The Arduino board will also communicate the recorded data to Simulink for visualization and analysis. The control logic will be specified within Simulink and initially the controller will run on-board the host computer. Eventually we will target this control logic to the microprocessor on the Arduino board. A schematic of the boost circuit we will control in this section is shown below including a list of the variables we will employ.
The purpose of this activity is to demonstrate how to design a controller using frequency response techniques based on an empirically derived, and imperfect, plant model. Furthermore, this activity demonstrates how embedded controllers are often designed and implemented in practice using modern design and code generation tools.
Referring to the analysis of Part b of this activity, we experimentally collected frequency response data from the boost converter circuit. Specifically, for a duty cycle input that was sinusoidally varied about a nominal duty cycle of approximately 0.
Frequency Hz 0. The above plot serves as an approximate model for our boost converter circuit in the neighborhood of the operating conditions that the experiment was performed for. We will use this data in designing a compensator for the boost converter circuit.
Since it is more convenient to have an actual transfer function or differential equation model to employ in design, we will attempt to fit a mathematical model to this data. The empirically-derived Bode diagram reflects a type 0 system with two poles.
The system is type 0 because the magnitude plot is flat at low frequencies and the phase approaches 0 degrees at low frequencies. Specifically, the low frequency portion of the magnitude plot approaches approximately 9. Since the frequency response data does not show a resonant peak, the magnitude does not increase in the neighborhood of the break, we can assume that the damping ratio is greater than 0.
By trial and error, choosing 0. Therefore, we will assume the following for our plant model. Alternatively, if you have access to the System Identification Toolbox for MATLAB, there are commands that numerically fit a model to the frequency response data that we have generated. Specifically, you can use the tfest command to fit a transfer function model to the our data represented in the frequency response data frd format magnitude and phase represented as a complex number.
The commands given below will return an estimated transfer function model with two poles and no zeros. Examination of the above model generated by the tfest command shows a relatively similar solution to the one we roughly estimated from inspection of our frequency response data.
Alternatively, one can generate a fitted model using the System Identification Tool GUI which can be launched from the command line with the command ident. Executing the following MATLAB commands demonstrate the agreement between the experimentally acquired magnitude data and the two models generated above. Similarly, we can examine the agreement for the phase data by adding the following additional commands. The relative accuracy shown in the above figures gives us some confidence that the extracted models of the plant given above will be suitable for control design purposes.
Note, however, that as our data is limited to frequencies below At this point, we will implement a control system for the boost converter circuit. A block diagram that conceptually represents this approach is shown below. If the operating conditions were constant and sufficient testing could be done ahead of time, one could implement an open-loop controller where the testing has revealed what duty cycle input is needed to generate a corresponding output voltage in steady-state.
For example, the input voltage source could change battery voltage decreases with use, source could be a generator, etc. Our hardware setup will be similar to that employed in Part b of this activity.
Furthermore, we will still use a hardware-generated PWM signal from the Arduino board. An Analog Input of the Arduino board will be used to measure the output voltage for use by our feedback controller.
One difference in hardware usage that will arise later is that we will employ the Arduino board for running the control logic.
The physical connections and components will, however, remain unchanged. For now, we will run our control logic on board the host computer. Our Simulink model for performing this closed-loop Voltage Mode Control system will be similar to our model from Part b of this activity. We will still employ the blockset from the IO package for interfacing with the Arduino board, further details can be found here. We will, however, add the logic for a feedback controller into our model.
To begin, we will assume a simple proportional controller with gain and will attempt to track a step change in the desired output voltage setpoint. Specifically, the desired setpoint will begin at 1. A depiction of the modified Simulink model is shown below and can be downloaded here. The layout of this model makes the feedback structure of the control system quite clear.
You can imagine that the plant being controlled, the boost converter, is physically located between the Analog Write block and the Analog Read block. The Analog Write block sends the PWM signal out into the physical world and the Analog Read block records the plant output and brings it back into the control software. Inspection of the provided model reveals that the controller acts on the error in deviation of the output voltage from some nominal level, that is, the error in.
Furthermore, the controller generates a duty cycle command that is a deviation from the duty cycle that corresponds to the nominal output voltage. Main Content. Open Model. You have a modified version of this example. Do you want to open this example with your edits?
No, overwrite the modified version Yes. Select a Web Site Choose a web site to get translated content where available and see local events and offers. For the implemented controllers, the limits of the saturation function were and. For all experiments, the observer gains and were used in observers 57 and The new controller in 60 was implemented with and gains. Results obtained with the KAO controller and the new scheme are given in Figure 6 , which depicts the output voltage , in Figure 7 , which shows the time evolution of the duty cycle percentage , and in Figure 8 , which illustrates the estimated supply voltage for each scheme.
Better results are obtained with new scheme. More specifically, the settling time is much smaller for the new scheme. See Table 2 for a comparison of the settling times for the controllers. Besides, as appreciated in Figure 6 , the implementation of new controller presented lower voltage peaks during the transients at the beginning of the experiment and at the time the supply voltage commutes from a value to the another. It is important to observe that, despite the fact that control action is saturated for short periods of time, the control objective of voltage regulation is satisfied by using both controllers, as predicted by theory.
The estimated input voltage for both implementations does not converge exactly to the actual value of. This is caused by the resistance present in the inductor, which is significative for high inductances. The value at which converges is different from one controller to another. The main reason is that, in the new controller, observer 62 compensates the value of , which results in a greater estimated supply voltage. In this case, the reduction of value is approximately 25 times.
The experimental platform uses the MBR diode, which presents a low forward voltage, low power loss, and high efficiency features. Since different components were tested, it should be stressed that the selection of the transistor and diode had a positive effect on the performance of evaluated controllers. However, the new control scheme presented the best regulation performance. See Figures 9 and 10 for the implementation the KAO controller 56 and the new controller 60 , respectively.
Results are the same as the ones displayed in Figure 6. The problem of voltage regulation under input saturation was addressed in this paper. Special attention was payed to the DC-DC boost converter model, which considered the losses due to parasitic effects in the inductor and capacitor.
A tuning guideline was derived, which guarantees global asymptotic stability. Besides, the problem of uncertain supply voltage and unmeasurable current was addressed. Based on known results in literature, a new observer-based controller was proposed. The new schemes were tested by using numerical simulations and real-time experiments presenting better performance with respect to other algorithms.
The authors declare that there is no conflict of interests regarding the publication of this paper. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Academic Editor: Alfred Hubler. Received 30 Jul Revised 14 Nov Accepted 06 Dec Published 15 Jan Abstract In this paper, a new controller for a boost DC-DC direct current to direct current power converter is proposed. Introduction The voltage of many electrical and electronic systems is often higher than the voltage of the main source, for example, in systems powered by batteries.
Better results are obtained with the new controller. Figure 1. The boost converter circuit having parasitic resistances and. Table 1. Figure 2. Capacitor voltage obtained for the new controller 17 and 18 and the open-loop controller Figure 3. Duty cycle percentage obtained for the new controller 17 and 18 and the open-loop controller Figure 4.
Block diagram on the representation of the experimental platform. The data acquisition board DAQE is used for data transferring from the computer to the external circuits and vice versa. Figure 5. Experimental platform equipped with measurement circuits for output voltage and inductor current, circuit for online modification of the input voltage , PWM circuit, and boost converter with replaceable capacitor, inductor, and resistance.
Figure 6. Experimental results: output voltage obtained with the KAO controller 56 and for the new controller in Figure 7. Experimental results: duty cycle percentage obtained with the KAO controller 56 and for the new controller in Figure 8. Experimental results: estimation of the supply voltage obtained with the KAO controller 56 and with the new controller in Table 2. Comparison of the settling times for the KAO controller 56 and the new controller Figure 9.
Experimental results: oscilloscope response to the output voltage of the KAO controller Figure Experimental results: oscilloscope response to the output voltage of the new controller References B. Bose, Ed. Ortega, A. Nicklasson, and H. Sira-Ramirez and R. View at: Publisher Site F. Bonanno, G. Capizzi, and G. Du, X. Lai, and C. Mohanraj, C. Danya Bersis, and S. View at: Google Scholar A. Tani, M. Camara, and B. Alvarez-Ramirez, G. Espinosa-Perez, and D.
Olalla, I. Queinnec, R. Leyva, and A.
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