is the servomotor input voltage, m(s) is the motor shaft angle, and the output (s) is the angle of the arm. (a) Suppose that the sampling-and-data-reconstruction process is implemented with an analog-to-dig- ital converter (A/D) and a digital-to-analog converter. Redraw Fig. P4.3-8 showing the A/D and the D/A. (b) Suppose that the units of ea(t) are volts, and of Om(t) are rpm. The servomotor is rated at 24 V (the volt- age ea(t) should be less than or equal to 24 V in magnitude). Commercially available D/As are usually rated with output voltage ranges of ±5 V, ± 10 V, 0 to 5 V, 0 to 10 V, or 0 to 20 V. If the gain of the power amplifier is 2.4, what should be the rated voltage of the D/A? Why? (c) Derive the analog transfer function a(s)/Ea(s). (d) With K = 2.4 and T = 0.1 s, derive the pulse transfer function(z)/M(z). (e) Derive the steady-state output for m(t) constant. Justify this value from the motor characteristics. (f) Verify the results of part (d) by computer. T 1-g-Ts S Power amplifier K FIG. P4.3-8 Model of robot arm joint. Ea Servomotor 200 0.5 s +1 m S 0, 'm Gears 1 100
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1 Refer to Figure in question for the openloop system The openloop system is shown in Figure 1 2 Ms ... View the full answer
Related Book For
Process Dynamics And Control
ISBN: 978-0471000778
2nd Edition
Authors: Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellich
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