Automática y Robótica en Latinoamérica. Alexander Martínez

(11)

      Such as it was described above, every component of last equation has matrix form. Also the polynomial solution gets the error as the dependence of desired signal in order to identify M2, Ky and KIL that are matrices as the equations 2 and 3, which were described in paragraphs above.

      Equation 12 helps to evaluate the error matrix as the dependence of desired signal and the measured signal S in every instance n.

      (12)

      (13)

      For every S is composed by adaptive weight coefficients that was correlated with the input signal (as measured or expected/simulated) X as it was described in equation 13. For this reason, the matrix of error is defined as:

      (14)

      By other side, the general response y(t) correlated with x(t) and u(t) through a nonlinear function , it is because to look for the optimal trajectory and to get the best position control, as it is represented in equation 15.

      (15)

      (16)

      It means to solve the costing equation 16 by J, the expected trajectory R, in which this expected position is given by equation 17. And the optimal excitation signal in order to find the optimal response is given by equation 18.

      (17)

      (18)

      Anodic Aluminum Oxide (AAO) membranes have quite good mechanical, optical and chemical properties, hence, it helps to study designed sensors that were based in them. By other side, AAO membranes have fast response and robustness that means sensors that were based in this kind of membranes, which can achieve these characteristics. In Figure 4 is shown an AAO membrane and, as indication of yellow raw, it is amplified in nanoscale view (from SEM PUCP) its porous [7].

      Figure 4

      The position sensor that was based in AAO membranes

      Source: Own elaboration.

      In Figure 5 is depicted the setup to measure positions of the Active Magnetic Bearing (AMB), due to get its control, which is the machine used to evaluate the algorithms that were proposed in this research.

      Figure 5

      Experimental setup

      Source: Own elaboration.

      1. Results

      The position of the rotor (shaft) around its own axis was selected as physical variable in order to get a desired control, for which there were fixed four position sensors in opposite side to every electromagnet actuator, owing to capture its position as the reference from the shaft axis Y. However, through the position sensors that were based in nanostructure, it can be possible to correlate another important physical variables: Sound and vibration. In Figure 6 is depicted as the flowchart, the summary of the procedure that was applied in this research. It starts from configuration parameters, measure sensors data: positions and temperatures. From this can be possible to find weights for adaptive algorithm in order to get better position control. In spite of the error signal (between desired and measured positions) can also get some predictions to optimal positions, but the energy needed to send over every electromagnet get losses, such as by the heat, but not because of friction. It is proposed by Joule effect. For this reason, it is necessary to measure temperatures and to estimate the heat evacuation from the AMB system, because of friction.

      Figure 6

      Flowchart to summarize steps sequence because to achieve the position control

      Source: Own elaboration.

      As it was described above, in order to test the shaft movement transmission, it was activated only the hybrid electromagnet that was separated from the motor connector. Hence, in Figure 7a is depicted all control position, when it is measured by “sharp” position sensors, from which curves in color light blue, green, brown and red are the position that was captured by every position sensor.

      Figure 7

      The position control under the nanostructure effect

      Source: Own elaboration.

      It is shown that system is under control owing to the desired signal is 0 mm and the rotor must to be avoided to get imbalance rotation at 2 mm from its own axis. However, as it can be analyzed, there were found some overshoots that were achieved even the adaptive algorithm that was proposed. By other side, while it is changed every position sensor by sensors that were based in nanostructures, the control improves as it can be seen in Figure 7b. According to help visual explanation, Figure 7c shows a shaft setup for position sensors around it [6].

      Finally, as it was detailed in paragraphs above: what is the consequence of heat that was produced by wires around hybrid magnets, which receive energy to produce the electromagnetic field (the main component to get equilibrium in AMB systems is depicted in Figure 8c)?

      Figure 8

      The energy evacuation as the nanostructure effect

      Source: Own elaboration.

      For this reason, Figure 8a shows power that was consumed, when there is not effect of sensors that were based in nanostructures, it is expected that no short response time makes the main control system could not get right response action. In otherwise, it can activate the hybrid actuators more time than it could be. So, does it mean that AMB cannot be in total efficient? To answer this question, it is necessary to get compromise between required range of work of the AMB, while it can be used to enhance movement transmission between rotating machines, the costing of the AMB in order to reduce the heat from lubrication of traditional mechanical bearings, but whether operating range of work can force the AMB according to increase energy that it needs to get operation, then of course, also this system can get losses by the heat.

      This work shows a suggestion to solve that problematic by sensors that were based in nanostructures, due to their robustness, short response time can help in extreme conditions that traditional sensors cannot get. This is depicted in Figure 8b, due to reduced consumed power from AMB, because of nanostructure effect over mechatronic systems. According to help visual explanation, Figure 8c shows a shaft setup for position of magnets (hybrid between passive magnet with electro-magnet) around it, from which electrical current can increase its temperature without a controlled model that was based in nanostructures, as it is proposed in this research.

      Discussion and conclusions

      It was verified the good effect to use position sensors that were based in nanostructures, because of the wide range of work, robustness and fast response time as a consequence of nanosystems integrated in macro systems: the mechatronic systems. By other side, it was evaluated that AMB systems can enhance by better way their performance, when it is analyzed strategies to evacuate the heat that was not produced,