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Particularly, the Distinction block calculates the motor's change in position (in counts) and the first Gain block divides by the sample time. Subsequent Gain obstructs transform the systems from counts/sec to revolutions/sec, and after that from revolutions/sec to revolutions/min. The constant representing the gear ratio needs to be specified in the MATLAB work space prior to the design can be run.
Lowering the length of the simulation then running the model generates the list below output for motor speed in RPM. Examining the above, we can see that the estimate for motor speed is rather noisy. This occurs for a number of factors: the speed of the motor is actually varying, encoder counts are being occasionally missed, the timing at which the board is polled does not precisely match the recommended sampling time, and there is quantization connected with reading the encoder.
Think about the following design with a simple first-order filter included to the motor speed quote. This design can be downloaded here. Running this model with the sample time increased to 0. 05 seconds and a filter time continuous 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 quote indeed is much less noisy. This is specifically helpful for enhancing the quote of the motor's speed when it is running at a steady speed. A downside of the filtering, nevertheless, is that it adds delay.
In essence we have actually lost details about the motor's actual response. In this case, this makes recognizing a model for the motor more difficult. When it comes to feedback control, this lag can break down the efficiency of the closed-loop system. Minimizing the time constant of the filter will minimize this lag, but 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 form of a first-order step action. Taking a look 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 constant, however, we need lower the filtering in order to much better see the true speed of the motor.
01 seconds, we get the following speed action. Remembering that a time constant specifies the time it takes a process to achieve 63. 2% of its overall modification, we can approximate the time continuous from the above chart. We will attempt to "eye-ball" a fitted line to the motor's response chart.
Assuming the exact same steady-state performance observed in the more greatly filtered data, we can estimate the time continuous based on the time it takes the motor speed to reach RPM. Considering that this appears to happen at 1. 06 seconds and the input appears to step at 1. 02 seconds, we can estimate the motor's time continuous to be around 0.
For that reason, our blackbox design for the motor is the following. (2) Recalling the design of the motor we stemmed from very first concepts, repeated below. We can see that we anticipated a second-order design, however 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 controls the reaction.
( 3) In addition to the reality that our design is reduced-order, the model is an additional approximation of the real life because it overlooks nonlinear aspects of the true physical motor. Based upon our linear model, the motor's output should scale with inputs of various magnitudes. For example, the response of the motor to a 6-Volt step need to have the exact same shape as its action to a 1-V step, simply 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 totally free" of the stiction. מנועים חשמליים לתעשיה. This nonlinear habits is not caught in our design. Usually, we use a viscous friction design that is linearly proportional to speed, instead of a Coulomb friction model that catches this stiction.
You might then compare the predictive ability of the physics-based model to the blackbox design. Another workout would be to generate a blackbox design for the motor based upon its frequency response, similar to what was made with the boost converter in Activity 5b. An advantage of utilizing a frequency action technique 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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