基于龙贝格算法的高精度数字积分算法

摘要

As the key link in the field of signal processing , the integrator is widely used in measurement in power system and control engineering . Generally , research on the digital integrator is based on traditional Newton Cotes algorithm , the high frequency response of low order Cotes formula is usually poor , and the design of the transfer function introduced by high order of the formula is too complex . Based on a study of error between the composite Cotes transmission function and ideal integration , the output signal which are weighted by Romberg algorithm at the same algorithm order before and after integrator sampling frequency are doubled , then the accuracy of digital integrator is improved and the composite is lower . The digital integrator designed with better transient and steady performance has an accuracy of 0 .01% as verified by simulation and test .%积分环节是信号处理领域的关键环节，广泛应用于电力系统测量及控制领域之中。目前对于数字积分算法的研究普遍基于传统牛顿科茨算法，低阶科茨公式高频响应普遍较差，高阶科茨公式所引入的传输函数设计则过于复杂。在研究复合科茨传输函数与理想积分误差的基础上，利用龙贝格算法将采样频率加倍前后的积分输出信号做线性组合处理，在算法阶数相同的情况下，提高了数字积分器的精度，降低了设计难度。仿真和试验测试证明，所设计算法准确度可以达到0．01％以内，具有优良的稳态和暂态性能。