With the advent of microprocessors and digital signal processors with ever-increasing data processing capabilities, digital control has become a viable method for DC switching power supply control. However, due to the limited computing power of existing microprocessors, digital control is currently only used in DC switching power supplies with relatively low switching frequencies. Moreover, the delay caused by zero-order hold, A/D conversion, calculation and PWM signal generation in the control loop structure reduces the response characteristics of the control loop and the bandwidth of the controller. Therefore, for control systems with high real-time requirements, digital control systems are difficult to apply. In order to improve the performance of DC converter digital control system, the research on delay compensation method has always been an important topic of digital control system. At present, the compensation method of time delay mainly focuses on the compensation of the indirect discretization of the control system and the compensation of the direct discretization of the control system based on the prediction technique.
2Digital Control Implementation of DC Converters Two methods for implementing digital control of DC converters are indirect discretization control and direct discretization control. For the indirect discretization method, the controller in the continuous time domain is designed first, and then the controller is discretized into a digital controller. The direct discretization method is to design the controller directly in the discrete domain (domain). The indirect discretization design is to establish a continuous time domain control system, and then discretize the continuous time domain control system into a digital control system. By optimizing the coefficients of the digital controller, the closed loop response characteristics of the digital control system are more accurately approximated to the analog. The closed loop response characteristic of the controller. The compensation method based on the estimation technique is to directly discretize the control system, and the delayed measurement is advanced to the regulator through the estimation technology, thereby obtaining good output performance.
3 Indirect Discretization Compensation As digital devices are applied to control systems, existing continuous data systems are converted to digital systems. The digital controller can be realized by indirect discretization by the controller, and the discretization method is different, so the method of implementing compensation is also different.
3.1 CAD mode compensation method to achieve more discretization methods of the controller. Tabak proposed in 1971 to convert the continuous compensator into a digital controller through a bilinear transformation method to realize the discretization of the continuous time domain control system. However, this method only considers the frequency response characteristics of the digital controller, and does not consider the frequency response characteristics of the whole system. Therefore, although this method is simple and easy to apply, the approximate continuous system response characteristics can be obtained only when the sampling frequency is high enough. Therefore, it is applied less now.
The digital controller is synthesized by minimizing the mean square error of the error between the frequency characteristic function of the data sampling system and the transfer function in the continuous mode, so that the frequency response characteristic of the sampled data system approximates the response characteristics of the continuous time domain system.
This mode is based on the pulse transfer function of the controlled object and the parameters of the closed-loop transfer function of the continuous time domain system, so a high sampling frequency is not required.
The compensator replaces and adds a data sampler with a digital controller.
The method in which the pulse transfer function of the digital controller can be expressed as the coefficient of the controller compensates for the delay generated by the system, but the calculation process is complicated and does not effectively compensate the zero-order hold delay.
The determination of the dependence on the coefficients a and ba and b is achieved by an algorithm that fits the frequency response characteristics of the sampled data system to the ideal frequency response characteristics. Let F() be the closed-loop ideal transfer function of the continuous time domain control system, G/((c) is the frequency characteristic function of the sampled data control system, and e(co) is the difference between the two, that is, the group of a and b The good solution can be obtained by satisfying the mean square error of the minimization error function e(c). As shown, by performing a Z-transform on the corresponding transfer function, a form in which a part of the function is expressed as a complex number is obtained. In this process, a feedback function is assumed. H(s)=1, then the 3.2 pole-zero compensation method can be obtained. In the case of low sampling frequency, if the compensation for zero-order hold is not considered, the response performance and stability of the whole closed-loop system will be reduced. And W.Djaja proposed a simple and very practical zero-order hold compensation technique to increase the zero pole of the digital controller through an appropriate discretization mode. The added zero and pole compensate the digital controller and significantly improve its performance and stability. Sex.
In general, the zero-order hold produces a delay of about half a sample period. When the frequency satisfies the zero-pole compensation formula, it provides a phase angle of the first half of the period, thereby compensating for the delay caused by the zero-order hold. For a stable closed-loop system, the characteristic polynomial of its discretized system must satisfy a unit circle in which all its multiple roots must be in the Z-domain. The D'(z) is the corresponding discretization of the controller transfer function Gc(s), and the minimized error function shown by the Smith predictive compensation method is widely used in digital control systems. By using Smith's predictive compensator, the delay is eliminated from the closed-loop characteristic equation, thereby overcoming the effect of delay on the overall system control.
A block diagram of the conventional Smith predictive compensation control algorithm is shown. In the figure, GO is the controller transfer function, GF(s) is the control object transfer function, and there is GF(s)=GP(s)e-Q, and GP(s) is GF(s) without delay. section. Gln(s)e is the model, Gm(s) is the predictor, and Tm is the estimated value of the object model delay. In the case of accurate model, the system characteristic equation becomes under the condition of accurate model. The Smith predictive compensation algorithm is used to control the system, which can make the system have good dynamic characteristics. However, Smith predicts that the compensation method is poorly robust. When the prediction model does not match the actual control object, it may cause oscillation or even divergence. It is very sensitive to the deviation of the model, especially the delay error and gain error of the model. When the parameters of the model change, the output of the system will become significantly worse, and even unstable.
4.2 Predictive compensation method based on linearized speculation Predictive compensation method can obtain better control effect under certain conditions. This method not only compensates for the delay generated by the zero-order hold, but also compensates for the entire digital control system.
In the traditional discrete control system, it is controlled by calculating the control variable Un at Tn! The amount of output. The prediction method obtains the predicted control variable M*n+1 through the output at the time of pre-estimation at Tn, so that the delayed modulated amount is advanced to the controller, thereby compensating for the delay of the system.
As shown, Dc(z) is a discretized form of the continuous time domain controller Gc(), which is the transfer function of the controlled object. The effect of H(), which can be expressed as the compensation method shown in equation (23), depends on the accuracy of the coefficient k1. When the parameter error of the system is large or the system changes, the effect of the compensation method is not satisfactory. The compensation method shown in formula (24) is not affected by the system parameters, and can better combine the control performance and stability of the system, and the algorithm is simple, and the system computing resources occupied are less.
5 Conclusion This paper summarizes the main compensation methods of digital controllers, and analyzes the characteristics of each method in detail. Some new techniques are applied to the discretization of continuous time domain control systems for DC converters, and their control performance is improved by optimizing the coefficients of the control system. Direct discretization digital control of DC converters has wider control bandwidth and better system stability, and its control performance is better than indirect discretization digital control at lower sampling frequencies. Therefore, with the development of digital signal processors and microprocessors, predictive compensation methods will be widely used in digital control design. The predictive compensation method based on linearized speculation proposed by Bibian and Huajin has attracted attention due to its strong real-time performance. However, how to establish a good predictive compensation model and algorithm to make the control performance of the system more perfect will be one of the main research topics of digital control technology of switching power supply.
2Digital Control Implementation of DC Converters Two methods for implementing digital control of DC converters are indirect discretization control and direct discretization control. For the indirect discretization method, the controller in the continuous time domain is designed first, and then the controller is discretized into a digital controller. The direct discretization method is to design the controller directly in the discrete domain (domain). The indirect discretization design is to establish a continuous time domain control system, and then discretize the continuous time domain control system into a digital control system. By optimizing the coefficients of the digital controller, the closed loop response characteristics of the digital control system are more accurately approximated to the analog. The closed loop response characteristic of the controller. The compensation method based on the estimation technique is to directly discretize the control system, and the delayed measurement is advanced to the regulator through the estimation technology, thereby obtaining good output performance.
3 Indirect Discretization Compensation As digital devices are applied to control systems, existing continuous data systems are converted to digital systems. The digital controller can be realized by indirect discretization by the controller, and the discretization method is different, so the method of implementing compensation is also different.
3.1 CAD mode compensation method to achieve more discretization methods of the controller. Tabak proposed in 1971 to convert the continuous compensator into a digital controller through a bilinear transformation method to realize the discretization of the continuous time domain control system. However, this method only considers the frequency response characteristics of the digital controller, and does not consider the frequency response characteristics of the whole system. Therefore, although this method is simple and easy to apply, the approximate continuous system response characteristics can be obtained only when the sampling frequency is high enough. Therefore, it is applied less now.
The digital controller is synthesized by minimizing the mean square error of the error between the frequency characteristic function of the data sampling system and the transfer function in the continuous mode, so that the frequency response characteristic of the sampled data system approximates the response characteristics of the continuous time domain system.
This mode is based on the pulse transfer function of the controlled object and the parameters of the closed-loop transfer function of the continuous time domain system, so a high sampling frequency is not required.
The compensator replaces and adds a data sampler with a digital controller.
The method in which the pulse transfer function of the digital controller can be expressed as the coefficient of the controller compensates for the delay generated by the system, but the calculation process is complicated and does not effectively compensate the zero-order hold delay.
The determination of the dependence on the coefficients a and ba and b is achieved by an algorithm that fits the frequency response characteristics of the sampled data system to the ideal frequency response characteristics. Let F() be the closed-loop ideal transfer function of the continuous time domain control system, G/((c) is the frequency characteristic function of the sampled data control system, and e(co) is the difference between the two, that is, the group of a and b The good solution can be obtained by satisfying the mean square error of the minimization error function e(c). As shown, by performing a Z-transform on the corresponding transfer function, a form in which a part of the function is expressed as a complex number is obtained. In this process, a feedback function is assumed. H(s)=1, then the 3.2 pole-zero compensation method can be obtained. In the case of low sampling frequency, if the compensation for zero-order hold is not considered, the response performance and stability of the whole closed-loop system will be reduced. And W.Djaja proposed a simple and very practical zero-order hold compensation technique to increase the zero pole of the digital controller through an appropriate discretization mode. The added zero and pole compensate the digital controller and significantly improve its performance and stability. Sex.
In general, the zero-order hold produces a delay of about half a sample period. When the frequency satisfies the zero-pole compensation formula, it provides a phase angle of the first half of the period, thereby compensating for the delay caused by the zero-order hold. For a stable closed-loop system, the characteristic polynomial of its discretized system must satisfy a unit circle in which all its multiple roots must be in the Z-domain. The D'(z) is the corresponding discretization of the controller transfer function Gc(s), and the minimized error function shown by the Smith predictive compensation method is widely used in digital control systems. By using Smith's predictive compensator, the delay is eliminated from the closed-loop characteristic equation, thereby overcoming the effect of delay on the overall system control.
A block diagram of the conventional Smith predictive compensation control algorithm is shown. In the figure, GO is the controller transfer function, GF(s) is the control object transfer function, and there is GF(s)=GP(s)e-Q, and GP(s) is GF(s) without delay. section. Gln(s)e is the model, Gm(s) is the predictor, and Tm is the estimated value of the object model delay. In the case of accurate model, the system characteristic equation becomes under the condition of accurate model. The Smith predictive compensation algorithm is used to control the system, which can make the system have good dynamic characteristics. However, Smith predicts that the compensation method is poorly robust. When the prediction model does not match the actual control object, it may cause oscillation or even divergence. It is very sensitive to the deviation of the model, especially the delay error and gain error of the model. When the parameters of the model change, the output of the system will become significantly worse, and even unstable.
4.2 Predictive compensation method based on linearized speculation Predictive compensation method can obtain better control effect under certain conditions. This method not only compensates for the delay generated by the zero-order hold, but also compensates for the entire digital control system.
In the traditional discrete control system, it is controlled by calculating the control variable Un at Tn! The amount of output. The prediction method obtains the predicted control variable M*n+1 through the output at the time of pre-estimation at Tn, so that the delayed modulated amount is advanced to the controller, thereby compensating for the delay of the system.
As shown, Dc(z) is a discretized form of the continuous time domain controller Gc(), which is the transfer function of the controlled object. The effect of H(), which can be expressed as the compensation method shown in equation (23), depends on the accuracy of the coefficient k1. When the parameter error of the system is large or the system changes, the effect of the compensation method is not satisfactory. The compensation method shown in formula (24) is not affected by the system parameters, and can better combine the control performance and stability of the system, and the algorithm is simple, and the system computing resources occupied are less.
5 Conclusion This paper summarizes the main compensation methods of digital controllers, and analyzes the characteristics of each method in detail. Some new techniques are applied to the discretization of continuous time domain control systems for DC converters, and their control performance is improved by optimizing the coefficients of the control system. Direct discretization digital control of DC converters has wider control bandwidth and better system stability, and its control performance is better than indirect discretization digital control at lower sampling frequencies. Therefore, with the development of digital signal processors and microprocessors, predictive compensation methods will be widely used in digital control design. The predictive compensation method based on linearized speculation proposed by Bibian and Huajin has attracted attention due to its strong real-time performance. However, how to establish a good predictive compensation model and algorithm to make the control performance of the system more perfect will be one of the main research topics of digital control technology of switching power supply.
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