A New Method for Extraction of Process Differential Signal Based onSingle-frequency-pass Filter
-
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.
-
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 
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
-
[1] 魏萍, 丁卯, 左信, 罗雄麟.基于微分方程对称的分布参数系统稳态控制.自动化学报, 2014, 40(10): 2163-2170 http://www.aas.net.cn/CN/abstract/abstract18491.shtmlWei Ping, Ding Mao, Zuo Xin, Luo Xiong-Lin. Steady-state control for distributed parameter systems by symmetry of differential equations. Acta Automatica Sinica, 2014, 40(10): 2163-2170 http://www.aas.net.cn/CN/abstract/abstract18491.shtml [2] 谭拂晓, 刘德荣, 关新平, 罗斌.基于微分对策理论的非线性控制回顾与展望.自动化学报, 2014, 40(1): 1-15 http://www.aas.net.cn/CN/abstract/abstract18261.shtmlTan Fu-Xiao, Liu De-Rong, Guan Xin-Ping, Luo Bin. Review and perspective of nonlinear systems control based on differential games. Acta Automatica Sinica, 2014, 40(1): 1-15 http://www.aas.net.cn/CN/abstract/abstract18261.shtml [3] Freidovich L B, Khalil H K. Performance recovery of feedback-linearization-based designs. IEEE Transactions on Automatic Control, 2008, 53(10): 2324-2334 https://www.researchgate.net/publication/224347247_Performance_Recovery_of_Feedback-Linearization-Based_Designs [4] Atassi A N, Khalil H K. Separation results for the stabilization of nonlinear systems using different high-gain observer designs. Systems & Control Letters, 2000, 39(3): 183-191 https://www.researchgate.net/publication/222062167_Separation_Results_for_the_Stabilization_of_Nonlinear_Systems_Using_Different_High-Gain_Observer_Designs [5] 刘希, 孙秀霞, 郝震, 刘宇坤.最速跟踪微分器的一种新型离散形式.信息与控制, 2013, 42(6): 729-734 http://www.cnki.com.cn/Article/CJFDTOTAL-XXYK201306011.htmLiu Xi, Sun Xiu-Xia, Hao Zhen, Liu Yu-Kun. A new discrete-time form of optimal tracking differentiator. Information and Control, 2013, 42(6): 729-734 http://www.cnki.com.cn/Article/CJFDTOTAL-XXYK201306011.htm [6] Guo B Z, Han J Q, Xi F B. Linear tracking-differentiator and application to online estimation of the frequency of a sinusoidal signal with random noise perturbation. International Journal of Systems Science, 2002, 33(5): 351-358 doi: 10.1080/00207720210121771 [7] 李军, 万文军, 张曦.基于非线性滤波环节的新型鲁棒PID控制策略的研究.动力工程学报, 2013, 33(2): 117-122 http://www.cnki.com.cn/Article/CJFDTOTAL-DONG201302009.htmLi Jun, Wan Wen-Jun, Zhang Xi. Study on novel robust PID control strategy based on non-linear filtering. Journal of Chinese Society of Power Engineering, 2013, 33(2): 117-122 http://www.cnki.com.cn/Article/CJFDTOTAL-DONG201302009.htm [8] 韩京清.自抗扰控制技术:估计补偿不确定因素的控制技术.北京:国防工业出版社, 2008.Han Jing-Qing. Active Disturbance Rejection Control Technique: the Technique for Estimating and Compensating the Uncertainties. Beijing: National Denfence Industry Press, 2008. [9] Guo B Z, Zhao Z L. On convergence of tracking differentiator. International Journal of Control, 2011, 84(4): 693-701 doi: 10.1080/00207179.2011.569954 [10] 李向阳.基于有限时间跟踪微分器的迭代学习控制.自动化学报, 2014, 40(7): 1366-1375 http://www.aas.net.cn/CN/abstract/abstract18408.shtmlLi Xiang-Yang. Iterative learning control based on finite time tracking differentiator. Acta Automatica Sinica, 2014, 40(7): 1366-1375 http://www.aas.net.cn/CN/abstract/abstract18408.shtml [11] Guo B Z, Zhao Z L. On convergence of the nonlinear active disturbance rejection control for MIMO systems. SIAM Journal on Control and Optimization, 2013, 51(2): 1727-1757 https://www.researchgate.net/publication/263932930_On_Convergence_of_the_Nonlinear_Active_Disturbance_Rejection_Control_for_MIMO_Systems [12] Jiang T T, Huang C D, Guo L. Control of uncertain nonlinear systems based on observers and estimators. Automatica, 2015, 59: 35-47 doi: 10.1016/j.automatica.2015.06.012 [13] Ran M P, Wang Q, Dong C Y. Stabilization of a class of nonlinear systems with actuator saturation via active disturbance rejection control. Automatica, 2016, 63: 302-310 doi: 10.1016/j.automatica.2015.10.010 [14] 程春华, 胡云安, 吴进华.非仿射纯反馈非线性系统的自抗扰控制.自动化学报, 2014, 40(7): 1528-1536 http://www.aas.net.cn/CN/abstract/abstract18423.shtmlCheng Chun-Hua, Hu Yun-An, Wu Jin-Hua. Auto disturbance controller of non-affine nonlinear pure feedback systems. Acta Automatica Sinica, 2014, 40(7): 1528-1536 http://www.aas.net.cn/CN/abstract/abstract18423.shtml [15] 李杰, 齐晓慧, 夏元清, 高志强.线性/非线性自抗扰切换控制方法研究.自动化学报, 2016, 42(2): 202-212 http://www.aas.net.cn/CN/abstract/abstract18810.shtmlLi Jie, Qi Xiao-Hui, Xia Yuan-Qing, Gao Zhi-Qiang. On linear/nonlinear active disturbance rejection switching control. Acta Automatica Sinica, 2016, 42(2): 202-212 http://www.aas.net.cn/CN/abstract/abstract18810.shtml [16] 高志强.自抗扰控制思想探究.控制理论与应用, 2013, 30(12): 1498-1510 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201312006.htmGao Zhi-Qiang. On the foundation of active disturbance rejection control. Control Theory & Applications, 2013, 30(12): 1498-1510 http://www.cnki.com.cn/Article/CJFDTOTAL-KZLY201312006.htm [17] 杨光达, 周游.非线性跟踪微分器稳态性能分析及仿真研究.光电技术应用, 2010, 25(5): 80-82 http://www.cnki.com.cn/Article/CJFDTOTAL-GDYG201005025.htmYang Guang-Da, Zhou You. Analysis and simulation of steady-state performance in nonlinear tracking-differentiator. Electro-Optic Technology Application, 2010, 25(5): 80-82 http://www.cnki.com.cn/Article/CJFDTOTAL-GDYG201005025.htm [18] 李军, 万文军, 刘志刚, 陈世和, 张曦.一种基于时域响应的控制系统频率特性分析方法.中国电机工程学报, 2012, 32(29): 116-122 http://www.cnki.com.cn/Article/CJFDTOTAL-ZGDC201229018.htmLi Jun, Wan Wen-Jun, Liu Zhi-Gang, Chen Shi-He, Zhang Xi. A method of frequency domain analysis for control systems based on process response in time domain. Proceedings of the CSEE, 2012, 32(29): 116-122 http://www.cnki.com.cn/Article/CJFDTOTAL-ZGDC201229018.htm [19] 李军, 万文军.一种基于序列零初相位调制的新型正弦信号频率测量方法.自动化学报, 2016, 42(10): 1585-1594 http://www.aas.net.cn/CN/abstract/abstract18945.shtmlLi Jun, Wan Wen-Jun. A novel sinusoidal frequency measurement method based on modulation of sequence with zero initial phase. Acta Automatica Sinica, 2016, 42(10): 1585-1594 http://www.aas.net.cn/CN/abstract/abstract18945.shtml -
点击查看大图
计量
- 文章访问数: 2788
- HTML全文浏览量: 439
- PDF下载量: 792
- 被引次数: 0
