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Specifically, 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 systems from counts/sec to revolutions/sec, and then from revolutions/sec to revolutions/min. The constant representing the gear ratio requires to be specified in the MATLAB work area before the model can be run.
Lowering the length of the simulation then running the model generates the list below output for motor speed in RPM. Taking a look at the above, we can see that the price quote for motor speed is rather loud. This emerges for numerous reasons: the speed of the motor is really varying, encoder counts are being occasionally missed out on, the timing at which the board is polled does not precisely match the recommended tasting time, and there is quantization related to checking out the encoder.
Consider the following model with an easy first-order filter added to the motor speed price quote. This model can be downloaded here. Running this design with the sample time increased to 0. 05 seconds and a filter time continuous of 0. 15 seconds produces the list below time trace for the motor speed.
05; filter_constant = 0. 15;. By increasing the tasting duration and adding the filter, the speed quote undoubtedly is much less noisy. This is specifically handy for improving the quote of the motor's speed when it is running at a stable speed. A drawback of the filtering, however, is that it includes hold-up.
In essence we have actually lost details about the motor's actual action. In this case, this makes identifying a design for the motor more challenging. In the case of feedback control, this lag can deteriorate the efficiency of the closed-loop system. Reducing the time constant of the filter will minimize this lag, however the tradeoff is that the noise won't be filtered also.
Considering that our input is a 6-Volt step, the observed response appears to have the form of a first-order step action. Looking 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 continuous, nevertheless, we need decrease the filtering in order to much better see the true speed of the motor.
01 seconds, we get the following speed response. Recalling that a time consistent specifies the time it takes a procedure to attain 63. 2% of its total change, we can estimate the time continuous from the above graph. We will attempt to "eye-ball" a fitted line to the motor's reaction chart.
Assuming the very same steady-state performance observed in the more heavily filtered information, we can estimate the time continuous based upon 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 approximate the motor's time consistent to be roughly 0.
Therefore, our blackbox design for the motor is the following. (2) Remembering the design of the motor we stemmed from first principles, duplicated below. We can see that we prepared for a second-order model, however the reaction looks more like a first-order design. The explanation is that the motor is overdamped (poles are real) which among the poles controls the response.
( 3) In addition to the reality that our design is reduced-order, the model is an additional approximation of the genuine world in that it overlooks nonlinear elements of the real physical motor. Based upon our direct model, the motor's output must scale with inputs of various magnitudes. For example, the reaction of the motor to a 6-Volt step should have the exact same shape as its action to a 1-V step, simply scaled by a factor of 6.
This is because of the stiction in the motor. If the motor torque isn't big enough, the motor can not "break complimentary" of the stiction. https://www.sherfmotion.co.il/. This nonlinear habits is not captured in our model. Typically, we utilize a thick friction model that is linearly proportional to speed, rather than a Coulomb friction model that records this stiction.
You could then compare the predictive capability 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 reaction, comparable to what was done with the increase converter in Activity 5b. An advantage of using a frequency response technique to identification is that it makes it possible for recognition of the non-dominant characteristics.
In Part (b) of this activity, we create a PI controller for the motor.
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