双率采样数据系统自校正广义预测控制方法
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摘要
传统离散时间采样数据系统,假设输入信号更新速率和输出信号采样速率相等,这类系统简称为单率采样数据系统。然而,在许多化工过程中,由于硬件条件的限制,系统的采样输出周期往往要比系统控制输入周期大。这样,在同一个控制系统中就出现了两组甚至多组不同频率的采样数据,对应得到的系统称为双率或多率采样数据系统。研究对这类系统广义预测控制具有重要的理论意义和实际应用价值。论文在查阅了双率(多率)辨识和预测控制文献基础上,讨论了带有不同噪声的双率系统控制问题,将双率系统参数辨识方法与广义预测控制算法相结合,提出了一些新的双率采样数据系统的控制算法,取得了如下主要成果。
1.针对参数未知的确定性双率采样数据系统,阐述了基于参数估计的自校正广义预测控制策略,采用了递推最小二乘辨识算法估计系统模型参数,提出了确定性双率系统自校正广义预测控制方法。
2.针对双率随机系统模型(ARX模型),应用了递推最小二乘辨识算法对系统模型参数进行估计,然后应用自校正广义预测控制原理,提出了随机系统的最小二乘参数估计的自校正广义预测控制方法。又使用多项式变换技术导出了双率系统数学模型,提出了基于多项式变换的最小二乘参数估计自校正广义预测控制方法,仿真例子说明提出的控制算法能够跟踪系统参考轨迹。
3.针对双率随机系统,应用了随机梯度辨识算法来估计系统模型参数,然后应用自校正广义预测控制原理,提出了基于随机梯度参数估计的双率随机系统自校正广义预测控制方法和基于多项式变换的随机梯度参数估计的自校正广义预测控制方法,仿真例子得到了满意的效果。
4.论文进一步研究了有色噪声干扰(ARMAX系统模型)的双率随机系统预测控制问题,采用多项式变换技术,用增广最小二乘算法和增广随机梯度算法来估计双率系统模型参数,并应用广义预测控制原理,提出了有色噪声干扰的双率随机系统自校正广义预测控制方法,给出了仿真例子。
论文最后对整篇论文做了一个简短的总结,提出了一些在研究过程中尚未解决的问题,并为今后的研究指明了方向。
The conventional discrete-time sampled-data systems, whose outputs are sampled at the same rates as the control updating rates, are called single-rate systems. But, in many chemical industry processes, because of the hardware limitation, the sampled outputs period is longer than the control updating period. In this case, there are two or even more groups of different sampled-data in a system, such systems are named as dual-rate (multi-rate) sampled-data systems. Therefore, how to control these class of systems effectively is not only significant in theory. but also potential values in applications. Base on some existing identification and control algorithms of dual-rate (multi-rate) systems, This thesis discusses the control problem of dual-rate systems with different noises. Combining the identification algorithms of dula-rate systems with generalized predictive control algorithms, this thesis proposes some new control methods of dual-rate sampled-data systems, and the results are as follows.
1. Aim at the certain dual-rate sampled-data system models whose parameters are unknown, this thesis shows the strategy of self-tuning generalized predictive control based on the parameters estimation, uses the recursive least square identification algorithm to estimate the parameters of system models, and proposes self-tuning general predictive control method for the certain dual-rate systems.
2. Aim at dual-rate stochastic system models (ARX system models), by using recursive least square identification algorithm to estimate the parameters of system models and applying self-tuning generalized predictive control theory to control systems, this thesis proposes self-tuning general predictive control method based on the least square identification. In addition, a polynomial transformation technique is used to educe dual-rate mathematic as models, and self-tuning generalized predictive control methods based on the polynomial transformation technique and least square identification algorithm is proposed. The simulation examples demonstrate that the proposed control algorithms can track the reference trail of the systems.
3. Aim at dual-rate stochastic systems, by using stochastic gradient identification algorithm and self-tuning generalized predictive control alogrithm to estimate and control systems, this thesis proposes self-tuning generalized predictive control method based on the stochastic gradient identification algorithm and the polynomial transformation technique. The simulation examples are pressented.
4. This thesis studys the predictive control problem of dual-rate stochastic systems which have colored noises (ARMAX models), further. By using a polynomial transformation technique, extended least square identification algorithm and extended stochastic gradient identification algorithm to estimate these class of systems, and by applying self-tuning generalized predictive control algorithm to control them, a self-tuning generalized predictive control method for dual-rate systems which have colored noises is proposed. The simulation examples are presented.
Finally, the thesis gives a simple conclusion, proposes some solvable problems and points out the direction for further study.
1.针对参数未知的确定性双率采样数据系统,阐述了基于参数估计的自校正广义预测控制策略,采用了递推最小二乘辨识算法估计系统模型参数,提出了确定性双率系统自校正广义预测控制方法。
2.针对双率随机系统模型(ARX模型),应用了递推最小二乘辨识算法对系统模型参数进行估计,然后应用自校正广义预测控制原理,提出了随机系统的最小二乘参数估计的自校正广义预测控制方法。又使用多项式变换技术导出了双率系统数学模型,提出了基于多项式变换的最小二乘参数估计自校正广义预测控制方法,仿真例子说明提出的控制算法能够跟踪系统参考轨迹。
3.针对双率随机系统,应用了随机梯度辨识算法来估计系统模型参数,然后应用自校正广义预测控制原理,提出了基于随机梯度参数估计的双率随机系统自校正广义预测控制方法和基于多项式变换的随机梯度参数估计的自校正广义预测控制方法,仿真例子得到了满意的效果。
4.论文进一步研究了有色噪声干扰(ARMAX系统模型)的双率随机系统预测控制问题,采用多项式变换技术,用增广最小二乘算法和增广随机梯度算法来估计双率系统模型参数,并应用广义预测控制原理,提出了有色噪声干扰的双率随机系统自校正广义预测控制方法,给出了仿真例子。
论文最后对整篇论文做了一个简短的总结,提出了一些在研究过程中尚未解决的问题,并为今后的研究指明了方向。
The conventional discrete-time sampled-data systems, whose outputs are sampled at the same rates as the control updating rates, are called single-rate systems. But, in many chemical industry processes, because of the hardware limitation, the sampled outputs period is longer than the control updating period. In this case, there are two or even more groups of different sampled-data in a system, such systems are named as dual-rate (multi-rate) sampled-data systems. Therefore, how to control these class of systems effectively is not only significant in theory. but also potential values in applications. Base on some existing identification and control algorithms of dual-rate (multi-rate) systems, This thesis discusses the control problem of dual-rate systems with different noises. Combining the identification algorithms of dula-rate systems with generalized predictive control algorithms, this thesis proposes some new control methods of dual-rate sampled-data systems, and the results are as follows.
1. Aim at the certain dual-rate sampled-data system models whose parameters are unknown, this thesis shows the strategy of self-tuning generalized predictive control based on the parameters estimation, uses the recursive least square identification algorithm to estimate the parameters of system models, and proposes self-tuning general predictive control method for the certain dual-rate systems.
2. Aim at dual-rate stochastic system models (ARX system models), by using recursive least square identification algorithm to estimate the parameters of system models and applying self-tuning generalized predictive control theory to control systems, this thesis proposes self-tuning general predictive control method based on the least square identification. In addition, a polynomial transformation technique is used to educe dual-rate mathematic as models, and self-tuning generalized predictive control methods based on the polynomial transformation technique and least square identification algorithm is proposed. The simulation examples demonstrate that the proposed control algorithms can track the reference trail of the systems.
3. Aim at dual-rate stochastic systems, by using stochastic gradient identification algorithm and self-tuning generalized predictive control alogrithm to estimate and control systems, this thesis proposes self-tuning generalized predictive control method based on the stochastic gradient identification algorithm and the polynomial transformation technique. The simulation examples are pressented.
4. This thesis studys the predictive control problem of dual-rate stochastic systems which have colored noises (ARMAX models), further. By using a polynomial transformation technique, extended least square identification algorithm and extended stochastic gradient identification algorithm to estimate these class of systems, and by applying self-tuning generalized predictive control algorithm to control them, a self-tuning generalized predictive control method for dual-rate systems which have colored noises is proposed. The simulation examples are presented.
Finally, the thesis gives a simple conclusion, proposes some solvable problems and points out the direction for further study.
引文
1.Li D G,Shah S L,Chen T,Qi K Z.Application of dual-rate modelling to CCR octane quality inferential control[J].IEEE Transactions Control Systems Technology,2003,11(1):43-51
2.Huang Z W,Xu Y M,Fang C Z,Tang J.Improvements in dynamic compartmental modelling of distillation columns[J].Journal of Process Control,1993,3(3):193-145
3.方崇智,萧德云.过程辨识[M].北京:清华大学出版社,1988
4.冯培悌.系统辨识[M].杭州:浙江大学出版社,2004
5.谢新民,丁锋.自适应控制系统[M].北京:清华大学出版社,2002
6.韩曾晋.自适应控制[M].北京:清华大学出版社,1995
7.Ljung L.System Identification:Theory for the User(2nd edition)[M].Englewood Cliffs,NJ:Prentice-Hall,1999
8.Goodwin G C,Sin K S.Adaptive Filtering,Prediction and Control[M].Englewood Cliffs,NJ:Prentice-hall,1984
9.Sheng J,Chen T,Shah S L.Generalized predictive control for non-uniformly sampled systems[J].Journal of Process Control,2002,26(10):1493-1500
10.Lee,J H,Gelormino M S,Morari M.Model predictive pontrol of multirate sampling-data systems:A state-space approach[J].International Journal of Control,1992,55(1):153-191
11.刘勇,丁锋.模型参数未知的双率采样数据系统广义预测控制方法[J].科学技术与工程,2007,23(7):6055-6061
12.Ding F,Chen T.Identification of dual-rate systems based on finite impulse response models[J].International Journal of Adaptive Control and Signal Processing,2004,18(7):589-598
13.Ding F,Chen T.Combined parameter and output estimation of dual-rate systems using an auxiliary model[J].Automatica,2004,40(10):1739-1748
14.Ding F,Chen T.Modeling and identification for multirate systems[J].Automatica,2005,31(1):105-112
15.Ding F,Chen T.Least squares based self-tuning control of dual-rate systems[J].International Journal of Adaptive Control and Signal Processing,2004,18(8):697-714
16.Ding F,Chen T.Adaptive digital control of Hammerstein nonlinear systems with limited output sampling[J].SIAM Journal on Control and Optimization,2007,45(6):2257-2276
17.Bai E W.A blind approach to the Hammerstein-Wiener model identification[J].Automatica,2002,38(6):967-979
18.Ishitobi M,Kawanaka M,Nishi H.Ripple-suppressed multirate adaptive control[C].15th World Congress of the International Federation of Automatic Control,Barcelona,Spain,July 2002,pp.21-26
19.(A|¨)str(o|¨)m K J,Wittenmark B.On self-tuning regulators[J].Automatica,1973,9(2):185-199
20.Ding F,Chen T.A gradient based adaptive control algorithm for dual-rate systema[J].Asian Journal of Control,2006,8(4):314-323
21.王德进.H_2/H_∞优化控制理论[M].哈尔滨:哈尔滨工业大学出版社,2000
22.肖永松,丁锋.基于多项式变换的双率系统最小方差自校正控制[J].科学技术与工程,2008,8(5):1169-1172
23.丁锋,陈通文.多率系统模型与辨识[J].自动化学报,2005,31(1):105-122
24.Scattolini R,Schiavoni N.A multirate model-based predictive controller[J].IEEE Transactions Automatic Control,1995,40(6):1093-1097
25.张春峰,邹新杰,余张国.预测控制在过程控制中的应用综述[J].可编程控制器与工厂自动化,2006,31(1)12-14
26.Lee J H,Morari M.Robust iuferential control of multirate sampled-data systems[J].Chemical Engineering Science,1992,47(1):865-885
27.Li D G,Shah S L,Chen T,etc.Application of dual-rate modeling to CCR octane quality inferential control[J].IEEE Transactions Control Systems Technology,2003,11(1):43-51
28.Qiu L,Chen T.Multirate sampled-data systems:all H_∞ suboptimal controllers and the minimum entropy controller [J].IEEE Transactions Automatic Control,1999,44(3):537-550
29.Chen T,Qiu L.H_∞ design of general multirate sampled-data control systems[J].Automatic Control,1994,30(7):1139-1152
30.Al-Rahmani H M,Franklin G F.New optimal multirate control of linear periodic and time-invarinat systems[J].IEEE Transactions Automatica,1990,35(4):406-415
31.蔡自兴.智能控制原理及应用[M].北京:清华大学出版社,2007
32.章卫国,杨向忠.模糊控制理论与应用[M].西安:西北工业大学出版社,1999
33.董长虹.神经网络与应用[M].北京:国防工业出版社,2005
34.丁锋,陈通文,萧德云.一般双率系统状态空间模型及其辨识[J].自动化学报,2004,30(5):652-663
35.丁锋,陈通文,萧德云.非均匀周期采样多率系统的一种辨识方法[J].电子学报,2004,32(9):1414-1420
36.Ding F,Chen T.Parameter estimation of dual-rate stochastic systems by using an output error method[J].IEEE Transactions on Automatic Control,2005,50(9):1436 - 1441
37.Ding F,Chen T.Hierarchical identification of lifted state-space models for general dual-rate systems[J].IEEE Transactions on Circuits and Systems,2005,52(6):1179 - 1187
38.Ding F,Liu X P,Shi Y.Convergence analysis of estimation algorithms of dual-rate stochastic systems[J].Applied Mathematics and Computation,2006,176(1):245 - 261
39.丁锋,杨家本.大系统频域模型简化的两种方法[J].系统工程,1998,16(5):60-66
40.Clarke D C,Mohtadi C,Tuffs S P.Generalized predictive control Part-Ⅰ the basic algorithm[J].Automatica,1987,23(2):137 - 148
41.Clarke D C,Mohtadi C,Tuffs S P.Generalized Predictive Control Part-Ⅱ Extensions and interpretations[J].Automatica,1987,23(2):149 - 160
42.王伟.广义预测控制理论及其应用[M].北京:科学出版社,1998
43.舒迪前.预测控制系统及其应用[M].北京:机械工业出版社,1996
2.Huang Z W,Xu Y M,Fang C Z,Tang J.Improvements in dynamic compartmental modelling of distillation columns[J].Journal of Process Control,1993,3(3):193-145
3.方崇智,萧德云.过程辨识[M].北京:清华大学出版社,1988
4.冯培悌.系统辨识[M].杭州:浙江大学出版社,2004
5.谢新民,丁锋.自适应控制系统[M].北京:清华大学出版社,2002
6.韩曾晋.自适应控制[M].北京:清华大学出版社,1995
7.Ljung L.System Identification:Theory for the User(2nd edition)[M].Englewood Cliffs,NJ:Prentice-Hall,1999
8.Goodwin G C,Sin K S.Adaptive Filtering,Prediction and Control[M].Englewood Cliffs,NJ:Prentice-hall,1984
9.Sheng J,Chen T,Shah S L.Generalized predictive control for non-uniformly sampled systems[J].Journal of Process Control,2002,26(10):1493-1500
10.Lee,J H,Gelormino M S,Morari M.Model predictive pontrol of multirate sampling-data systems:A state-space approach[J].International Journal of Control,1992,55(1):153-191
11.刘勇,丁锋.模型参数未知的双率采样数据系统广义预测控制方法[J].科学技术与工程,2007,23(7):6055-6061
12.Ding F,Chen T.Identification of dual-rate systems based on finite impulse response models[J].International Journal of Adaptive Control and Signal Processing,2004,18(7):589-598
13.Ding F,Chen T.Combined parameter and output estimation of dual-rate systems using an auxiliary model[J].Automatica,2004,40(10):1739-1748
14.Ding F,Chen T.Modeling and identification for multirate systems[J].Automatica,2005,31(1):105-112
15.Ding F,Chen T.Least squares based self-tuning control of dual-rate systems[J].International Journal of Adaptive Control and Signal Processing,2004,18(8):697-714
16.Ding F,Chen T.Adaptive digital control of Hammerstein nonlinear systems with limited output sampling[J].SIAM Journal on Control and Optimization,2007,45(6):2257-2276
17.Bai E W.A blind approach to the Hammerstein-Wiener model identification[J].Automatica,2002,38(6):967-979
18.Ishitobi M,Kawanaka M,Nishi H.Ripple-suppressed multirate adaptive control[C].15th World Congress of the International Federation of Automatic Control,Barcelona,Spain,July 2002,pp.21-26
19.(A|¨)str(o|¨)m K J,Wittenmark B.On self-tuning regulators[J].Automatica,1973,9(2):185-199
20.Ding F,Chen T.A gradient based adaptive control algorithm for dual-rate systema[J].Asian Journal of Control,2006,8(4):314-323
21.王德进.H_2/H_∞优化控制理论[M].哈尔滨:哈尔滨工业大学出版社,2000
22.肖永松,丁锋.基于多项式变换的双率系统最小方差自校正控制[J].科学技术与工程,2008,8(5):1169-1172
23.丁锋,陈通文.多率系统模型与辨识[J].自动化学报,2005,31(1):105-122
24.Scattolini R,Schiavoni N.A multirate model-based predictive controller[J].IEEE Transactions Automatic Control,1995,40(6):1093-1097
25.张春峰,邹新杰,余张国.预测控制在过程控制中的应用综述[J].可编程控制器与工厂自动化,2006,31(1)12-14
26.Lee J H,Morari M.Robust iuferential control of multirate sampled-data systems[J].Chemical Engineering Science,1992,47(1):865-885
27.Li D G,Shah S L,Chen T,etc.Application of dual-rate modeling to CCR octane quality inferential control[J].IEEE Transactions Control Systems Technology,2003,11(1):43-51
28.Qiu L,Chen T.Multirate sampled-data systems:all H_∞ suboptimal controllers and the minimum entropy controller [J].IEEE Transactions Automatic Control,1999,44(3):537-550
29.Chen T,Qiu L.H_∞ design of general multirate sampled-data control systems[J].Automatic Control,1994,30(7):1139-1152
30.Al-Rahmani H M,Franklin G F.New optimal multirate control of linear periodic and time-invarinat systems[J].IEEE Transactions Automatica,1990,35(4):406-415
31.蔡自兴.智能控制原理及应用[M].北京:清华大学出版社,2007
32.章卫国,杨向忠.模糊控制理论与应用[M].西安:西北工业大学出版社,1999
33.董长虹.神经网络与应用[M].北京:国防工业出版社,2005
34.丁锋,陈通文,萧德云.一般双率系统状态空间模型及其辨识[J].自动化学报,2004,30(5):652-663
35.丁锋,陈通文,萧德云.非均匀周期采样多率系统的一种辨识方法[J].电子学报,2004,32(9):1414-1420
36.Ding F,Chen T.Parameter estimation of dual-rate stochastic systems by using an output error method[J].IEEE Transactions on Automatic Control,2005,50(9):1436 - 1441
37.Ding F,Chen T.Hierarchical identification of lifted state-space models for general dual-rate systems[J].IEEE Transactions on Circuits and Systems,2005,52(6):1179 - 1187
38.Ding F,Liu X P,Shi Y.Convergence analysis of estimation algorithms of dual-rate stochastic systems[J].Applied Mathematics and Computation,2006,176(1):245 - 261
39.丁锋,杨家本.大系统频域模型简化的两种方法[J].系统工程,1998,16(5):60-66
40.Clarke D C,Mohtadi C,Tuffs S P.Generalized predictive control Part-Ⅰ the basic algorithm[J].Automatica,1987,23(2):137 - 148
41.Clarke D C,Mohtadi C,Tuffs S P.Generalized Predictive Control Part-Ⅱ Extensions and interpretations[J].Automatica,1987,23(2):149 - 160
42.王伟.广义预测控制理论及其应用[M].北京:科学出版社,1998
43.舒迪前.预测控制系统及其应用[M].北京:机械工业出版社,1996
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