基于FPGA实现预测控制算法
摘要
本文主要研究了预测控制算法在FPGA(Field-Programmable Gate Array)可编程智能芯片上的实现,并利用Link For ModelSim接口,通过Simulink和ModelSim进行了混合仿真,实现了对三容对象的控制,验证了其可行性。
模型预测控制MPC(Model Predictive Control)是20世纪70年代后期在工业过程控制中发展起来的一种新型计算机控制算法,它对模型的精度要求不高,跟踪性能好,与传统的最优控制、自适应控制相比更适应于复杂的工业过程控制中不确定环境的需要。此外,预测控制还可以灵活、方便地处理输入、输出约束问题。因此,预测控制在现代工业控制中得到了越来越广泛的应用。然而,由于其算法复杂,运算量大,实时性较差,导致现有的预测控制算法仍主要适用中、大规模系统的优化控制。
基于MPC应用中的特点以及未来发展的需要,本文采用FPGA实现了MPC算法。作为专用集成电路领域中的一种半定制电路,FPGA的出现既解决了定制电路的不足,又克服了原有可编程器件门电路数有限的缺点。利用FPGA实现预测控制算法,可以大幅提高MPC的在线优化速度,减小控制器体积,扩大MPC的应用领域。
Model Predictive Control (MPC) has received increased industrial acceptance during recent years, mainly because of its ability to handle constraints explicitly and the natural way in which it can be applied to multi-variable processes. The computational requirements of MPC, which is typically a quadratic optimization problem solved on-line in every sample time, has previously prohibited its application in the areas where fast sampling is required. Therefore, MPC has mostly been applied to slow processes, for example in the chemical industry. How to find out the global optimum solution quickly is the most difficult aspect of the predictive control algorithms.
Lots of researchers have designed many efficient optimization algorithms, which have improved the speed of the algorithm’s performing. Among these people, some premote the method of FPGA inplement. This thesis presents a method which use the FPGA chip to implement the MPC controller. Compared to the traditional method, the FPGA can not only improve the speed of MPC, but also strengthen the stabilization of the controller. Furthermore, the method can reduce the area of the controller, so it can improve the embedded performance.
Refer to the hardware realization, there are two methods recently, one is to use the FPGA to achieve the MPC controller totally, the other is treating the FPGA as a co- processor. Between the two methods, because of the first is more simple the the second, I choose the first method to achieve the MPC algorithm. Otherwise, my thesis is to implement the linear MPC, it is simple so I decide to use the first method.
My thesis have done the following job.
First, based on the three tank object, build up the state space model of the system, and then linearize and disperse the model.
Second, using the VHDL language to achieve the models of the MPC controller. Including the matrix subtracter, the matrix adder, the Delta model, the Ep model and so on. Then, simulate the programs and change it to achieve the better performance.
Third, using the Link For ModelSim toolbox in simulink to link the Simulink and the ModelSim. Then control the three tank model by encapsulate the VHDL entity to the HDL Cosimulation model. Finally, amend the programs further based on the simulation map, so that it can achieve the perfect performance.
Above all, my thesis implement the FPGA into the MPC, and we can see that by using the FPGA, the speed of MPC controller can be improved more or less. The result indicate that the method is feasible and valuable.
模型预测控制MPC(Model Predictive Control)是20世纪70年代后期在工业过程控制中发展起来的一种新型计算机控制算法,它对模型的精度要求不高,跟踪性能好,与传统的最优控制、自适应控制相比更适应于复杂的工业过程控制中不确定环境的需要。此外,预测控制还可以灵活、方便地处理输入、输出约束问题。因此,预测控制在现代工业控制中得到了越来越广泛的应用。然而,由于其算法复杂,运算量大,实时性较差,导致现有的预测控制算法仍主要适用中、大规模系统的优化控制。
基于MPC应用中的特点以及未来发展的需要,本文采用FPGA实现了MPC算法。作为专用集成电路领域中的一种半定制电路,FPGA的出现既解决了定制电路的不足,又克服了原有可编程器件门电路数有限的缺点。利用FPGA实现预测控制算法,可以大幅提高MPC的在线优化速度,减小控制器体积,扩大MPC的应用领域。
Model Predictive Control (MPC) has received increased industrial acceptance during recent years, mainly because of its ability to handle constraints explicitly and the natural way in which it can be applied to multi-variable processes. The computational requirements of MPC, which is typically a quadratic optimization problem solved on-line in every sample time, has previously prohibited its application in the areas where fast sampling is required. Therefore, MPC has mostly been applied to slow processes, for example in the chemical industry. How to find out the global optimum solution quickly is the most difficult aspect of the predictive control algorithms.
Lots of researchers have designed many efficient optimization algorithms, which have improved the speed of the algorithm’s performing. Among these people, some premote the method of FPGA inplement. This thesis presents a method which use the FPGA chip to implement the MPC controller. Compared to the traditional method, the FPGA can not only improve the speed of MPC, but also strengthen the stabilization of the controller. Furthermore, the method can reduce the area of the controller, so it can improve the embedded performance.
Refer to the hardware realization, there are two methods recently, one is to use the FPGA to achieve the MPC controller totally, the other is treating the FPGA as a co- processor. Between the two methods, because of the first is more simple the the second, I choose the first method to achieve the MPC algorithm. Otherwise, my thesis is to implement the linear MPC, it is simple so I decide to use the first method.
My thesis have done the following job.
First, based on the three tank object, build up the state space model of the system, and then linearize and disperse the model.
Second, using the VHDL language to achieve the models of the MPC controller. Including the matrix subtracter, the matrix adder, the Delta model, the Ep model and so on. Then, simulate the programs and change it to achieve the better performance.
Third, using the Link For ModelSim toolbox in simulink to link the Simulink and the ModelSim. Then control the three tank model by encapsulate the VHDL entity to the HDL Cosimulation model. Finally, amend the programs further based on the simulation map, so that it can achieve the perfect performance.
Above all, my thesis implement the FPGA into the MPC, and we can see that by using the FPGA, the speed of MPC controller can be improved more or less. The result indicate that the method is feasible and valuable.
引文
[1] 席裕庚.预测控制,北京:国防出版社,1993
[2] Richalet J. Rault O. Testud J. L. Paon J.,Model Predictive heuristic control:Applica,Lions L.IndusLrial Processes, AuLomaLic, 1978, 14:413-428
[3] 席裕庚,许晓鸣,张钟俊.预测控制的研究现状和多层智能预测控制,控制理论及应用,1989,6(2):1-7
[4] 席裕庚,耿晓军,陈虹.预测控制性能研究的新进展.控制理论与应用,2000,17(4):469-475
[5] 徐立鸿.预测控制的研究现状及问题[J].控制理论与应用,1994,11(1):121-125
[6] 席裕庚.关于预测控制的进一步思考[J].控制理论与应用,1994,11(2):219-221
[7] 陈虹,刘志远,解晓华.非线性模型预测控制的现状与问题.控制与决策,2001,16(4):385-391
[8] Chen H,Allgower F. Nonlinear model predictive control schemes with guaranteed stability. Nonlinear Model Predictive Based Process Control[M]. Kluwer Academic Publishers,Netherlands:1998,465-494.
[9] H. Chen and F. Allgower. A computationally attractive nonlinear predictive control scheme with guaranteed stability for stable systems. J. Proc. Cont. 8(5-6):475-485,1998
[10] Chen H. Stability and robustness consideration in nonlinear model predictive control[M].Guessldorf.VDIVerlag,1997
[11] 杜晓宁,席裕庚,李少远.约束预测控制的一种快速算法.上海交通大学学报,2001,35(11):1624-1627
[12] 金元郁.一种约束输入的广义预测控制新算法. 控制与决策,2002,17(4):506-508
[13] 庞中华,金元郁.一种广义预测控制的快速算法.自动化技术与应用, 2005,24(3):03-05
[14] 赵怀彬,王诗宓.快速递推广义预测控制.控制理论与应用,1998,15(2):190-196
[15] 夏晓华,刘波,栾志业,金以慧.基于 PSO 的预测控制及在聚丙烯中的应用.控制工程,2006,13(5):401-403
[16] Leonidas G.Bleris,Panagiotis D.Vouzis,Mark G.Amold,Mayuresh V.Kothare. A Co-Processor FPGA Platform for the Implementation of Real-Time Model Predictive Control. Proceedings of the 2006 American Control Conference USA June 14-16 2006
[17] K.V.Ling,S.P.Yue and J.M.Maciejowski. A FPGA Implementation of Model Predictive Control. Proceedings of the 2006 American Control Conference USA,June 14-16 2006
[18] 朱明程.FPGA原理及应用设计.北京:电子工业出版社,1994.5
[19] Wayne Wolf 著,闫敬文等译.基于 FPGA 的系统设计= FPGA-based system design (美).北京:机械工业出版社,2006
[20] 王丹利, 王丽英.CPLD/FPGA 可编程逻辑器件实用教程.北京:机械工业出版社,2006
[21] 罗苑棠.CPLD/FPGA 常用模块与综合系统设计实例精讲.北京:电子工业出版社,2007
[22] 求是科技.CPLD/FPGA 应用开发技术与工程实践.北京:人民邮电出版社,2005
[23] 刘爱荣.EDA 技术与 CPLD/FPGA 开发应用简明教程.北京:清华大学出版社,2007.8
[24] 杨恒.零起点学单片机与 CPLD/FPGA.北京:北京航空航天大学出版社,2007
[25] 史小波,程梦璋,许会芳.集成电路设计 VHDL 教程.北京:清华大学出版社,2005
[26] 张昌凡,龙永红,彭涛.可编程逻辑器件及 VHDL 设计技术.广州:华南理工大学出版社,2001
[27] ModelSim SE Tutorial. ModelSim Advanced Verification and Debugging
[28] Mentor Graphics. ModelSim 高级 HDL 仿真和验证平台
[29] The Mathworks. Link For ModelSim 2 Cosimulate and verify VHDL and Verilog using ModelSim.
[30] R.Rouhani and R.K.Mehra. Model Algorithmic Control(MAC),Basic Theoretical Properties. Automatica,1982,18(4):401-414
[31] D.W.Clarke,C.Mohtadi and P.S.Tuffs. Generalized predictive control.pt.1. The Basic Algorithm,pt.2. Extensions and Interpretations. Automatica,1987,23(2):137-160
[32] E.Zafiriou. Robust model predictive control of processes with hard constraints. Computers chem..Engng,1990,14(4/5):359-371
[33] J.Richalet , A.Rault , J.L.Testud and J.Papon. Algorithmic control of industrial processes.Proc.4th IFAC Symposium on Identification and System Parameter Estimation.1119-1167,Tbilisi,1976
[34] Mayne D.Q. Optimization in model predictive control[A].Proc IFACDYCORD[C].Helsingor,1995,229-242
[35] 王献忠,杜维.模型预测控制发展概况.自动化与仪器仪表,1999(4):04-09
[36] 陈虹.Model Predictive Control 讲义.2007 年 4 月
[37] 王庆凤,陈虹.基于 LMI 的鲁棒 MPC 及其在三容系统中的应用.吉林大学学报,2006 年 3 月
[38] 高兴泉,刘淳,马苗苗,陈虹.基于非线性静态反馈解耦的三容系统 PI 控制.控制工程,2004 年 7 月
[39] 韩光信,张桂芹,施云贵.三容系统 H∞ 控制.吉林化工学院学报,2004 年 12 月
[40] 来晓岚、赵佳明、卢焕章.电子技术应用.长沙:国防科技大学,ATR 实验室,2006.08I
[41] 张伟.基于 Nios 的 SOPC 嵌入式系统的研究.计算机应用技术,2005.05
[42] 陆重阳,卢东华.FPGA 技术及其发展趋势.微电子技术,2003 年 2 月第三卷第一期
[43] FPGA/CPLD 数字电路设计经验分享,技术交流讲义
[44] 汤山俊夫著,彭军译.数字电路设计与制作.北京,科学出版社,2005
[45] John F. Wakerly 著,林生等译.数字设计原理与实践.北京:机械工业出版社,2003
[46] Charles H. Roth, Jr.著,解晓萌,黎永志,王坤等译.逻辑设计基础.北京:机械工业出版社,2005
[47] 陈燕东.可编程器件 EDA 应用开发技术.北京:国防工业出版社,2006
[48] 王开军,姜宇柏.面向 CPLD/FPGA 的 VHDL 设计.北京:机械工业出版社,2007
[49] 廖日坤.CPLD/FPGA 嵌入式应用开发技术白金手册.北京:中国电力出版社,2005
[50] Andrej Zemva, Matjaz Verderber. FPGA-oriented HW/SW implementation of the MPEG-4 video decoder.Science direct. 2006
[51] The Mathworks. Link For ModelSim 2 User’s Guide
[52] 蔡明发,周家荣,张逸凡,黄彦腾,王瑞坤.藉由 ModelSim 结合 Matlab 学习单相相控整流器原理与其实验验证.明新学报 32 期,2006 年
[2] Richalet J. Rault O. Testud J. L. Paon J.,Model Predictive heuristic control:Applica,Lions L.IndusLrial Processes, AuLomaLic, 1978, 14:413-428
[3] 席裕庚,许晓鸣,张钟俊.预测控制的研究现状和多层智能预测控制,控制理论及应用,1989,6(2):1-7
[4] 席裕庚,耿晓军,陈虹.预测控制性能研究的新进展.控制理论与应用,2000,17(4):469-475
[5] 徐立鸿.预测控制的研究现状及问题[J].控制理论与应用,1994,11(1):121-125
[6] 席裕庚.关于预测控制的进一步思考[J].控制理论与应用,1994,11(2):219-221
[7] 陈虹,刘志远,解晓华.非线性模型预测控制的现状与问题.控制与决策,2001,16(4):385-391
[8] Chen H,Allgower F. Nonlinear model predictive control schemes with guaranteed stability. Nonlinear Model Predictive Based Process Control[M]. Kluwer Academic Publishers,Netherlands:1998,465-494.
[9] H. Chen and F. Allgower. A computationally attractive nonlinear predictive control scheme with guaranteed stability for stable systems. J. Proc. Cont. 8(5-6):475-485,1998
[10] Chen H. Stability and robustness consideration in nonlinear model predictive control[M].Guessldorf.VDIVerlag,1997
[11] 杜晓宁,席裕庚,李少远.约束预测控制的一种快速算法.上海交通大学学报,2001,35(11):1624-1627
[12] 金元郁.一种约束输入的广义预测控制新算法. 控制与决策,2002,17(4):506-508
[13] 庞中华,金元郁.一种广义预测控制的快速算法.自动化技术与应用, 2005,24(3):03-05
[14] 赵怀彬,王诗宓.快速递推广义预测控制.控制理论与应用,1998,15(2):190-196
[15] 夏晓华,刘波,栾志业,金以慧.基于 PSO 的预测控制及在聚丙烯中的应用.控制工程,2006,13(5):401-403
[16] Leonidas G.Bleris,Panagiotis D.Vouzis,Mark G.Amold,Mayuresh V.Kothare. A Co-Processor FPGA Platform for the Implementation of Real-Time Model Predictive Control. Proceedings of the 2006 American Control Conference USA June 14-16 2006
[17] K.V.Ling,S.P.Yue and J.M.Maciejowski. A FPGA Implementation of Model Predictive Control. Proceedings of the 2006 American Control Conference USA,June 14-16 2006
[18] 朱明程.FPGA原理及应用设计.北京:电子工业出版社,1994.5
[19] Wayne Wolf 著,闫敬文等译.基于 FPGA 的系统设计= FPGA-based system design (美).北京:机械工业出版社,2006
[20] 王丹利, 王丽英.CPLD/FPGA 可编程逻辑器件实用教程.北京:机械工业出版社,2006
[21] 罗苑棠.CPLD/FPGA 常用模块与综合系统设计实例精讲.北京:电子工业出版社,2007
[22] 求是科技.CPLD/FPGA 应用开发技术与工程实践.北京:人民邮电出版社,2005
[23] 刘爱荣.EDA 技术与 CPLD/FPGA 开发应用简明教程.北京:清华大学出版社,2007.8
[24] 杨恒.零起点学单片机与 CPLD/FPGA.北京:北京航空航天大学出版社,2007
[25] 史小波,程梦璋,许会芳.集成电路设计 VHDL 教程.北京:清华大学出版社,2005
[26] 张昌凡,龙永红,彭涛.可编程逻辑器件及 VHDL 设计技术.广州:华南理工大学出版社,2001
[27] ModelSim SE Tutorial. ModelSim Advanced Verification and Debugging
[28] Mentor Graphics. ModelSim 高级 HDL 仿真和验证平台
[29] The Mathworks. Link For ModelSim 2 Cosimulate and verify VHDL and Verilog using ModelSim.
[30] R.Rouhani and R.K.Mehra. Model Algorithmic Control(MAC),Basic Theoretical Properties. Automatica,1982,18(4):401-414
[31] D.W.Clarke,C.Mohtadi and P.S.Tuffs. Generalized predictive control.pt.1. The Basic Algorithm,pt.2. Extensions and Interpretations. Automatica,1987,23(2):137-160
[32] E.Zafiriou. Robust model predictive control of processes with hard constraints. Computers chem..Engng,1990,14(4/5):359-371
[33] J.Richalet , A.Rault , J.L.Testud and J.Papon. Algorithmic control of industrial processes.Proc.4th IFAC Symposium on Identification and System Parameter Estimation.1119-1167,Tbilisi,1976
[34] Mayne D.Q. Optimization in model predictive control[A].Proc IFACDYCORD[C].Helsingor,1995,229-242
[35] 王献忠,杜维.模型预测控制发展概况.自动化与仪器仪表,1999(4):04-09
[36] 陈虹.Model Predictive Control 讲义.2007 年 4 月
[37] 王庆凤,陈虹.基于 LMI 的鲁棒 MPC 及其在三容系统中的应用.吉林大学学报,2006 年 3 月
[38] 高兴泉,刘淳,马苗苗,陈虹.基于非线性静态反馈解耦的三容系统 PI 控制.控制工程,2004 年 7 月
[39] 韩光信,张桂芹,施云贵.三容系统 H∞ 控制.吉林化工学院学报,2004 年 12 月
[40] 来晓岚、赵佳明、卢焕章.电子技术应用.长沙:国防科技大学,ATR 实验室,2006.08I
[41] 张伟.基于 Nios 的 SOPC 嵌入式系统的研究.计算机应用技术,2005.05
[42] 陆重阳,卢东华.FPGA 技术及其发展趋势.微电子技术,2003 年 2 月第三卷第一期
[43] FPGA/CPLD 数字电路设计经验分享,技术交流讲义
[44] 汤山俊夫著,彭军译.数字电路设计与制作.北京,科学出版社,2005
[45] John F. Wakerly 著,林生等译.数字设计原理与实践.北京:机械工业出版社,2003
[46] Charles H. Roth, Jr.著,解晓萌,黎永志,王坤等译.逻辑设计基础.北京:机械工业出版社,2005
[47] 陈燕东.可编程器件 EDA 应用开发技术.北京:国防工业出版社,2006
[48] 王开军,姜宇柏.面向 CPLD/FPGA 的 VHDL 设计.北京:机械工业出版社,2007
[49] 廖日坤.CPLD/FPGA 嵌入式应用开发技术白金手册.北京:中国电力出版社,2005
[50] Andrej Zemva, Matjaz Verderber. FPGA-oriented HW/SW implementation of the MPEG-4 video decoder.Science direct. 2006
[51] The Mathworks. Link For ModelSim 2 User’s Guide
[52] 蔡明发,周家荣,张逸凡,黄彦腾,王瑞坤.藉由 ModelSim 结合 Matlab 学习单相相控整流器原理与其实验验证.明新学报 32 期,2006 年