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Fig. 6-5.
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Building the governor.
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Hysteresis
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Think back to the hypothetical robot car with the bumper. Assume, for a minute, that the car goes into reverse whenever the bumper is pressed, and goes forward when it is not pressed. What do you think happens Your car is happily motoring forward when it hits a wall. The bumper senses this event and the car backs up for a fraction of a second until the bumper releases. You haven t escaped the wall. Instead, the car is going to
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Fig. 6-6.
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Car bumper with immediate response.
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twitch back and forth until random forces make it turn away from the wall or the batteries run down. This is illustrated in Fig. 6-6. In the graph below the picture there are two lines that represent di erent events. The bottom, solid, line is the bumper signal. When it is high the bumper is pressed. The top, dashed, line is the reverse signal to the car. When it is high the car is going backward and, preferably, in a slight circle so it avoids the obstacle. Clearly, this strategy is not working very e ciently. What you need is some kind of delay between the sensed event (the bumper signal) and its e ect (the reverse signal), so that the released bumper doesn t let the car go forward again until after a su cient delay. This delay between cause and e ect is called hysteresis, and it is important to many control systems. An example of this is shown in Fig. 6-7. When the bumper hits the wall the car immediately starts to back up. The bumper moves away from the wall and its signal returns to normal but, with hysteresis in the system, the car continues to back up for a predetermined time delay t. This provides enough of a retreat that when the car starts moving forward again it misses the wall, at least for a while. Another example of hysteresis is in your home thermostat. These have two set points, one to turn the heater on, for example, and another to turn the heater o (Fig. 6-8). When the room temperature drops below the Turn On point, the heater turns on. This is an all-or-nothing proposition, there is no medium setting on your house heater. With the heater on, the temperature
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Fig. 6-7. Car bumper with hysteresis.
Fig. 6-8.
Temperature control.
stops its fall and begins to rise again. It quickly passes the Turn On point, but the heater remains on until it passes the Turn O point.
MECHANICAL SWITCH
Try This: Our third, and nal, example of hysteresis is a mechanical switch. It is similar to the falling pencil example earlier in the chapter, but has two states, up and down, instead of just one, fallen. See Fig. 6-9.
CHAPTER 6 Control
Fig. 6-9.
Mechanical switch.
The rubber band holds the lever against the post in an energy well. It takes energy to move the lever, since the arc of motion pulls against the rubber band. Putting enough energy into the lever causes the lever to escape its well. However, the pull of the rubber band snaps it down into the other energy well. There it sits until disturbed again. This arrangement of force is useful for holding something in place, without having to use motors to keep it there. The only time you need to use force is to switch the position, or state, of the switch. Try to extend this design into a mechanical gripping hand that stays closed under its own power.
Summary
In this chapter we continued to lay down a foundation of concepts for our later work. We started with passive control, a form of control where you don t have to do anything to manage it. From there we looked at some active control concepts, starting with openloop control where the controller doesn t have any con rmation, or feedback, as to what the system is doing. A more powerful form of control is closed-loop control, where feedback is used to adjust the system. Feedback doesn t imply fancy sensors, electronics, or computers. Very simple systems use feedback to good e ect, and these simple principles can be used in more complicated systems as well. Whenever you can make it work, simple mechanisms are better than complex ones less likely to break, easier to understand, and more likely to work throughout the life of the system.
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