The boost converter is widely used in voltage regulation applications and active power factor correction (PFC), its proper operation and performance are directly related to final design of its control loop. The design of this control is somewhat complex due to the nonlinearity of its behavior; the commutation of a switch (power transistor) makes the equivalent circuit change continually over time (two alternating circuits in time). In this work, it is defined the poles of the transfer function in closed loop for the average model (linear model approximate) of the boost converter using evolutionary principles of genetic algorithms, with the idea of improving the dynamic response of voltage regulator. The design outline is successfully verified by simulation and on a laboratory prototype, and improvements were found in the dynamic (voltage overshoot and response time) compared to classical schemes.El convertidor boost es ampliamente utilizado en aplicaciones de regulación de voltaje y corrección activa del factor de potencia (PFC), su adecuada operación y desempeño están directamente relacionados al diseño final de su lazo de control. El diseño de éste control es bastante complejo debido a la no linealidad de su comportamiento; la conmutación de un interruptor (transistor de potencia) hace que el circuito equivalente cambie continuamente a lo largo del tiempo (dos circuitos alternados en el tiempo). En éste trabajo, se definen los polos de la function de transferencia en lazo cerrado para el modelo promedio (modelo lineal aproximado) del convertidor boost utilizando los principios evolutivos de los algoritmos genéticos, con la idea de mejorar la respuesta dinámica del regulador de voltaje. El principio de diseño es verificado exitosamente por simulación y sobre un prototipo de laboratorio, sobre los cuales se encontró mejoras en la respuesta dinámica (sobrepaso de voltaje y tiempo de respuesta) frente a esquemas clásicos

Castiblanco Ortiz, Mariela

Jacinto Gómez, Edwar

Martínez Sarmiento, Fredy Hernán

Universidad Distrital de la ciudad de Bogotá: Open Journal Systems

10 Tecnura    Vol. 17    Número Especial 2    pp. 10 - 17    diciembre de 2013Power factor corrector with PID loop fit  by genetic algorithmCorrector de factor de potencia con lazo PID sintonizado  por algoritmos genéticosFredy Hernán Martínez SarMientoCandidato Ph. D. en Ingeniería. Docente de la Universidad Distrital Francisco José de Caldas. Bogotá, Colombia. Contacto: fhmartinezs@udistrital.edu.coedwar Jacinto GóMez Candidato a magíster en Ciencias de la Información y Comunicaciones. Docente de la Universidad Distrital Francisco José de Caldas. Bogotá, Colombia. Contacto: ejacintog@udistrital.edu.coMariela caStiblanco ortizCandidata a magíster en Ingeniería Industrial. Docente Universidad Distrital Francisco José de Caldas. Bogotá, Colombia. Contacto: mcastiblancoo@udistrital.edu.coFecha de recepción: 15 de agosto de 2013  Clasificación del artículo: investigaciónFecha de aceptación: 1 de noviembre de 2013  Financiamiento: Universidad Distrital Francisco José de CaldasABSTRACTThe boost converter is widely used in voltage regulation applications and active power fac-tor correction (PFC), its proper operation and performance are directly related to final design of its control loop. The design of this control is somewhat complex due to the nonlinearity of its behavior; the commutation of a switch (power transistor) makes the equivalent circuit change continually over time (two alternating circuits in time). In this work, it is defined the poles of the transfer function in closed loop for the average model (linear model approximate) of the boost converter using evolutionary principles of ge-netic algorithms, with the idea of improving the dynamic response of voltage regulator. The de-sign outline is successfully verified by simulation and on a laboratory prototype, and improvements Key words: Boost converter, genetic algorithms, PID control, power factor.Palabras clave: algoritmos genéticos, control PID, convertidor boost, factor  de potencia.investigación11Power factor corrector with pid loop fit by genetic algorithmFredy Hernán Martínez SarMiento / edwar Jacinto GóMez / Mariela caStiblanco ortiz*   *   *were found in the dynamic (voltage overshoot and response time) compared to classical schemes.RESUMENEl convertidor boost es ampliamente utilizado en aplicaciones de regulación de voltaje y corrección activa del factor de potencia (PFC), su adecuada operación y desempeño están directamente rela-cionados al diseño final de su lazo de control. El diseño de éste control es bastante complejo de-bido a la no linealidad de su comportamiento; la conmutación de un interruptor (transistor de po-tencia) hace que el circuito equivalente cambie continuamente a lo largo del tiempo (dos circui-tos alternados en el tiempo). En éste trabajo, se definen los polos de la function de transferencia en lazo cerrado para el modelo promedio (mode-lo lineal aproximado) del convertidor boost utili-zando los principios evolutivos de los algoritmos genéticos, con la idea de mejorar la respuesta di-námica del regulador de voltaje. El principio de diseño es verificado exitosamente por simulación y sobre un prototipo de laboratorio, sobre los cua-les se encontró mejoras en la respuesta dinámica (sobrepaso de voltaje y tiempo de respuesta) fren-te a esquemas clásicos.INTRODUCTIONThe boost converter (step-up converter), is a to-pology of power to regulate voltage DC/DC that can be implemented like intermediate component of a more complex system, and that is widely used for the active correction of power factor (PFC) (Martínez, 2004). The input to this converter is often an unregulated rectifier line voltage, which will fluctuate due to changes of the line volt-age magnitude. The main objective of control of this circuit is to convert the unregulated DC in-put voltage into a controlled DC output voltage in front of changes in the load. Additionally, in many applications it is desired to maintain a sinu-soidal input current (PFC). The problem of regu-lating the output voltage of these converters has been a subject of great interest for many years, due to the switching property included in their structure, DC/DC converters have a non-linear behavior and consequently their controlling de-sign is accompanied with complexities. In addi-tion, due to the nonminimum phase nature of the boost converter, much effort has been directed at the control of this configuration.Mathematical modelling of power DC/DC con-verters is a historical problem accompanying with the development of the DC/DC conversion technology since 1940’s (Lin and Ye, 2004). The preliminary work on the mathematical modeling for DC/DC converters followed the traditional calculation manner using impedance analysis to obtain transfer function in the s-domain (Laplace transform) (Chan, 2007).In this article, a PID current mode control fit by genetic algorithms (GA) is proposed and its char-acteristics and application to the regulation of the power converters and PFC are investigated. The advantage of the proposed hybrid control is that not only it retains the advantages of the exist-ing current mode control, but it also affords an additional tuning parameter which can be used to modify the output response. Finally, it is pre-sented some experimental results to illustrate the features of the proposed control.BOOST CONVERTERConsider the DC/DC boost converter circuit shown in figure 1. During the interval when switch Q is off, diode D conducts the current iL of inductor L towards the capacitor C0 and the load R. During the interval when switch Q is on, diode D is open and the capacitor C0 discharges through the load R. The converter transfers the energy be-investigación12 Tecnura    Vol. 17    Número Especial 2    diciembre de 2013tween input and output using the inductor. The continuous commutation of these two circuits gives to the converter its nonlinear characteristic.The small signal model of boost converter is shown in equation (1) (Severns and Bloom, 1985) (Martínez, 2011), it is obtained using standard state-space averaging techniques (Chan, 2007). (1)Where: ●  = average input current in the inductor L [A] ●  = average output voltage [V] ● d = duty cycle ● Vin = input voltage [V] ● L = boost inductor [H] ● C0 = output capacitor [F] ● R = boost load [W] ● RC = parasitic resistance of C0 [W] ● RL = parasitic resistance of L [W]Figure 1. The DC/DC boost converter. This switching-mode converter contain two semiconductor switches (Q and D) and one energy storage element (L). The output capacitor (Co) works as filter.Source: Own source.The transfer function is a second order, low-pass filter with two zeros. The low-pass filter’s cut off frequency is calculated through of the equation (2).   (2)The ideal voltage in the output is Vref. The zero in the left half plane is determined by the equa-tion (3).   (3)And the zero in the right half plane is determined by the equation (4).       (4)investigación13Power factor corrector with pid loop fit by genetic algorithmFredy Hernán Martínez SarMiento / edwar Jacinto GóMez / Mariela caStiblanco ortizThe cut off frequency and the zero in the right half plane depend on the output and input volt-ages, reason for which the transfer function in closed loop must change continuously. As the op-eration point varies, it is difficult for the linear PID controller to respond well (designed for one operating point).For the experimental boost converter utilized in this work, the input voltage is the alternate of 120 Figure 2. Step response of boost converter (simulation open loop). Starting current greater to 60 A.Source: Own source.V AC to 60 Hz rectified with a diode full bridge, the output voltage is 400 V DC, C0 is 330 μF, L is 2 mH, and R is 800 Ω. The parasitic elements, RC and RL, are measured in laboratory with values of 0,5 Ω and 1,5 Ω respectively.The step response (constant duty cycle of 0,61) in open loop are plotted in figure 2.CONTROL OF THE BOOST CONVERTERThe primary objective of converter is the regula-tion of output voltage, reason for which is neces-sary to eliminate the stationary error of the same. Of the classic theory of control, it’s knows that is possible adding a PID network of compensa-tion. The proportional and the integral component allow reducing the rise time and stationary state error, whereas the part differential allows control-ling the overshoot.Figure 3 shows the scheme of proposed control. In this, two feedback loops, structure very com-mon in the active correctors of power factor, one of current and one of voltage can be appreciated. In (Sira-Ramirez, 1987) appears a study of the sur-face of control for constant current in the inductor, demonstrating that the equilibrium point is stable. In agreement with this, the block PID constructs a current of reference starting the error of output voltage. This current of reference is compared with the current in the inductor to determine the current error, which is given to the PWM to obtain the present value of the duty cycle.investigación14 Tecnura    Vol. 17    Número Especial 2    diciembre de 2013Figure 3. Control system configuration of research target. Two loops control, one in voltage mode and another in current mode are used.Source: Own source.The advantage of this scheme is not only its sta-bility. In addition, when owning a reference cur-rent, is possible to modify this signal to respond to additional criteria of high speed, as it is the reconstruction of the waveform of input current. The voltage loop (of smaller speed), is in charge essentially of the regulation of the output voltage.The integral part of the PID helps to eliminate the error and improves the speed of the answer, nev-ertheless, the presence of this also entails to the appearance of problems during the starting transi-tory, since this will prevent the change of sign in the control surface. In addition, the selection of the parameters the feedback loop becomes diffi-cult, since if it looks for a robust system, will also be finished with one slow one in the answer in variations in the load. It is here where the design supports in the GA (Meng and Song, 2007).A lot of methods about PID controller parameter tuning have been proposed, and most of them are based on: ● Empirical methods, such as Ziegler-Nichols methods. ● Analytical methods, for instance, the root lo-cus based techniques. ● Methods based on optimization, such as Cian-cone or López methods.Nevertheless, the parameters tuning of PID con-troller is the combination and optimization of mu-ti-variables; simple genetic algorithm could solve the shortcoming of current methods of parameters tuning (Yao and Sethaves, 1994), which can only satisfy single requirement of system.GENETIC ALGORITHM OPERATIONArtificial intelligence techniques have come to be the most widely used tool for solving many optimization problems. GA is a relatively new approach of optimun searching (Mitchell, 1999), becoming increasingly popular in science and en-gineering disciplines.GA inherits its ideas from evolution of the nature. Even a simple GA algorithm appears to be robust, and the complexity of algorithm and result of GA is irrelevant to the length of genetic string and the original state of population. GA is so simple that it only involves some selection, crossover and mutation operations, but it is so efficient that it can find a nearly optimum solution even for a large scale problem (Mitchell, 1999).investigación15Power factor corrector with pid loop fit by genetic algorithmFredy Hernán Martínez SarMiento / edwar Jacinto GóMez / Mariela caStiblanco ortizIn this case, a random population of 20 real numbers double precision chromosomes is cre-ated, representing the solution space for the PID controller (KP, KI and KD codified like the genes of the chromosomes, in the range 0 to 1). Each member of this random population represents a different possible solution for de GA.The GA proceeds to find the optimal solution through several generations, the reproduction use crossover fraction of 0,6 with 2 elite count, the mu-tation function is adaptive feasible, and the cross-over function is scattered. The objective function to minimize equation (5) was constructed using parameters of the response to step of the system, considering the magnitudes of the variables.       (5)Where: ● Tr = Rise time [s]. ● Ess = Steady-state error [V]. ● Ts = Settling Time [s]. ● Mpu = Overshoot [V]. ● Imax = Current maximum in the inductor [A].DESIGN AND SIMULATIONFor the design of the control, we development in MatLab the function to optimize (equation 5) by the GA, being calculated each 40 us the corre-sponding values of Tr, Ess, Ts, Mpu and Imax. For this, average model of the converter in equation (1) was used, calculating the values of the current in the inductor and the output voltage whenever the value of the duty cycle is updated. With the output voltage the error of voltage is calculates in each interval as equation (6).   (6)This voltage error is injected to PID block to de-termine the value of the reference current, which is compared with the current calculated in the in-ductor to determine the new value of the duty cy-cle. The initial values equal takings to zero. This calculation is realized for all the individuals of the population of GA algorithm. Figure 4 shows the convergence of GA algorithm.Figure 4. Convergence of the GA algorithm (one hour and 55 minutes of simulation in a AMD Athlon 64 3200+).Source: Own source.investigación16 Tecnura    Vol. 17    Número Especial 2    diciembre de 2013The values determined by GA algorithm were: KP = 0.98, KI = 0,51 and KD = 0. With these values, a simulation of the transitory answer was realized in closed loop using the average model of the boost converter, the results are in figure 5.In the simulation, it is possible to be observed as the starting current is limited to less than 25 A, and that the control places to the system in its equilibrium point in 100 ms.Figure 5. Step response of boost converter (simulation closed loop). Starting current smaller to 25 A.Source: Own source.Nevertheless, in the scheme not yet it is had in-cluding the PFC action for the input current. In order to reconstruct the waveform sine, the cur-rent of reference by the waveform of the rectified input voltage is due to multiply, of such form that the value average of the new current of reference stays, but its instantaneous value changes to be-have like the rectified input voltage.Therefore, the scheme of proposed control requires taking samples from three signals of the converter: current in the inductor (iL), output voltage (v0) and rectified input voltage. That is to say, the two state variables and the sine reference input.EXPERIMENTAL RESULTSThe control scheme was evaluated in laboratory on a prototype of 200 W, 400 V. The control se-quence was programmed on a microcontroller PSoC CY8C29566 of Cypress.Figure 6. Input voltage and current in prototype with scheme of control in closed loop (THD = 18,32%).Source: Own source.investigación17Power factor corrector with pid loop fit by genetic algorithmFredy Hernán Martínez SarMiento / edwar Jacinto GóMez / Mariela caStiblanco ortizChan, C. Y. (january, 2007). A nonlinear control for DC–DC power converters. IEEE Transac-tions on Power Electronics, 22(1), 216-222.Lin, F. and Ye, H. (november, 2004). Mathemati-cal modeling of power DC/DC converters. International Conference Power System Technology 2004-PowerCon 2004, 1, 17-22.Martínez, F. H. (2004). Corrección activa del fac-tor de potencia en cargas no lineales. Re-vista Tecnura, 14, 40-47.Martínez, F. H. (2011) Algunas Aplicaciones de la Lógica Difusa en el Control de Conver-tidores DC/DC. Bogotá: Universidad Dis-trital Francisco José de Caldas.Meng, X. and Song, B. (august, 2007). Fast genetic algorithm used for PID parameter optimiza-REFERENCEStion. IEEE International Conference on Au-tomation and Logistics 2007, 1, 2144-2148.Mitchell, M. (1999). An introduction to genetic algorithms. London: Massachusetts Insti-tute of Technology MIT Press.Severns, R. P. and Bloom, G. (1985). Modern DC-to-DC Switchmode Power Converter Circuits. New York: Van Nostrand Reinhold Company.Sira-Ramirez, H. (1987). Sliding motions in bilin-ear switched networks. IEEE Transactions on Circuits and Systems. 34, 919-933.Yao, L. and Sethaves, W. A. (april, 1994). Non linear parameter estimation via the genetic algorithm. IEEE Transaction on Signal Processing, 42 (4), 927-935.The system demonstrated an excellent regula-tion of voltage (within the 1.4% of the nominal value) without overshoot as it was expected of the design. In relation to the PFC, for an effective input current of 2,31 A, a real THD of 18,32% was obtained (figure 6), improving schemes of direct fuzzy control on the same converter (THD = 21,1%) [10]. The maximum value of the input current was limited to 25,5 A, and was observed a approximate settling time of 90 ms.CONCLUSIONIn this paper we proposed a new hybrid algorithm for the regulation of voltage of the boost convert-er, and the active correction of the power factor. The algorithm integrates the main features of the current mode control (dynamic response, stability and PFC), and the reliability and design of PID controls.As alternative of optimal adjustment of the pa-rameters of loop PID, considering the problem of combination and optimization of muti-variables, intends to use a genetic algorithm whose objec-tive function is evaluated on the parameters of the answer of the model calculated from the average model of the boost converter.The scheme of control proposed was evaluated successful by simulation and on a laboratory pro-totype of 200 W, having demonstrated its viability and high performance in terms of output voltage regulation and PFC.

Corrector de factor de potencia con lazo PID sintonizado por algoritmos genéticos

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Corrector de factor de potencia con lazo PID sintonizado por algoritmos genéticos

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