Methodology for testing a regulator in a DC/DC Buck Converter using Bode 100 and SpCard J. M. Molina. Abstract Power Electronic Engineers spend a lot of time designing their controls, nevertheless they spend even more time during the testing stage of their controllers. The models of the converters and regulators developed by simulations include some parasitic, however, when these models are applied to the real converters, some non-desired effects appear in the results and the regulators should be tuned to find the desired response. In this Application Note, the design of a Voltage Mode Control for a Buck converter using tools for accelerating the adjustment of the parameters is shown. Index Terms DC/DC, Digital Control, SpCard, Bode 100, Buck, Voltage Mode Control. S I. INTRODUCTION Witch Mode Power Supplies (SMPS) can be found in most of the electronic system around us. There is a huge number of power supplies types, AC/DC, known as rectifiers, DC/AC known as inverters and DC/DC converters. All of them usually include, in most of the applications, a control loop to keep a parameter as the output voltage controlled. Nowadays, the design of a power supply is a very hard work. Power electronic engineers are trying to decrease the size and the weight of the SMPS to allow consumer electronic companies decrease the size of their products and Aircraft companies to decrease the fuel consumption or the electric cars to be more efficient. To achieve these goals, engineers are looking for new materials or new topologies, using less and smaller components. However, in SMPS, some of the key elements which defines the minimum size of the system usually are the energy storage components, inductors and capacitors. To decrease the size of the magnetics, the most common way is increasing the switching frequency. The size of the capacitors, considering new capacitor technologies presents a minor impact on the total size, however a lot of control techniques are presented in the literature [1]-[2]. Therefore, increase the switching frequency and apply complex controls are some of keys to increase the power density of the actual SMPS. These two parameters are intrinsically related with the control implementation. It is clear that solutions using traditional analog control can be found in the literature, nevertheless, analog control does not provides the flexibility that the actual market speed needs, where the SMPS should be designed in months. Of course, the final product can use an analog control, but during the designing stage, where some of the parameters, as the communication protocol, is still not decided, Digital Control tools help to accelerate this process. Today, several companies provide products to help designers during the implementation and test of their design. During the design of a new topology, the test stage is much longer than the designing stage, therefore it is important to use tools that help us during the test period. In this paper two of this tools are going to be used for designing a Voltage Mode Control for a Buck converter. SpCard is a tool for rapid prototyping and testing, and Bode100 is a Frequency response analyzer. With the SpCard, the designed regulator is implemented while Bode100 shows the modifications in the Bode of the plant plus the regulator. II. CONTROL SCHEME FOR A VOLTAGE MODE BUCK CONVERTER The Buck converter is a very common topology in different applications where galvanic isolation is not needed. In Figure 1, is shown the circuit of this topology. In this picture, can be appreciated the resonance frequency and the zero corresponding to the ESR of the capacitor, calculated with equations: 1 f res = 2π L C 1 f zesr = 2 π C RESR Figure 1. Synchronous Buck converter topology
TABLE I SPECIFICATIONS FOR THE BUCK CONVERTER Figure 2. Buck converter with voltage mode control Parameter Input Voltage Output Voltage Max. Power Switching Frequency Output Inductance ESR of the inductance Output Capacitance ESR of the capacitance Value a 12 V 5 V 12 W 100 khz 22 uh 5 m 40 uf 1 m It is very common using this topology in low power and low voltage power supplies included in common electronics consumer to supply the microprocessors or FPGA. In these cases, the transient response requirements are very demanding, because the converter should provide a fast response to the load transients produced by these devices. Although this is not a typical requirement for every application, the transient response of a Buck converter that behaves as Power Supply of any system should be as fast as possible, therefore, the control design is very important. Since shown a complex design it is not the goal for this work, in this paper, the methodology of testing a control loop using the SpCard and Bode 100 are shown. The control used to verify the methodology proposed in this paper is a Voltage Mode Control applied to a Buck Converter. The scheme of this control is shown in Figure 2. In this scheme the duty cycle is calculated as follow: First, the error between the reference voltage and the voltage measured in the output is obtained, this error is introduced in the compensator, where dependently of the used type, registration of the error and multiplications by coefficients are applied. The output of this block is the duty cycle, which is send it to a PWM generator, compared with a saw tooth signal generating the signals to drive the switches. III. DESIGN THE VOLTAGE MODE CONTROL FOR THE BUCK CONVERTER The control proposed in this article is designed using Simulink. In Figure 3 is shown the used model. It is appreciated that in this model, the ESR is considered. As studied in the literature [3], the ESR value of the capacitance is important because includes a zero in the bode plot of the plant and consequently to the compensator. The value of the ESR is very dependent of the technology used, electrolytic capacitor presents higher values of ESR compared with ceramic technologies. Other parasitic as the series resistance of the inductance is considered. Once the model is designed, the values shown in TABLE I are included. To design the compensator, the model developed is included as part of a complete system, including the compensator. This diagram is shown in Figure 4. Using Sisotool from Simulink, the bode plot of the system without any regulator is shown. In Figure 5 is represented the bode plot of the system without any regulator for the specifications stablished. As appreciated, the response of the system under a step does not correspond to the desired response. Figure 3. Simulink Model of a Buck Converter. Figure 4. Simulink model including the Regulator
Figure 5. a) Gain and Phase of the system without compensate. b) Response of the system to a step However, if we add a simple integrator, the system becomes stable. To increase lightly the band width of the system, the gain is incremented and the resulting response is show in Figure 6. In the bode can be observed that the system presents a band width of 102 Hz. To verify this methodology, this regulator is used as the starting point, with the goal of improve practically its frequency response using SpCard and Bode 100. The first step, is implementing this regulator in the SpCard. To achieve the coefficients need it. The continuous transfer function of this regulator should be translated to the discrete domain. The regulator designed is represented as: R(s) = 44 s Applying the function c2d(r, f samp) in Matlab, where f samp is the sampling frequency, which should be a multiple of the switching frequency in order to avoid aliasing problems, the output is the regulator in discrete domain, R(z). Figure 6. a) Gain and Phase of the system including an integrator b) Response of the system to a step R(s) = 0.00044 z 1 Regarding the equivalence between the template of the PID block we see that using the parameter obtained (0.00044) in the coefficient A0 of the PID block in the SpTool. In Figure 7 is shown the SpTool and it is marked the parameter of A0 to configure the PI compensator. As it can be observed, in this picture, the rest of the parameters as the Switching period, the limits for the duty cycle or the reference, are introduced. In the right side of the image it is shown the output pins where the PWM are located and the specific input for the output voltage measurement, which should be between 0 and 1V, therefore a voltage divider should be used. The basic implementation of the control loop is implemented and can be modified online, with the converter working to observe its effects.
Figure 7. SpTool configuring a PI regulator A. SpCard IV. DESCRIPTION OF THE TOOLS Spcard [3] is a tool developed by SP Control Technologies and commonly used for designing modulation and controls for power converters or tests for other electronic systems. This tool is powered by a Zynq device from Xilinx. SpCard includes a library of the most common blocks used in power electronics for controlling any power topology as PWM generators, PID, protections, modulators for specific topologies, ADC, DAC, etc. In this case, a PID block configured as a simple PI is used for the Voltage Mode Control. The equation which is defined in this block is represented as follows: d k = d k 1 + A 0 e k + A 1 e k 1 + A 2 e k 2 The coefficients A0, A1 and A2 multiply the error registered in previous sampling periods. Additionally, the SpCard has an application called µgenius for introducing your own controls in C language, which will run in the ARM processor of the Zynq therefore, this control scheme can be also implemented in software using the hardware libraries of SpCard. control the device. V. EXPERIMENTAL RESULTS To verify the stability and the behavioral of the close loop system, the regulator is configured in the SpCard and the SpCard is connected to the converter. Additionally, the Bode 100 is connected to inject a perturbation in the system and measure its effect, giving the actual bode of the plant. The setup of connections is presented in Figure 8. The Bode100 injects its perturbation to a 50 Ω resistor in series with the voltage divider of the output voltage, which is send to the PID in the SpCard. There are two measurements for analyzing the frequency response represented in the picture as Channel 1 and Channel 2. For the first test, the simple integrator previously calculated with Matlab at a crossover frequency of 100 Hz is introduced in the SpTool. The measurement of the bode to this integrator is shown in Figure 9. It is appreciated that the crossover frequency is close to 100 Hz and the phase margin is enough, therefore, it is verified that the system is stable. Nevertheless, a crossover frequency of 100 Hz is very low for this converter. The goal of the methodology proposed in this paper is to B. Bode 100 Bode 100 [4] is a tool developed by the company Omicron. With the multifunctional Bode 100 is possible to get an exact picture of the electronic circuits and components in a frequency range from 1 Hz to 40 MHz. The Bode 100 is not only a state of the art Vector Network Analyzer, it also works as: Frequency Response Analyzer Impedance Meter Gain Phase Meter The Bode 100 is controlled via the Bode Analyzer Suite software that offers an intuitive and easy-to use interface to Figure 8. Configuration of the setup for adjusting the regulator measuring the frequency response
f c =99,3 Hz PM= 94 º f c =9,2 khz PM= 35 º UNSTABLE!! Figure 9. Bode response for the system with the compensator calculated at a crossover frequency of 100 Hz improve the frequency response, tuning the coefficients A0, A1 and A2 of the PID block and analyze the response. It is recommended to enable the protections of the SpCard for this process, limiting the output voltage and preferably the current through the inductor. Once the starting point is stablished as the integrator with a value of A0 of 0.00044, the first approach it is multiply this coefficient by 10. Appling 0.0044 to A0 and measuring with Bode 100 the response is shown in Figure 11. As it is observed, the crossover frequency has increased up to almost 1 khz with a phase margin of 88º. With this first approach, the frequency response has been improved 10 times, however, the methodology proposed go forward until the limits of stability. In the next iteration A0 is again multiplied by 10, applying 0.044 to A0. In this case the response cross the limit of stability. The measurement is shown in Figure 12. The crossover frequency has increased up to 9,2 khz, but the phase margin is less than 45º, is 35º, therefore, the system is unstable. Analyzing the current and voltage in the oscilloscope is difficult to appreciate that the system is unstable, for this reason, this methodology use Bode 100 while the system is Figure 11. Bode response for the system with the compensator tuned with the SpCard at a crossover frequency of 9,2 khz tuned. To become the system stable, in this case it is proposed to introduce a negative gain to the coefficient A1, which is related to the error measured in the previous period. It is important that this value should be negative and relatively similar to A0 but smaller. In this case, the value for A0=0.04, therefore A1= - 0.01. Using this values, the frequency response of the system is shown in Figure 10. It is appreciated that in this case the crossover frequency is lightly smaller (7,7 khz) but the phase margin is higher than 45º, therefore this regulator is considered stable and with an acceptable crossover frequency. VI. CONCLUSION A compensator based on a PID structure is designed to regulate a Synchronous Buck converter. During the test of the designed regulator the tools SpCard and Bode100 are used to accelerate the test. Both tools are working online simultaneously, allowing the engineer to analyze in real time the results while is adjusting the parameters. In the case analyzed in this paper, the starting point is an integrator. This integrator is tuned up to increase the f c =986 Hz PM= 88 º f c =7,7 khz PM= 45,7 º Figure 10. Bode response for the system with the compensator tuned with the SpCard at a crossover frequency of 1 khz Figure 12. Bode response for the system with the compensator tuned with the SpCard at a crossover frequency of 7,7 khz.
crossover frequency of the system. During the process, has been detected an unstable regulator which has been detected thanks to Bode100, because the measurements of the power stage does not present any sign of instability. Therefore, this methodology to accelerate the adjustment in detail of a compensator has been validated, adjusting a compensator in a reduced time and obtaining the desired result. REFERENCES [1] V. Šviković, J. J. Cortés, P. Alou, J. A. Oliver, O. García and J. A. Cobos, "Multiphase Current-Controlled Buck Converter With Energy Recycling Output Impedance Correction Circuit (OICC)," in IEEE Transactions on Power Electronics, vol. 30, no. 9, pp. 5207-5222, Sept. 2015 USA: Abbrev. of Publisher, year, ch. x, sec. x, pp. xxx xxx [2] M. del Viejo, P. Alou, J. A. Oliver, O. García and J. A. Cobos, "Fast control technique based on peak current mode control of the output capacitor current," 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, 2010, pp. 3396-3402. [3] J. Wang, B. Bao, J. Xu, G. Zhou and W. Hu, "Dynamical Effects of Equivalent Series Resistance of Output Capacitor in Constant On-Time Controlled Buck Converter," in IEEE Transactions on Industrial Electronics, vol. 60, no. 5, pp. 1759-1768, May 2013. doi: 10.1109/TIE.2012.2190956 [4] http://www.spcontroltechnologies.com/en/spcard/. [5] https://www.omicronlab.com/fileadmin/assets/manuals/bode_100_manual_ae4_hr.pd f. Jose María Molina (M 11) was born in Albacete, Spain, in 1986. He received the master s degree in industrial electronics from the Universidad Politecnica de Madrid, Madrid, Spain, in 2011, and the PhD in 2016. He has been a researcher in UPM from 2008 to 2015 working in Three Phase Rectifiers, EMI filters, dc/dc converters and soft switching techniques. Since 2015 he is working as CEO in SP Control Technologies, a company which he was also founded. Additionally, he is Power Electronic Manager with interest in topics as new semiconductor devices and Digital Control.