ABSTRACT

In Fig. 3-39 the power amp and motor have been combined into a single block with a gain of (2.0 amps/volt) (0.5lb1jamp) = 1.0 lb1jvolt. The Newton's law equation is implemented in our usual way with a summer, gain blocks for 1/ M and B, and two integrators. For our first test, I set the computational delay at zero. Delays of any kind degrade feedback system performance, so we start with the best possible situation first. As mentioned earlier, the sensor quantization was deliberately set too coarse, to illustrate an important general feature of digital systems. The commanded position is 0.08203 inch, whereas the only values available from the A/D are increments of size 0.0078125. Thus the tenth increment would be 0.078125 and the eleventh would be 0.0859375. That is, the system is "looking for" 0.08203 but "can't find it"; thus it will "hunt" or oscillate between the two values it can find. This hunting is usually unacceptable but must occur when quantized (rather than smoothly varying) signals are used. Of course one usually can (and does) set the sensor quantization resolution fine enough to make the hunting unnoticeable. (Real effects such as Coulomb friction in the load bearings may also stop the hunting.)

Figure 3-40 shows this behavior for the system parameters set as in Fig. 3-39. Note that the load displacement xc is a smooth curve but its quantized measurement xdig follows it inaccurately in a stepwise fashion. Also, xc never "settles down," but goes into a continuous oscillation, called a limit cycle. The average value of this xc oscillation is also not the desired value of 0.08203, but is offset from it by a steadystate error. In Fig. 3-41 I have made the A/D resolution equal to the D/A (0.00001526) and all these problems disappear. Actually, xc is still hunting around the desired value but now the amplitude is so small that it can't be seen on the graph.