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Particularly, the Difference block computes the motor's modification in position (in counts) and the first Gain block divides by the sample time. Subsequent Gain blocks transform the units from counts/sec to revolutions/sec, and then from revolutions/sec to revolutions/min. The continuous representing the equipment ratio needs to be specified in the MATLAB work space before the design can be run.
Decreasing the length of the simulation then running the design produces the following output for motor speed in RPM. Examining the above, we can see that the estimate for motor speed is quite loud. This develops for numerous reasons: the speed of the motor is in fact differing, encoder counts are being occasionally missed, the timing at which the board is polled doesn't precisely match the prescribed tasting time, and there is quantization associated with reading the encoder.
Think about the following model with a basic first-order filter contributed to the motor speed estimate. This design 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 tasting duration and including the filter, the speed price quote indeed is much less loud. This is especially practical for enhancing the estimate of the motor's speed when it is performing at a consistent speed. A downside of the filtering, however, is that it adds delay.
In essence we have lost info about the motor's actual reaction. In this case, this makes determining a design for the motor more difficult. In the case of feedback control, this lag can deteriorate the efficiency of the closed-loop system. Lowering the time consistent of the filter will decrease this lag, but the tradeoff is that the sound won't be filtered also.
Considering that our input is a 6-Volt step, the observed response appears to have the kind of a first-order action response. Looking at the filtered speed, the DC gain for the system is then roughly 170 RPM/ 6 Volts 28 RPM/V. In order to estimate the time constant, nevertheless, we require lower the filtering in order to better see the real speed of the motor.
01 seconds, we get the following speed reaction. Recalling that a time constant defines the time it takes a procedure to accomplish 63. 2% of its total change, we can approximate the time consistent from the above chart. We will attempt to "eye-ball" a fitted line to the motor's action graph.
Presuming the same steady-state efficiency observed in the more heavily filtered data, we can approximate the time constant based upon 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 consistent to be approximately 0.
Therefore, our blackbox design for the motor is the following. (2) Remembering the model of the motor we obtained from first concepts, repeated listed below. We can see that we prepared for a second-order design, but the action looks more like a first-order model. The description is that the motor is overdamped (poles are genuine) and that one of the poles controls the action.
( 3) In addition to the reality that our design is reduced-order, the design is an additional approximation of the genuine world in that it overlooks nonlinear aspects of the true physical motor. Based upon our direct model, the motor's output ought to scale with inputs of different magnitudes. For instance, the response of the motor to a 6-Volt step need to have the exact same shape as its reaction to a 1-V step, simply scaled by an aspect of 6.
This is because of the stiction in the motor. If the motor torque isn't large enough, the motor can not "break free" of the stiction. בקרי מהירות למנועים https://www.sherfmotion.co.il/. This nonlinear habits is not recorded in our design. Usually, we utilize a viscous friction model that is linearly proportional to speed, instead of a Coulomb friction model that catches this stiction.
You might then compare the predictive capability of the physics-based design to the blackbox design. Another exercise would be to produce a blackbox model for the motor based upon its frequency action, comparable to what was finished with the increase converter in Activity 5b. A benefit of using a frequency reaction method to recognition is that it allows identification of the non-dominant characteristics.
In Part (b) of this activity, we create a PI controller for the motor.
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