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Particularly, the Distinction block computes the motor's modification in position (in counts) and the very first Gain block divides by the sample time. Subsequent Gain blocks transform the units from counts/sec to revolutions/sec, and after that from revolutions/sec to revolutions/min. The consistent representing the gear ratio needs to be specified in the MATLAB work space prior to the model can be run.
Reducing the length of the simulation then running the design creates 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 develops for numerous reasons: the speed of the motor is actually differing, encoder counts are being occasionally missed out on, the timing at which the board is surveyed does not exactly match the prescribed tasting time, and there is quantization connected with reading the encoder.
Think about the following design with a simple first-order filter added to the motor speed estimate. This model can be downloaded here. Running this model with the sample time increased to 0. 05 seconds and a filter time constant of 0. 15 seconds produces the following time trace for the motor speed.
05; filter_constant = 0. 15;. By increasing the sampling period and adding the filter, the speed quote certainly is much less noisy. This is particularly handy for improving the estimate of the motor's speed when it is performing at a constant speed. A drawback of the filtering, however, is that it adds hold-up.
In essence we have actually lost details about the motor's real action. In this case, this makes recognizing a design for the motor more tough. When it comes to feedback control, this lag can degrade the performance of the closed-loop system. Lowering the time continuous of the filter will decrease this lag, however the tradeoff is that the noise won't be filtered also.
Considering that our input is a 6-Volt action, the observed reaction appears to have the type of a first-order step action. Looking at the filtered speed, the DC gain for the system is then approximately 170 RPM/ 6 Volts 28 RPM/V. In order to approximate the time continuous, nevertheless, we need reduce the filtering in order to much better see the real speed of the motor.
01 seconds, we get the following speed reaction. Recalling that a time consistent defines the time it takes a procedure to achieve 63. 2% of its total change, we can approximate the time continuous from the above chart. We will try to "eye-ball" a fitted line to the motor's action graph.
Assuming the very same steady-state performance observed in the more greatly filtered data, we can estimate the time consistent based on the time it takes the motor speed to reach RPM. Given that this appears to occur at 1. 06 seconds and the input appears to step at 1. 02 seconds, we can estimate the motor's time consistent to be approximately 0.
Therefore, our blackbox design for the motor is the following. (2) Recalling the model of the motor we obtained from first principles, repeated listed below. We can see that we anticipated a second-order design, but the action looks more like a first-order model. The explanation is that the motor is overdamped (poles are genuine) which one of the poles dominates the response.
( 3) In addition to the fact that our model is reduced-order, the design is a more approximation of the real life because it neglects nonlinear aspects of the true physical motor. Based on our linear design, the motor's output need to scale with inputs of different magnitudes. For instance, the response of the motor to a 6-Volt action need to have the same shape as its action to a 1-V action, simply scaled by an element of 6.
This is due to the stiction in the motor. If the motor torque isn't large enough, the motor can not "break totally free" of the stiction. רובוט 6 צירים. This nonlinear habits is not captured in our model. Normally, we use a viscous friction design that is linearly proportional to speed, instead of a Coulomb friction model that records this stiction.
You might then compare the predictive capability of the physics-based design to the blackbox model. Another workout would be to produce a blackbox model for the motor based upon its frequency action, similar to what was made with the boost converter in Activity 5b. An advantage of using a frequency action approach to identification is that it allows identification of the non-dominant characteristics.
In Part (b) of this activity, we develop a PI controller for the motor.
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