A New Method for Extraction of Process Differential Signal Based onSingle-frequency-pass Filter
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摘要: 针对经典微分方法存在显著的干扰放大效应和非线性微分方法的不足，提出了一种新型线性微分方法.文中分析了对象阶跃激励响应和正弦激励响应的内在关联.指出了在一定的条件下，可通过对象的正弦激励响应获取对象阶跃激励响应的微分信号.并给出了一种点频滤波器能够实现阶跃激励到正弦激励的转换方法.进而由点频滤波器和一种新型正弦跟踪滤波器等构建了一种新型微分信号提取的逻辑回路结构.文中提出的方法具有良好的抗噪声干扰特性，是线性滤波技术的发展与延伸，并具有良好的理论意义和实际应用前景，可作为经典控制理论的有益补充.数学分析、仿真实验和实际应用的结果进一步证实了文中所述方法的正确性和有效性.Abstract: Aimed at the severely amplified disturbance in the traditional differential operators and non-linear differential methods, a novel linear differential method is proposed. In this paper, the inter-relationship between step response and sine response of plants is analyzed. It is pointed out that under certain conditions, the differential component of the step response of a plant could be extracted from the sinusoidal excitation signal upon the same plant. And a new method is proposed that step excitations of a plant could be transformed to sinusoidal excitations through single-frequency-pass filter. Furthermore, a logic structure to extract the differential component of process signals is constructed via single-frequency-pass filters and a new type sinusoid tracking filter. Superior anti-noise characteristics could be obtained with the proposed method, which is the development and extension of linear filters, and possesses good theoretical significance and practical application prospect. Mathematical analysis, simulation experiment, and practical application results have shown that the new method is correct and valid.
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图 4 新型正弦跟踪器的二阶微分激励特性示意图
Fig. 4 The 2nd order differential excitation response of a new type sinusoid tracker
图 7 激励方式转换频域幅频特性示意图
Fig. 7 Amplitude frequency characteristics diagram of incentive method conversion
图 8 新型正弦跟踪滤波器频域幅频特性示意图
Fig. 8 Amplitude frequency characteristics of a new type sinusoid tracking filter
图 11 四阶微分信号对比仿真实验结果示意图
Fig. 11 Comparison of simulation results and 4th order differential signal
图 12 二阶微分信号对比仿真实验结果示意图
Fig. 12 Comparison of simulation results and 2th order differential signal
图 14 传统微分运算抗白噪声干扰实验结果 (意图 2)
Fig. 14 Resistance to white noise of traditional differential operation (NO. 2)
图 15 新方法抗白噪声干扰实验结果示 (意图 3)
Fig. 15 Resistance to white noise of the new method (NO. 3)
图 16 传统微分运算抗白噪声干扰实验结果 (意图 4)
Fig. 16 Resistance to white noise of traditional differential operation (NO. 4)
图 18 二阶跟踪微分器变形结构示意图
Fig. 18 The deformation structure diagram of 2nd order tracking differentiator
表 1 相对比例1
Table 1 Relative proportion of 1
成分 Y $_{\textrm{d4}}$ (t) Y $_{\textrm{d3}}$ (t) Y $_{\textrm{d2}}$ (t) Y $_{\textrm{d1}}$ (t) 稳态正弦 相对比例 1.0 0.0198 -0.0095 -0.00038 0.00098 
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表 2 相对比例2
Table 2 Relative proportion of 2
成分 Y $_{\textrm{d2}}$ (t) Y $_{\textrm{d1}}$ (t) 稳态正弦 相对比例 1.0 0.0198 0.0995
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表 3 相对比例3
Table 3 Relative proportion of 3
信号 Y $_{\textrm{d2}}$ (t) Y $_{\textrm{d1}}$ (t) 稳态正弦 正弦激励转换器 0.1979 0.00391 0.0197 余弦激励转换器 -0.0099 0.0097 0.0099 加法器合成信号 0.1880 0.01361 0.02204 相对比率 1.0 0.07239 0.1172
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