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The rotation speed R of the motor is measured by a tachometer. You should measure R every 20 ms with a resolution of 1 rps

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The rotation speed R of the motor is measured by a tachometer. You should measure R every 20 ms with a resolution of 1 rps. The rotational speed will vary from 0 to 250 rps (0 ≤ R ≤ 250 rps). The output of the tachometer is an ugly-looking digital wave with a frequency 100 times the motor speed. Thus, 0 ≤ f ≤ 25 kHz (Figure 13.26).

Figure 13.26

Tachometer frequency is a function of the motor rotation speed.

The desired rotational speed (R* also in rps) comes from an 8-bit parallel input port. A new value is available on the rise of Ready. The fall of Done is an acknowledge signal back to the input device signifying that the microcomputer no longer needs the data. The timing is shown in Figure 13.27.

Figure 13.27

Sensor timing.

The interrupt-driven control algorithm should be implemented at 50 Hz (U(t) is the duty cycle in percent):

U(t) = ∫0 (R* − R(t))dt where R* and R(t) are in rps and t is in seconds

a) Let u(n) equal the cycle count (500 ns each) that controls the duty cycle of the outputcomparevariable-duty cycle 50 Hz squarewave. If the range of duty cycle is 0 < U(t)< 100, what is the relaTonshipbetween u(n) and U(t)?b) Let R(n) be the sampled sequence of measured rotaTonal speed in rps. Convert the above integralcontrol equaTon into discrete form. ±hat is, determine the relaTonship that calculates u(n) from u(n − 1),u(n − 2) …, R(n), R(n − 1), R(n − 2) …, and R*.±he objecTve of this exercise is to control the rotaTonal speed of a DC motor. ±he +5 V DC motor has aresistance of 10 Ω. Your control system will apply a variable power to the motor by varying the duty cycleof a 50 Hz signal, as shown in Figure 13.25, for example.Figure 13.25PWM outputto actuator.±he rotaTon speed R of the motor is measured by a tachometer. You should measure R every 20 mswith a resoluTon of 1 rps. ±he rotaTonal speed will vary from 0 to 250 rps (0 ≤ R ≤ 250 rps). ±he outputof the tachometer is an ugly-looking digital wave with a frequency 100 Tmes the motor speed. ±hus, 0 ≤f ≤ 25 kHz (Figure 13.26).Figure 13.26±achometerfrequency is a funcTon of the motor rotaTon speed.
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