自适应逆控制及其应用研究
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摘要
传统的控制和自适应控制采用的反馈控制方式是将输出和干扰同时反馈来提高系统性能和消除干扰，这样在两者之间只能折衷实现。而自适应逆控制需要很少的先验知识，不需要知道被控对象的数学模型，就可以设计出性能优良的自适应逆控制系统。自适应逆控制对对象动态响应的控制和消除扰动的控制是分别进行控制的，二者互不影响，这样就可尽量提高系统动态性能和尽可能消除干扰。设计出的自适应逆控制系统，不仅可以得到好的动态响应，还可以使噪声和扰动减小到最小。本课题主要研究自适应逆控制及其应用。
首先，论文研究了针对线性对象的自适应逆控制，在经典的自适应逆控制理论的基础上，提出了两种改进的自适应逆控制系统。在原来的X-滤波LMS算法自适应逆控制和-滤波LMS算法自适应逆控制方法的基础上，引入了新的变步长LMS算法，在计算量增加不多的前提下，能同时获得较快的收敛速度和较小的稳态误差；引入自适应的反馈补偿控制克服了被控系统的直流零频漂移，使控制系统在初开始工作阶段快速收敛；还引入自适应扰动消除器，它能最大限度的消除扰动。
其次，论文研究了非线性自适应逆控制。给出一种结构新颖的非线性自适应滤波器进行自适应建模，逆建模，及控制器的设计。提出了一种带自适应扰动消除器和反馈补偿的非线性自适应逆控制系统。仿真结果证明了这种非线性自适应逆控制系统收敛速度非常快，消除扰动能力很强。具有应用价值。
最后，给出了自适应逆控制的两个应用。第一个应用是用自适应逆控制的原理设计了一种新的抗噪声电话。第二个应用是将自适应逆控制应用到可控硅直流调速系统中。
The feedback control mode of conventional control and adaptive control is to enhance the system's performance and to erase disturbance through feeding back output and disturbance simultaneously. Adaptive inverse control doesn't need too much advanced knowledge. We can design good adaptive inverse control without knowing plant's mathematic model. The control of plant's dynamic response and plant's disturbance erasion is respectively done. They don't impact each other. So we can best enhance the system's performance and erase disturbance. We can not only acquire good dynamic response, but also make noise and disturbance minimum. In this paper, we concentrate on adaptive inverse control and its appliance.
Firstly, based on the classical adaptive inverse control theories, linear adaptive control is studied and two kind of improved adaptive inverse control is put forward. Based on X-filtered LMS algorithm and -filtered LMS algorithm adaptive inverse control, we use a new variable step size LMS algorithm. Adding little computation, variable step size LMS algorithm can result in fast convergence speed and low residual error simultaneously. The adaptive feedback control can counteract the beginning error of the system. The adaptive disturbance canceler can best erase noises and disturbances.
Secondly, nonlinear adaptive inverse control is researched. We introduce a kind of shunt-wound structure with a linear adaptive filter and a nonlinear adaptive filter. Using it, we design adaptive modeling, adaptive inverse modeling and controller. This paper presents a kind of nonlinear adaptive inverse control with -filtered algorithm, which has adaptive disturbance canceler and feedback compensation in it. Simulation studies have shown that this nonlinear adaptive inverse control system can erase disturbances and result in fast convergence speed. So it is convenient for appliance.
Finally, two appliance of adaptive inverse control are given in this paper. The first appliance is a new anti-noise telephone based on adaptive inverse control theories. The second appliance is designing adaptive speed regulating systems using the theories of adaptive inverse control.
首先，论文研究了针对线性对象的自适应逆控制，在经典的自适应逆控制理论的基础上，提出了两种改进的自适应逆控制系统。在原来的X-滤波LMS算法自适应逆控制和-滤波LMS算法自适应逆控制方法的基础上，引入了新的变步长LMS算法，在计算量增加不多的前提下，能同时获得较快的收敛速度和较小的稳态误差；引入自适应的反馈补偿控制克服了被控系统的直流零频漂移，使控制系统在初开始工作阶段快速收敛；还引入自适应扰动消除器，它能最大限度的消除扰动。
其次，论文研究了非线性自适应逆控制。给出一种结构新颖的非线性自适应滤波器进行自适应建模，逆建模，及控制器的设计。提出了一种带自适应扰动消除器和反馈补偿的非线性自适应逆控制系统。仿真结果证明了这种非线性自适应逆控制系统收敛速度非常快，消除扰动能力很强。具有应用价值。
最后，给出了自适应逆控制的两个应用。第一个应用是用自适应逆控制的原理设计了一种新的抗噪声电话。第二个应用是将自适应逆控制应用到可控硅直流调速系统中。
The feedback control mode of conventional control and adaptive control is to enhance the system's performance and to erase disturbance through feeding back output and disturbance simultaneously. Adaptive inverse control doesn't need too much advanced knowledge. We can design good adaptive inverse control without knowing plant's mathematic model. The control of plant's dynamic response and plant's disturbance erasion is respectively done. They don't impact each other. So we can best enhance the system's performance and erase disturbance. We can not only acquire good dynamic response, but also make noise and disturbance minimum. In this paper, we concentrate on adaptive inverse control and its appliance.
Firstly, based on the classical adaptive inverse control theories, linear adaptive control is studied and two kind of improved adaptive inverse control is put forward. Based on X-filtered LMS algorithm and -filtered LMS algorithm adaptive inverse control, we use a new variable step size LMS algorithm. Adding little computation, variable step size LMS algorithm can result in fast convergence speed and low residual error simultaneously. The adaptive feedback control can counteract the beginning error of the system. The adaptive disturbance canceler can best erase noises and disturbances.
Secondly, nonlinear adaptive inverse control is researched. We introduce a kind of shunt-wound structure with a linear adaptive filter and a nonlinear adaptive filter. Using it, we design adaptive modeling, adaptive inverse modeling and controller. This paper presents a kind of nonlinear adaptive inverse control with -filtered algorithm, which has adaptive disturbance canceler and feedback compensation in it. Simulation studies have shown that this nonlinear adaptive inverse control system can erase disturbances and result in fast convergence speed. So it is convenient for appliance.
Finally, two appliance of adaptive inverse control are given in this paper. The first appliance is a new anti-noise telephone based on adaptive inverse control theories. The second appliance is designing adaptive speed regulating systems using the theories of adaptive inverse control.
引文
1 B.Widrow, K.M.Duvall, R.P.Gooch, and W.C.Newman. Signal Cancellation Phenomena in Adaptive Antennas:Causes and Curses. IEEE Trans.Antennas Propag,1982,30:469-478
2 R.T.Compton, JR., R.J.Huff, W.G.Swarnet, and A.A.Ksienski. Adaptive Arrays for Communication Systems:An Overview of Research at the Ohio State University. IEEE Trans.Antennas Propag,1976,24(5):599-606
3 E.Walach. On Superresolution Effects in Maximum-likelihood Antenna Arrays. IEEE Trans.Antennas Propag,1984,32(3):259-263
4 N.K.Jablon. Steady Stateanalysis of the Generalized Sidelobe Canceller by Adaptive Noise Canceling Techniques. IEEE Trans.Antenna Progag,1986,34: 330-337
5 R.D.Gitlin, J.F.Hayes and S.B.Weinstein. Data Communications Principles. New York:Plenum ,1992
6 S.Qureshi. Adaptive Equalization－a Comprehensive Review. IEEE Communications Magazine,1982:9-16
7 S.J.Campanella, H.G.Suyderhoud and M.Onufry. Analysis of an Adaptive Impulse Response Echo Canceller. Comsat Tech,1972,2(1):1-37
8 D.L.Duttweiler. A Twelve-channel Digital Echo Canceller. IEEE Trans. Communication,1978,26:647-653
9 D.L.Duttweiler, Y.S.Chen. Preformance and Features of a Single Chip FLSI Echo Canceller. NTC 79,Washington,1979:17-19
10 D.D.Falconer, K.H.Mueller and s.b.Weinstein. Simultaneous Two-way Data Transmission over a Two-wire Circuit. Proc.NTC,Dallas,1976
11 B.Widrow. Adaptive Noise Cancelling－Principles and Applications. Proc.IEEE,1975,63(12):1692-1716
12 J.Glover. Adaptive Noise cancellig Applied to Sinusoidal Interferences. IEEE Trans.Acoust,1977,25(6):484-491
13 M.J.Shensha. Non-Wiener Solutions of the Adaptive Noise Canceller with a Noisy Reference. IEEE Trans.Acoust,1980,28:468
14 L.J.Griffiths. An Adaptive Lattice Structure for Noise-Cancelling Applications. Proc.ICASSP-78,1978:87
15 L.J.Griffiths, R.S.Medaugh. Convergence Properties of an Adaptive Noise Cancelling Lattice Structure. Proc.1978 IEEE Conf.Decision and Control,1979:1357-1361
16 L.J.Griffiths. Rapid Measurement of Instantaneous Frequency. IEEE Trans.Acoust,1975,23:209-222
17 J.I.Makhoul, L.K.Cosell. Adaptive Lattice Analysis of Speech. IEEE Trans.Acoust,1981,29:654
18 F.Itakura, S.Saito. Digital Filtering Techniques for Speech Analysis and Synthesis. Proc.7th Int.Conf.Acoust,1971,3:261
19 K.Astrom, B.Wittenmark. Adaptive Control. Reading, Mass: Addison-Wesley, 1989
20 Widrow, E.Walach.自适应逆控制. 刘树棠,韩崇昭.西安:西安交通大学,2000
21 B.WIDROW. Adaptive Model Control Applied to Real-time Blood-pressure Regulation. Pattern Recognition and Machine Learning, New York, Plenum Rress,1971:310-324
22 B.Widrow, J.Mccool, and B.MEDOFF. Adaptive control by inverse modeling. Conf.Rec.of 12th Asilomar Conference on Circuits, Sant Clara, Systems and Computers,1978:90-94
23 B.Widrow, D.Shur and S.Shaffer. On Adaptive Inverse Control. Conf.Rec.of 15th Asilomar Conference on Circuits,Santa Clara, Systems and Computers,1981:185-189
24 S.Shaffer. Adaptive Inverse-model Control. Stanford University,1982
25 B.Wirow, S.D.Stearns. Adaptive Signal Processing. Englewood Cliffs:Prentice Hall,1985
26 E.Walach and B.Widrow. Adaptive Signal Processing For Adaptive Control. IFAC Workshop on Adaptive Systems in Control and Signal Processing,Sweden,1986
27 D.Psaltis, A.Sideris and A.A.Yamamamura. A Multilayered Neural Network Controller. IEEE Control Systems Magazine,1988,8:17-21
28 K.J.Hunt, D.Sbarbaro. Neural networks for Nonlinear Internal Model Control. IEEE Proceedings-D,1991,38(5):431-438
29 K.J.Hunt, D.Sbarbaro, R.Zbikowski and P.J.Ganthrop. Neural Networks for Control Systems-a Survey. Automatica,1992,28(6):1083-1112
30 B.Widrow, M.E.Hoff. Adaptive switching circuits. IRE WESCON Conv, 1960:96-104
31 B.Wirow, M.E.Hoff. Adaptive Switching Cricuits. IRE WESCON Conv, 1960:96-104
32 B.Wirow, J.M.Mccool. A Comparison of Adaptive Algorithms Based on the Methods of Steepest Descent and Random Search. IEEE Trans. Antennas Propag,1976,24(5):615-637
33 B.WIDROW, J.M.McCOOL, M.G.LARIMORE and C.R.JOHNSON. Stationary and Nonstationary Learning Characteristics of the LMS Adaptive Filter. Proc.IEEE,1976, 64(8):615-1162
34 B.Wirow. Adaptive Filters. R.E.Kalman and N.De Claris. Aspercts of Network and System Theory. New York,Holt, Rinehart and Winston,1970: 563-587
35 B.Wirow , E.Walach. On the Statistical Efficiency of the LMS Algorithm with Nonstationary Inputs. IEEE Trans.Info.Theory－Special Issue on Adaptive Filtering,1984,30(2):211-221
36 G.C.Goodwin, K.S.Sin. Adaptive Filtering,Prediction and Control. NJ:Prentice Hall,1984
37 L.LJung. System Identification－Theary for the User.NJ:Prentice Hall,1987
38 B.Widrow, S.D.Stearns. Adaptive Signal Processing. Englewood Cliffs: Prentice Hall, 1985
39 S.Haykin. Introduction to Adaptive Filter. New York:Macmillan,1984
40 S.Haykin. Adaptive Filter Theory. Englewood Cliffs:Prentice Hall,1986
41 J.R.Treichler, C.R.Johnson and M.G.Larimore. Theory and Design of Adaptive Filters. New York:John-Wiley,1987
42 C.F.N.Cowan, P.M.Grant. Adaptive Filters. Englewood Cliffs:Prentice Hall,1985
43 L.LJung. System Identification. MA:Addison-Wesley,1989
44 G.F.Franklin, J.D.Powell and M.L.Workman. Digital Control of Dynamic Systems. 2nd ed.MA:Addison-Wesley,1990
45 B.Widrow, J.M.Mccool. A Comparison of Adaptive algorithms Based on the Methods of Steepest Descent and Random Search. IEEE Trans.On Antennas and Propag,1976,24(5):615-637
46 B.Widrow, J.Mccool and B.Medoff. Adaptive Control by Inverse Modeling. Conf.Rec.of 12th Asilomar Conf,Santa Clara,CA,1978:90-94
47 B.Widrow, S.D.Stearns. Adaptive Signal Processing. NJ:Prentice Hall, 1985:288-300
48 Gitlin.R.D, Weinstein.S.B. On the Design of Gradient Algorithms for Digitally Implemented Adaptive Filters. IEEE Trans on CT,1973,(2):125-136
49 Yasukawa.H, Shimada.S and Furukrawa.I. Acoustic Echo Cancellers with High Speech Quality. ICASSP,1987:2125-2128
50 Gitlin.R.D, Weinstein.S.B. The Effects of Large Interference on the Tracking Capability of Digitally Implemented Echo Cancellers. IEEE Trans on COM,1978,(6):833-839
51 Clark.G.A, Mitra.S.K and Parker.S.R. Block Implementation of Adative Digital Filters. IEEE Trans on ASSP,1981,(3):744-753
52 叶华,吴伯修.变步长自适应滤波算法的研究.电子学报,1990,18(4):63-69.
53 覃景繁,欧阳景正.一种新的变步长LMS自适应滤波算法.数据采集与处理,1997,12(3):171-174
威德罗 B,史蒂恩斯 S D.自适应信号处理.王永德,龙宪惠.成都:四川大学出版
54 社,1989:40-56
55 沈福民.自适应信号处理.西安:西安电子科技大学出版社,2001:206-207
56 李仁厚等.智能控制理论与方法.西安:西安电子科技大学出版社, 1999:81-86
57 徐丽娜.神经元网络控制.哈尔滨:哈尔滨工业大学出版社,1999: 76-80
58 王永骥,涂健.神经元网络控制.北京:机械工业出版社,1998
59 王龙建.我国抗噪声电话技术的现状及其发展方向.电信科学，1998,(2):50-51
60 Courtiol.B and I.D.Landau, High Speed Adaptation System for Controlled Electrical Drives.Automatic,1975,11:119-127
61 英锐男,张茂青.可控硅直流调速系统的模型参考自适应控制. 中国自动化学会电气自动化委员会控制理论与应用学术交流会论文,1985
62 王礼信.一类模型参考自适应系统的工程设计方法.电气传动, 1987,3:51-54
63 陈伯时.自动控制系统.北京:机械工业出版社,1981
64 吴士昌,臧瀛芝,方敏.一种从参考模型取状态的MRACS设计方法.控制与决策,1986,4
65 路正午,吴忠强,吴士昌.任意相对阶数从模型取状态MRACS设计方法.控制与决策,1992,2
2 R.T.Compton, JR., R.J.Huff, W.G.Swarnet, and A.A.Ksienski. Adaptive Arrays for Communication Systems:An Overview of Research at the Ohio State University. IEEE Trans.Antennas Propag,1976,24(5):599-606
3 E.Walach. On Superresolution Effects in Maximum-likelihood Antenna Arrays. IEEE Trans.Antennas Propag,1984,32(3):259-263
4 N.K.Jablon. Steady Stateanalysis of the Generalized Sidelobe Canceller by Adaptive Noise Canceling Techniques. IEEE Trans.Antenna Progag,1986,34: 330-337
5 R.D.Gitlin, J.F.Hayes and S.B.Weinstein. Data Communications Principles. New York:Plenum ,1992
6 S.Qureshi. Adaptive Equalization－a Comprehensive Review. IEEE Communications Magazine,1982:9-16
7 S.J.Campanella, H.G.Suyderhoud and M.Onufry. Analysis of an Adaptive Impulse Response Echo Canceller. Comsat Tech,1972,2(1):1-37
8 D.L.Duttweiler. A Twelve-channel Digital Echo Canceller. IEEE Trans. Communication,1978,26:647-653
9 D.L.Duttweiler, Y.S.Chen. Preformance and Features of a Single Chip FLSI Echo Canceller. NTC 79,Washington,1979:17-19
10 D.D.Falconer, K.H.Mueller and s.b.Weinstein. Simultaneous Two-way Data Transmission over a Two-wire Circuit. Proc.NTC,Dallas,1976
11 B.Widrow. Adaptive Noise Cancelling－Principles and Applications. Proc.IEEE,1975,63(12):1692-1716
12 J.Glover. Adaptive Noise cancellig Applied to Sinusoidal Interferences. IEEE Trans.Acoust,1977,25(6):484-491
13 M.J.Shensha. Non-Wiener Solutions of the Adaptive Noise Canceller with a Noisy Reference. IEEE Trans.Acoust,1980,28:468
14 L.J.Griffiths. An Adaptive Lattice Structure for Noise-Cancelling Applications. Proc.ICASSP-78,1978:87
15 L.J.Griffiths, R.S.Medaugh. Convergence Properties of an Adaptive Noise Cancelling Lattice Structure. Proc.1978 IEEE Conf.Decision and Control,1979:1357-1361
16 L.J.Griffiths. Rapid Measurement of Instantaneous Frequency. IEEE Trans.Acoust,1975,23:209-222
17 J.I.Makhoul, L.K.Cosell. Adaptive Lattice Analysis of Speech. IEEE Trans.Acoust,1981,29:654
18 F.Itakura, S.Saito. Digital Filtering Techniques for Speech Analysis and Synthesis. Proc.7th Int.Conf.Acoust,1971,3:261
19 K.Astrom, B.Wittenmark. Adaptive Control. Reading, Mass: Addison-Wesley, 1989
20 Widrow, E.Walach.自适应逆控制. 刘树棠,韩崇昭.西安:西安交通大学,2000
21 B.WIDROW. Adaptive Model Control Applied to Real-time Blood-pressure Regulation. Pattern Recognition and Machine Learning, New York, Plenum Rress,1971:310-324
22 B.Widrow, J.Mccool, and B.MEDOFF. Adaptive control by inverse modeling. Conf.Rec.of 12th Asilomar Conference on Circuits, Sant Clara, Systems and Computers,1978:90-94
23 B.Widrow, D.Shur and S.Shaffer. On Adaptive Inverse Control. Conf.Rec.of 15th Asilomar Conference on Circuits,Santa Clara, Systems and Computers,1981:185-189
24 S.Shaffer. Adaptive Inverse-model Control. Stanford University,1982
25 B.Wirow, S.D.Stearns. Adaptive Signal Processing. Englewood Cliffs:Prentice Hall,1985
26 E.Walach and B.Widrow. Adaptive Signal Processing For Adaptive Control. IFAC Workshop on Adaptive Systems in Control and Signal Processing,Sweden,1986
27 D.Psaltis, A.Sideris and A.A.Yamamamura. A Multilayered Neural Network Controller. IEEE Control Systems Magazine,1988,8:17-21
28 K.J.Hunt, D.Sbarbaro. Neural networks for Nonlinear Internal Model Control. IEEE Proceedings-D,1991,38(5):431-438
29 K.J.Hunt, D.Sbarbaro, R.Zbikowski and P.J.Ganthrop. Neural Networks for Control Systems-a Survey. Automatica,1992,28(6):1083-1112
30 B.Widrow, M.E.Hoff. Adaptive switching circuits. IRE WESCON Conv, 1960:96-104
31 B.Wirow, M.E.Hoff. Adaptive Switching Cricuits. IRE WESCON Conv, 1960:96-104
32 B.Wirow, J.M.Mccool. A Comparison of Adaptive Algorithms Based on the Methods of Steepest Descent and Random Search. IEEE Trans. Antennas Propag,1976,24(5):615-637
33 B.WIDROW, J.M.McCOOL, M.G.LARIMORE and C.R.JOHNSON. Stationary and Nonstationary Learning Characteristics of the LMS Adaptive Filter. Proc.IEEE,1976, 64(8):615-1162
34 B.Wirow. Adaptive Filters. R.E.Kalman and N.De Claris. Aspercts of Network and System Theory. New York,Holt, Rinehart and Winston,1970: 563-587
35 B.Wirow , E.Walach. On the Statistical Efficiency of the LMS Algorithm with Nonstationary Inputs. IEEE Trans.Info.Theory－Special Issue on Adaptive Filtering,1984,30(2):211-221
36 G.C.Goodwin, K.S.Sin. Adaptive Filtering,Prediction and Control. NJ:Prentice Hall,1984
37 L.LJung. System Identification－Theary for the User.NJ:Prentice Hall,1987
38 B.Widrow, S.D.Stearns. Adaptive Signal Processing. Englewood Cliffs: Prentice Hall, 1985
39 S.Haykin. Introduction to Adaptive Filter. New York:Macmillan,1984
40 S.Haykin. Adaptive Filter Theory. Englewood Cliffs:Prentice Hall,1986
41 J.R.Treichler, C.R.Johnson and M.G.Larimore. Theory and Design of Adaptive Filters. New York:John-Wiley,1987
42 C.F.N.Cowan, P.M.Grant. Adaptive Filters. Englewood Cliffs:Prentice Hall,1985
43 L.LJung. System Identification. MA:Addison-Wesley,1989
44 G.F.Franklin, J.D.Powell and M.L.Workman. Digital Control of Dynamic Systems. 2nd ed.MA:Addison-Wesley,1990
45 B.Widrow, J.M.Mccool. A Comparison of Adaptive algorithms Based on the Methods of Steepest Descent and Random Search. IEEE Trans.On Antennas and Propag,1976,24(5):615-637
46 B.Widrow, J.Mccool and B.Medoff. Adaptive Control by Inverse Modeling. Conf.Rec.of 12th Asilomar Conf,Santa Clara,CA,1978:90-94
47 B.Widrow, S.D.Stearns. Adaptive Signal Processing. NJ:Prentice Hall, 1985:288-300
48 Gitlin.R.D, Weinstein.S.B. On the Design of Gradient Algorithms for Digitally Implemented Adaptive Filters. IEEE Trans on CT,1973,(2):125-136
49 Yasukawa.H, Shimada.S and Furukrawa.I. Acoustic Echo Cancellers with High Speech Quality. ICASSP,1987:2125-2128
50 Gitlin.R.D, Weinstein.S.B. The Effects of Large Interference on the Tracking Capability of Digitally Implemented Echo Cancellers. IEEE Trans on COM,1978,(6):833-839
51 Clark.G.A, Mitra.S.K and Parker.S.R. Block Implementation of Adative Digital Filters. IEEE Trans on ASSP,1981,(3):744-753
52 叶华,吴伯修.变步长自适应滤波算法的研究.电子学报,1990,18(4):63-69.
53 覃景繁,欧阳景正.一种新的变步长LMS自适应滤波算法.数据采集与处理,1997,12(3):171-174
威德罗 B,史蒂恩斯 S D.自适应信号处理.王永德,龙宪惠.成都:四川大学出版
54 社,1989:40-56
55 沈福民.自适应信号处理.西安:西安电子科技大学出版社,2001:206-207
56 李仁厚等.智能控制理论与方法.西安:西安电子科技大学出版社, 1999:81-86
57 徐丽娜.神经元网络控制.哈尔滨:哈尔滨工业大学出版社,1999: 76-80
58 王永骥,涂健.神经元网络控制.北京:机械工业出版社,1998
59 王龙建.我国抗噪声电话技术的现状及其发展方向.电信科学，1998,(2):50-51
60 Courtiol.B and I.D.Landau, High Speed Adaptation System for Controlled Electrical Drives.Automatic,1975,11:119-127
61 英锐男,张茂青.可控硅直流调速系统的模型参考自适应控制. 中国自动化学会电气自动化委员会控制理论与应用学术交流会论文,1985
62 王礼信.一类模型参考自适应系统的工程设计方法.电气传动, 1987,3:51-54
63 陈伯时.自动控制系统.北京:机械工业出版社,1981
64 吴士昌,臧瀛芝,方敏.一种从参考模型取状态的MRACS设计方法.控制与决策,1986,4
65 路正午,吴忠强,吴士昌.任意相对阶数从模型取状态MRACS设计方法.控制与决策,1992,2