Simulation design of digital control power supply system based on SABER software

1. Introduction

With the rapid development of digital signal processing technology, digital control has become an important research direction in power electronics due to the continuous improvement of its control theory and implementation methods, and its advantages of highly integrated control circuits, precise control accuracy, stable working performance, good design continuity, etc. Power electronic devices based on digital control have good system performance and have been widely used; and digital control is also an effective means to ultimately achieve modularization, integration, digitization, and greening of power supplies.

In order to complete the design of power supply system efficiently and quickly, computer simulation is one of the important methods. Computer simulation refers to the process of using computer software to build a virtual model to conduct experiments on the system under study. ^[1] Since it is not restricted by actual experimental conditions, it greatly saves hardware consumption and shortens the development cycle. Through simulation, circuit design, principle analysis, control scheme selection and parameter setting can be easily carried out. When simulating digital control power supply system, since the closed loop of digital control system is realized by programming digital processor, and digital control scheme is mostly evolved from analog method, the usual method is to restore the digital control scheme to analog scheme, and then use analog devices to build a closed loop system to complete closed loop simulation. However, the simulation of digital control system is different from the simulation of analog system. First, the digital processor processes data in a discrete manner; second, the digital processor is not real-time control, but has its own working rhythm; in addition, the analog-to-digital interface part has a certain degree of influence on the simulation results. Therefore, only by recognizing the difference between digital control and analog control and making the model as close to the actual system as possible during the modeling process can satisfactory results be achieved.

This paper analyzes the working characteristics of digital control systems in detail and proposes a modeling and simulation method suitable for digital control power systems. Since the simulation model is closer to the actual digital control system, it can be used for principle analysis and parameter setting of digital systems, and has important reference value.

2. Principles and characteristics of digital control power supply system

For a typical digital signal processing system, the system structure shown in Figure 1 is usually adopted. In nature, a large number of signals are analog signals, so the digital signal processing system generally inputs an analog signal xa ₍ t); the analog signal xa ₍ t) is sampled to obtain a discrete signal xa ₍ n), which is then quantized by A/D to obtain a digital signal x(n), which is input to the digital processing unit; after digital processing, the input digital signal x(n) is transformed into an output digital signal y(n); the output digital signal y(n) is then D/A converted and smoothed to obtain an analog signal ya ₍ t) output.

Figure 1 Typical digital signal processing system architecture

Digital control power supply systems generally consist of two parts: a digital processor and a controlled object. The digital processor is a discrete part, and the controlled object is a continuous part, or they are called the digital part and the analog part respectively. ^[2] To realize the control of the controlled object by the digital processor, the analog output of the system must first be sampled at a certain sampling frequency through the AD function module inside or outside the processor, and the continuous signal must be converted into a discrete digital signal, and then converted into a digital quantity after quantization for calculation inside the processor. The sampling of analog control systems is real-time and continuous. In data processing, the digital processor processes data in a discrete manner. The digital processor only processes each discrete sample value, while the continuous system is based on a continuous signal. With the gradual improvement of power supply functions, in addition to completing the control function, the digital processor must also be able to realize various functions such as protection, display, and remote monitoring. With the increase in functions, the required processing time will increase accordingly. Therefore, the processing frequency of the core algorithm of the processor is subject to certain restrictions. Generally, the processing frequency of the core algorithm is lower than the switching frequency of the power supply, which makes it difficult for digital control to achieve real-time control. In addition, in order to achieve control of continuous controlled objects, the discrete output of the processor's internal calculation results must be converted into a continuous signal. For digital control switching power supply systems, the output link of the digital processor is generally an internal or externally extended PWM function module, which has a zero-order hold function, that is, it always keeps the current output value before the next output update.

3. Design of simulation model for digital control power supply system

3.1 Discretization simulation processing method

Since digital control systems consist of digital processors and control objects, which belong to the digital part and the analog part respectively, simulation models should be established for these two parts separately, and then combined together for simulation. ^[2]

The modeling of the analog part is relatively simple. It only needs to use the analog devices provided in the simulation software to build the circuit. The digital control part is relatively complex and needs to consider the digital-to-analog interface and data processing. The digital-to-analog interface is divided into AD sampling and DA conversion, which realize the interface between the power part and the control part. When analyzing the control system, AD sampling can be regarded as a series connection of an ideal switch and a proportional term. It realizes the conversion from the continuous domain to the discrete domain. In the simulation, it can be realized by the analog-to-digital conversion interface "a2z". DA conversion has a zero-order hold function to complete the conversion from the discrete domain to the continuous domain. For digital control switching power supply systems, digital-to-analog conversion is often replaced by the PWM function module of the digital processor. Therefore, according to the mechanism of PWM signal generation inside the digital processor, the calculated control quantity can be intersected with a triangular carrier with a fixed switching frequency to obtain a PWM drive signal. ^[3] Finally, the control system block diagram of the digital control power supply can be obtained, as shown in Figure 2. Among them, Hm(s) is the equivalent proportional link of the sampling circuit; Vref is the voltage reference given inside the digital processor; S1 is the equivalent switch, which completes the continuous to discrete conversion; Gc(s) is the digital processing link, where the PI algorithm is used; zoh is the equivalent zero-order holder of the PWM output link; Gud(s) is the control transfer function between the output voltage and duty cycle of the power circuit.

[page] The AD module of the digital processor chip samples the output voltage at a fixed frequency, converting the continuous voltage signal into a discrete digital signal. The control quantity generated by the discretized mathematical operation of the sampled value is output to the PWM module of the DSP chip at the same frequency, thereby changing the duty cycle of the PWM. Therefore, the PWM signal is updated once per sampling cycle, that is, the duty cycle of the PWM signal remains unchanged within a sampling cycle. It can be considered that the PWM output link has a zero-order hold function. The control algorithm part within the dotted box in Figure 2 is implemented in the digital processor through software programming. When modeling, the arithmetic and logical operation elements of the Z domain can be used according to certain operation relationships.

Figure 2 Control system block diagram

3.2 Simulation design of digital control algorithm

The modeling of the analog part is relatively simple. You only need to select the corresponding components in the simulation component library according to the actual circuit that has been designed and make necessary settings. For the digital control part, since the data processing process is discrete, in order to fully simulate this process, a programmed control algorithm simulation design can be used.

First, the control algorithm is analyzed because it is an important part of the control circuit and the key to forming a closed loop. In this example, the control algorithm uses the PI algorithm because it is simple and reliable and has a wide range of applications in engineering practice. If other control algorithms are used, the corresponding control algorithm block diagram can also be obtained in a similar way using the following method.

In the simulation system, the expression of PI control algorithm is:

(1)

Where u(t) is the output signal of the regulator, i.e. the control quantity; e(t) is the deviation signal between the reference and the sampling value; Kp is the proportional coefficient; TI _is the integral time constant. Since the digital control system is a sampling control system, the control quantity can only be calculated based on the deviation at the sampling time. Therefore, in order to make PI control applicable to digital control systems, the above expression should be discretized as

(2)

This formula is called the position PI control algorithm of PI regulation ^[4] . Let (called the integral coefficient), then the programming expression of the discretized position PI control algorithm can be obtained as

(3)

Let , then expression (3) can be rewritten as

(4)

When the actual digital control system has large changes such as startup or shutdown, the system output will have a large deviation. After integral accumulation, the integral term in the formula is prone to integral saturation, resulting in poor control effect. Therefore, an anti-saturation term is added to the integral term, that is,

(5)

Where, Ksat is the anti-saturation integral coefficient. ^[5] When the control quantity is too high, the integral term is subtracted by a certain value, which is related to the difference between the calculated value of the control quantity and the upper limit; on the contrary, a certain value is added, which is related to the difference between the calculated value of the control quantity and the lower limit, thereby effectively suppressing integral saturation.

Considering the feasibility of the expression, the integral term is changed to the previous integral result, thus obtaining the following expression:

(6)

From expressions (4), (5) and (6), we can get the PI calculation block diagram shown in Figure 3. The input is the error between the reference value and the current sampling value, and the output is the PI calculation output with an anti-saturation link. This block diagram will serve as the main basis for modeling the control part of the simulation circuit.

Figure 3 PI calculation block diagram

[page]4 Digital control system simulation example

The main circuit of this simulation example adopts a synchronous rectifier active clamp forward converter, and the control method is voltage single loop control. The system structure is shown in Figure 4. Vin is the input DC voltage, S1 and S2 are the main tube and clamp tube of the forward converter respectively, C _c is the clamp capacitor, Tr is the transformer, SR1 and SR2 are the synchronous tubes of the secondary side of the converter, Lf and Cf form the output filter link, and Ro is the resistive load. When S1 and SR1 are turned on, energy is transferred from the primary side to the secondary side, and the DC output voltage is obtained after rectification and filtering; when S2 and SR2 are turned on, the transformer realizes magnetic reset through the clamp capacitor, and the secondary side continues current through SR2. The digital processor samples the output voltage and adjusts the voltage loop according to the internal voltage reference. The output of the voltage loop changes the duty cycle of the PWM drive signal, thereby changing the conduction time of the four switch tubes, and finally stabilizes the output voltage.

Figure 4 System structure diagram

The following is the modeling and simulation process implemented by Saber software. The main parameters are as follows: input is 48VDC, output is 3.3V/20A, switching frequency is 300KHz, DSP sampling frequency is 50KHz, and the operating frequency of the selected DSP chip is 32MHz.

The main circuit is composed of analog components in the simulation library. The input is a 48V DC voltage source. The main tube S1, the clamp tube S2 and the two synchronous tubes on the secondary side are all ideal N-channel MOSFETs. The clamp capacitor C _c is 2.2uF, the transformer turns ratio is 4:1, the filter inductor is 1uH, and the filter capacitor is 300uF. The discrete simulation model of the control part can be obtained according to the block diagrams given in Figures 2 and 3. First, the AD sampling link is implemented by an analog-to-digital conversion interface "a2z". The voltage reference is a Z-domain given signal. The difference between the above two is the error term. Then the Z-domain gain, adder, comparator (for integral limiting) and delay components are connected according to the method shown in Figure 3 to form the entire PI calculation link. Finally, the output of the PI calculation is increased and decreased by a small amount and then intersected with a triangle wave with a frequency of 300KHz to generate a PWM complementary output with a dead zone. After passing through the digital-to-analog conversion interface "z2a", it is converted into a voltage value, and then the two signals are amplified and electrically isolated through the voltage-controlled voltage source, and then used as the driving signal for the transformer primary side main tube and clamp tube and the two synchronous tubes on the secondary side in the main circuit. The overall simulation circuit diagram of the power supply system is shown in Figure 5. Most of the Z-domain components in the simulation circuit except the gain require a Z-domain sampling pulse signal for control. In this example, the sampling frequency is set to 50KHz. In addition, the triangle wave generator is implemented by a Z-domain pulse source, and its control signal frequency should be the operating frequency of the DSP chip 32MHz, and the output triangle wave frequency is 300KHz.

Figure 5 Digital control module power supply simulation circuit

[page] By adjusting the voltage loop PI control parameters, the steady-state simulation waveform is obtained as shown in Figure 6. The waveforms are the main tube drive, clamp tube drive, output voltage and duty cycle signal (i.e. PI loop output) from top to bottom. It can be seen from the figure that the two drive signals are complementary and there is a certain dead time. The output voltage is stable at 3.3V, the peak-to-peak value of the ripple voltage is 0.012V, and the PI loop output is stable. It can be seen from the duty cycle waveform that the duty cycle is updated once every 6 switching cycles, i.e. 1 sampling cycle, which is completely consistent with the actual digital control system. Figure 7 shows the dynamic simulation waveform. The waveforms are the unloading control signal, the output voltage waveform when the full load is suddenly unloaded to half load, the loading control signal and the output voltage waveform when the half load is suddenly increased to full load.

Figure 6 Steady-state simulation waveform

Figure 7 Dynamic simulation waveform

The control parameters obtained by simulation are applied to the prototype. After repeated experimental debugging, a set of better actual control parameters are obtained, as shown in Table 1. By comparison, it can be seen that the simulation parameters are very close to the actual parameters, which strongly illustrates that the modeling and simulation method has important reference value for control parameter setting.

Table 1 PI control parameters

From the above discussion and simulation, it can be seen that this digital control system modeling and simulation method simulates the internal data processing process of the digital processor very well. It can not only be used for principle analysis, but also has important reference value for the control parameter setting of the digital control system.

5 Conclusion

Based on a detailed analysis of the internal data processing mechanism of the digital processor, this paper introduces a modeling and simulation method of digital control systems, and demonstrates the entire modeling and simulation process through specific examples. The simulation analysis verifies that this method can realistically reflect the data processing process of the digital control system and fully reflect the characteristics of digital control. It will create favorable conditions for the control parameter setting of the digital control system and the research of digital control algorithms.

References:
[1] Chen Jianye. Computer simulation of power electronic circuits. Beijing: Tsinghua University Press, October 2003.
[2] Zhang Shaoning. Simulation methods of digital control systems. Tactical Missile Technology, July 2002.
[3] David M. Van de Sype, Koen De Gusseme, Alex P. Van den Bossche, and Jan A. Melkebeek. “Small-signal z-domain analysis of digitally controlled converters”. PESC 04. 2004 IEEE 35th Annual. pp. 4299~4305.
[4] Lai Shouhong. Microcomputer Control Technology. Beijing: Machinery Industry Press, May 2001.
[5] Li Chunyan. Power supply control based on DSP. Master’s degree thesis of Nanjing University of Aeronautics and Astronautics, 2003.