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Specifically, the Distinction block computes the motor's modification in position (in counts) and the first Gain block divides by the sample time. Subsequent Gain blocks convert the systems from counts/sec to revolutions/sec, and after that from revolutions/sec to revolutions/min. The consistent representing the equipment ratio needs to be defined in the MATLAB work area before the model can be run.
Decreasing the length of the simulation then running the model generates the following output for motor speed in RPM. Taking a look at the above, we can see that the estimate for motor speed is rather loud. This arises for numerous reasons: the speed of the motor is really varying, encoder counts are being regularly missed out on, the timing at which the board is surveyed does not exactly match the recommended sampling time, and there is quantization related to checking out the encoder.
Consider the following model with a basic first-order filter included to the motor speed estimate. This design can be downloaded here. Running this design with the sample time increased to 0. 05 seconds and a filter time consistent of 0. 15 seconds produces the following time trace for the motor speed.
05; filter_constant = 0. 15;. By increasing the tasting duration and adding the filter, the speed estimate indeed is much less loud. This is particularly useful for enhancing the estimate of the motor's speed when it is running at a consistent speed. A drawback of the filtering, nevertheless, is that it adds delay.
In essence we have lost information about the motor's real reaction. In this case, this makes determining a design for the motor more challenging. In the case of feedback control, this lag can deteriorate the performance of the closed-loop system. Minimizing the time constant of the filter will decrease this lag, however the tradeoff is that the noise won't be filtered as well.
Thinking about that our input is a 6-Volt action, the observed response appears to have the kind of a first-order action reaction. Taking a look at the filtered speed, the DC gain for the system is then roughly 170 RPM/ 6 Volts 28 RPM/V. In order to approximate the time consistent, nevertheless, we require minimize the filtering in order to much better see the true speed of the motor.
01 seconds, we get the following speed reaction. Remembering that a time consistent defines the time it takes a process to achieve 63. 2% of its total modification, we can estimate the time continuous from the above chart. We will attempt to "eye-ball" a fitted line to the motor's reaction graph.
Presuming the exact same steady-state performance observed in the more heavily filtered information, we can approximate the time consistent based on the time it takes the motor speed to reach RPM. Since this appears to take place at 1. 06 seconds and the input appears to step at 1. 02 seconds, we can estimate the motor's time continuous to be roughly 0.
Therefore, our blackbox design for the motor is the following. (2) Recalling the model of the motor we stemmed from very first concepts, repeated below. We can see that we prepared for a second-order model, however the action looks more like a first-order design. The description is that the motor is overdamped (poles are real) which among the poles dominates the response.
( 3) In addition to the fact that our design is reduced-order, the design is a more approximation of the real life in that it overlooks nonlinear aspects of the true physical motor. Based on our direct design, the motor's output ought to scale with inputs of various magnitudes. For instance, the action of the motor to a 6-Volt action must have the same shape as its response to a 1-V action, just scaled by an aspect of 6.
This is due to the stiction in the motor. If the motor torque isn't large enough, the motor can not "break complimentary" of the stiction. Sherf. This nonlinear behavior is not captured in our model. Typically, we use a thick friction model that is linearly proportional to speed, instead of a Coulomb friction design that records this stiction.
You could then compare the predictive ability of the physics-based model to the blackbox model. Another exercise would be to generate a blackbox design for the motor based on its frequency action, similar to what was made with the increase converter in Activity 5b. An advantage of using a frequency action technique to recognition is that it makes it possible for identification of the non-dominant dynamics.
In Part (b) of this activity, we create a PI controller for the motor.
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