Universal fractional-order design of linear phase lead compensation multirate repetitive control for PWM inverters

Repetitive control (RC) with linear phase lead compensation provides a simple but very effective control solution for any periodic signal with a known period. Multirate repetitive control (MRC) with a downsampling rate can reduce the need of memory size and computational cost, and then leads to a more feasible design of the plug-in repetitive control systems in practical applications. However, with fixed sampling rate, both MRC and its linear phase lead compensator are sensitive to the ratio of the sampling frequency to the frequency of interested periodic signals: (1) MRC might fails to exactly compensate the periodic signal in the case of a fractional ratio; (2) linear phase lead compensation might fail to enable MRC to achieve satisfactory performance in the case of a low ratio. In this paper, a universal fractional-order design of linear phase lead compensation MRC is proposed to tackle periodic signals with high accuracy, fast dynamic response, good robustness, and cost-effective implementation regardless of the frequency ratio, which offers a unified framework for housing various RC schemes in extensive engineering application. An application example of programmable AC power supply is explored to comprehensively testify the effectiveness of the proposed control scheme

Virtual variable sampling discrete fourier transform based selective odd-order harmonic repetitive control of DC/AC converters

This paper proposes a frequency adaptive discrete Fourier transform (DFT) based repetitive control (RC) scheme for DC/AC converters. By generating infinite magnitude on the interested harmonics, the DFT-based RC offers a selective harmonic scheme to eliminate waveform distortion. The traditional DFT-based selective harmonic RC, however, is sensitive to frequency fluctuation since even very small frequency fluctuation leads to a severe magnitude decrease. To address the problem, virtual variable sampling method, which creates an adjustable virtual delay unit to closely approximate a variable sampling delay, is proposed to enable the DFT-based selective harmonic RC to be frequency adaptive. Moreover, a selective odd-order harmonic DFT filter is developed to deal with the dominant odd order harmonic. Because it halves the number of sampling delays in the DFT filter, the system transient response gets nearly 50% improvement. A comprehensive series of experiments of the proposed VVS DFT-based selective odd-order harmonic RC controlled programmable AC power source under frequency variations are presented to verify the effectiveness of the proposed method

Fractional Order and Virtual Variable Sampling Design of Repetitive Control for Power Converters

With the growth of electricity demand and renewable energy power source, power converter becomes a more and more significant component in electrical power systems. The requirement of the power converter controller is to produce an accurate and low-distorted voltage or current under different load conditions. Although the conventional controller can meet the requirement of some applications, it requires accurate knowledge of the system model and cannot provide a satisfactory result especially under nonlinear loads or sudden load change. Repetitive control (RC) presents an attractive solution to achieve excellent steady-state tracking error and low total harmonic distortion for periodic signals, and it is increasingly applied to power converter systems. However, there are still some limitations or requirements of RC when it is applied to power electronics system: first, RC requires the system sampling frequency is a fixed value and needs to be an integral multiple of the reference frequency; second, low controller sampling frequency results in low phase lead compensation resolution in RC, which leads to control inaccuracy; third, conventional RC does not have frequency adaptability to reference frequency fluctuation, and even a small reference frequency fluctuation can lead to severe performance degradation. To overcome the conventional RC limitations, two advanced design methods are proposed in the thesis: fractional order delay and virtual variable sampling. The method of fractional order delay approximates the non-integer delay part by building a finite impulse response filter. This improved method is not only able to be applied on a period delay unit but also on phase-lead compensation. The accurate period delay and phase lead compensation show a noticeable improvement in RC performance. Although fractional order delay can meet the requirement on most of the applications, it also has a minimal adjustable range on the reference frequency. To achieve an essential solution to this problem, the virtual variable sampling (VVS) method is developed. The VVS approximates a variable sampling unit instead of the fixed system unit for RC and its filters, in which RC is able to be frequency adaptive. Comparing with the method of fractional order delay, the VVS method can provide a much more extensive adjustable range on the reference frequency. Based on the system performance under the conventional controller, power converter always has uneven distortion distribution. To further improve the stability and eliminate harmonic distortions efficiently, two selective harmonic RC schemes are introduced - nk ± m order harmonic RC and DFT-based selective harmonic RC. However, these selective RC schemes also suffer from the particular requirement of system sampling frequency and low reference frequency adaptability. Applying VVS methods on these two schemes can effectively present an improvement on their frequency adaptability. To verify the proposed methods’ effectiveness, a complete series of power electronics applications are carried out. These applications include single-phase and three-phase DC/AC power converter, single-phase AC/DC power converter, and single-phase grid-connected power converter. The detailed system modeling and the proposed RC schemes are presented for each power electronics application