Specifically, the Difference block calculates the motor's change in position (in counts) and the first Gain block divides by the sample time. Subsequent Gain obstructs convert the units from counts/sec to revolutions/sec, and after that from revolutions/sec to revolutions/min. The constant representing the equipment ratio needs to be specified in the MATLAB workspace prior to 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 quite noisy. This occurs for a number of reasons: the speed of the motor is really differing, encoder counts are being occasionally missed out on, the timing at which the board is polled doesn't exactly match the recommended tasting time, and there is quantization connected with checking out the encoder.
Consider the following model with a simple first-order filter added 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 continuous of 0. 15 seconds produces the list below time trace for the motor speed.
05; filter_constant = 0. 15;. By increasing the tasting period and including the filter, the speed price quote indeed is much less noisy. This is particularly useful for enhancing the price quote of the motor's speed when it is performing at a consistent speed. A disadvantage of the filtering, nevertheless, is that it adds hold-up.
In essence we have actually lost details about the motor's real reaction. In this case, this makes recognizing a model for the motor more challenging. In the case of feedback control, this lag can degrade the efficiency of the closed-loop system. Reducing the time continuous of the filter will reduce this lag, however the tradeoff is that the noise won't be filtered too.
Considering that our input is a 6-Volt step, the observed response appears to have the kind of a first-order step action. Looking at the filtered speed, the DC gain for the system is then around 170 RPM/ 6 Volts 28 RPM/V. In order to approximate the time constant, however, we require decrease 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 specifies the time it takes a process to attain 63. 2% of its total modification, we can estimate the time constant from the above graph. We will attempt to "eye-ball" a fitted line to the motor's response graph.
Assuming the exact same steady-state performance observed in the more greatly filtered data, we can approximate 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 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 originated from very first principles, duplicated below. We can see that we anticipated a second-order design, but the response looks more like a first-order design. The explanation is that the motor is overdamped (poles are genuine) and that one of the poles dominates the reaction.
( 3) In addition to the truth that our design is reduced-order, the model is an additional approximation of the real life in that it neglects nonlinear elements of the real physical motor. Based upon our linear model, the motor's output need to scale with inputs of different magnitudes. For example, the action of the motor to a 6-Volt step ought to have the exact same shape as its response to a 1-V step, 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 complimentary" of the stiction. מומנט מנוע https://www.sherfmotion.co.il/. This nonlinear habits is not caught in our model. Generally, we utilize a viscous friction model that is linearly proportional to speed, instead of a Coulomb friction model that captures 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 design for the motor based on its frequency action, comparable to what was made with the boost 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 characteristics.
In Part (b) of this activity, we create a PI controller for the motor.