基于滚动时域的卫星姿态最优控制研究
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摘要
在轨卫星的姿态机动中,经常会希望系统满足某种意义上的最优条件。但是,卫星姿态控制中经常有模型非线性、不确定性和各种干扰存在。这些因素使得经典最优控制很难在卫星姿态控制中应用。另一方面,预测控制中的滚动时域方法能够实现近似的最优控制,然而其缺乏稳定性理论基础,而且这一控制律的仅能实现局部的最优控制。本文通过结合经典最优控制和滚动时域方法,构造了一种可应用于卫星姿态控制的最优控制方法,这一控制方法在保证全局稳定性的同时,在一定条件下能够实现全局的最优控制。之后对这种方法进行了仿真。对仿真结果进行了分析,研究了控制方法各部分计算量的来源,并结合计算量分析的结果,对控制算法进行了优化。
本文首先对最优控制的理论进行了分析,讨论了最优控制中代价函数和控制李雅普诺夫函数之间的联系。结合逆最优理论,分析了由控制李雅普诺夫函数求解最优控制的条件。研究了在特定条件下最优控制的解法,以及对应的最优控制问题的特点。对滚动时域控制的方法进行了分析。将滚动时域控制和控制李雅普诺夫函数的最优控制方法结合起来,证明了这种方法的条件最优性。
针对实际卫星控制的模型,本文考察姿态机动的控制特点,提出了控制李雅普诺夫函数的选取方法。结合卫星非线性的特性,提出了一种可行的数值滚动时域优化的计算方法。采用控制李雅普诺夫函数与设计的滚动时域优化方法进行了仿真。
针对滚动时域控制带来的计算量繁重的问题,本文分析了所用控制方法的计算过程,提出了一系列算法的优化方案,并对优化的效果进行了仿真验证。
In the control of satellite attitude maneuver, we always want the system meets optimal requirement. As the satellite usually has model uncertainty, nonlinearity and disturbance, it is difficult to use the classical optimal control on it. On the other hand, receding horizon control, which is a method of predictive control, can achieve a approximate optimal control. But the control law lacks stability proof and it only achieves a local optimal control. This dissertation combines the classical optimal control with receding horizon control, creates a kind of optimal control which can be used on the control of satellite attitude maneuver. The control law guarantees the global stability as well as achieves the global optimal control under certain condition. A simulation of this method is made. Based on the result of the simulation and the analyse of the algorithm, research on the computation amount is made. Several techniques are proposed to relieve the computational burden.
At first we discuss the theory of optimal control, the contact between the value function in optimal control and control Lyapunov function is analyzed. Basis on the theory of inverse optimal, the condition for calculating optimal control from control Lyapunov function is summarized. The algorithm under certain condition is proposed and its applicable range is analyzed. Also we analyze the method of receding horizon control. A control law which combines control Lyapunov function and receding horizon control is created and its optimality is proved.
Considering the features of attitude maneuver, rule of selecting control Lyapunov function is proposed based on the model of satellite in practice. A numerical algorithm of receding horizon control is proposed for the nonlinear system. A simulation is made with this control Lyapunov function and receding horizon control combined function.
As the receding horizon control brings a heavy burden of computation. We analyze the calculation process in control. Some techniques are proposed to simplified the algorithm. A simulation is made to check the effect of these techniques.
本文首先对最优控制的理论进行了分析,讨论了最优控制中代价函数和控制李雅普诺夫函数之间的联系。结合逆最优理论,分析了由控制李雅普诺夫函数求解最优控制的条件。研究了在特定条件下最优控制的解法,以及对应的最优控制问题的特点。对滚动时域控制的方法进行了分析。将滚动时域控制和控制李雅普诺夫函数的最优控制方法结合起来,证明了这种方法的条件最优性。
针对实际卫星控制的模型,本文考察姿态机动的控制特点,提出了控制李雅普诺夫函数的选取方法。结合卫星非线性的特性,提出了一种可行的数值滚动时域优化的计算方法。采用控制李雅普诺夫函数与设计的滚动时域优化方法进行了仿真。
针对滚动时域控制带来的计算量繁重的问题,本文分析了所用控制方法的计算过程,提出了一系列算法的优化方案,并对优化的效果进行了仿真验证。
In the control of satellite attitude maneuver, we always want the system meets optimal requirement. As the satellite usually has model uncertainty, nonlinearity and disturbance, it is difficult to use the classical optimal control on it. On the other hand, receding horizon control, which is a method of predictive control, can achieve a approximate optimal control. But the control law lacks stability proof and it only achieves a local optimal control. This dissertation combines the classical optimal control with receding horizon control, creates a kind of optimal control which can be used on the control of satellite attitude maneuver. The control law guarantees the global stability as well as achieves the global optimal control under certain condition. A simulation of this method is made. Based on the result of the simulation and the analyse of the algorithm, research on the computation amount is made. Several techniques are proposed to relieve the computational burden.
At first we discuss the theory of optimal control, the contact between the value function in optimal control and control Lyapunov function is analyzed. Basis on the theory of inverse optimal, the condition for calculating optimal control from control Lyapunov function is summarized. The algorithm under certain condition is proposed and its applicable range is analyzed. Also we analyze the method of receding horizon control. A control law which combines control Lyapunov function and receding horizon control is created and its optimality is proved.
Considering the features of attitude maneuver, rule of selecting control Lyapunov function is proposed based on the model of satellite in practice. A numerical algorithm of receding horizon control is proposed for the nonlinear system. A simulation is made with this control Lyapunov function and receding horizon control combined function.
As the receding horizon control brings a heavy burden of computation. We analyze the calculation process in control. Some techniques are proposed to simplified the algorithm. A simulation is made to check the effect of these techniques.
引文
1 Ding B, Li S. Design and analysis of constrained nonlinear quadratic regulator [J]. ISA Transactions, 2003, 42(3).
2 Kwon W H. Receding horizon control: model predictive control of state space model [M]. Springer-Verlag, 2004.
3 Johansen T A. Approximate explicit receding horizon control of constrained nolinear systems [J]. Automatica, 2004(40).
4 Ding B, Xi Y, Cychowski M T, et al. Improving off-line formulation of robust MPC based-on nominal performance cost [J]. Automatica, 2007.
5 Pluymers B, Suykens J A K, de Moor B. Min-max feedback MPC using a time-varying terminal constraint set and comments on“Efficient robust constrained model predictive control with a time-varying terminal constraint set”[J]. Systems and Control letters, 2005.
6 J. C. Doyle, K. Glover, P. Khargonekar, and B. Francis. State-space solutions to standard H 2 and H∞control problems. IEEE Trans. Aut. Control, 34(8):831{847, August 1989.
7 M. A. Dahleh and J. B. Pearson. l1 optimal feedback controllers for mimo discrete-time systems. IEEE Trans. Aut. Control, 32(4):314-322, 1987.
8 H. K. Khalil. Nonlinear systems. Macmillan Publishing Company, 1992.
9 E.D. Sontag. A 'universal' construction of Artstein's theorem on nonlinear stabilization. System & Control Letters, 13(2):117-123, 1989.
10 M. Krstic, I. Kanellakopoulos, and P. Kokotovic. Nonlinear and Adaptive Control Design. John Wiley & Sons, New York, 1995.
11 R. Kalman. When is a linear control system optimal. Trans. ASME Ser. D: J. Basic Eng., 86:1-10, 1964.
12 P. J. Moylan and B. D. O. Anderson. Nonlinear regulator theory and an inverse optimal control problem. IEEE Trans. Aut. Control, 18:460-464, October 1973.
13 R. Freeman and P. Kokotovic. Optimal nonlinear controllers for feedback linearizable systems. In Proceedings of the 1995 American Control Conference, pages 2722-2726, Seattle, Washington, June 1995.
14 R. Freeman and P. Kokotovic. Inverse optimality in robust stabilization. SIAM J. Contr. Optimiz., 34:1365-1391, July 1996.
15 C. E. Garc a, D. M. Prett, and M. Morari. Model predictive control: Theoryand practice - A survey. Automatica, 25(3):335-348, May 1989.
16 C. R. Cutler and B. L. Ramaker. Dynamic matrix control- A computer control algorithm. In Proceedings of the AIChE 86th National Meeting, Houston, Texas, April 1979.
17 J. Richalet, A. Rault, J. L. Testud, and J. Papon. Model predictive heuristic control: Applications to industrial processes. Automatica, 14(5):413-428, 1978.
18 J. Richalet. Industrial applications of model based predictive control. Automatica, 29:1251-1274, 1993.
19刘刚,李传江,马广富等.应用控制力矩陀螺的卫星姿态快速机动控制.航空学报,2011.
20金磊,徐世杰,采用单框架控制力矩陀螺和动量轮的航天器姿态跟踪控制研究.宇航学报,2008.
21李鹏奎,钱山,郭才发等.零动量轮卫星姿态控制系统研究.中国空间科学技术,2009.
22贾飞蕾,徐伟,李恒年等.基于联合飞轮和磁力矩器的航天器姿态控制算法研究.航天控制,2010.
23陈闽,张世杰,张迎春.基于反作用飞轮和磁力矩器的小卫星姿态联合控制算法.宇航学报, 2010.
24党冀萍,钱静.纳米卫星发展现状及纳米卫星中的微电子技术.半导体情报,1999.
25 S.W.Janson, H.Helvajian, E.Y.Tobinson. The concept of“nanosatellite”for revolutionary low-cost space systems, Proeeedings of the 44th Interantional Astronautics Federation Conference, Graz, Austria, Oct.1993.
26朱毅麟.电推进的现状与展望.上海航天,1998.
27 LUO JW. Fixed points and stability of neutral stochastic delay differential equations[J]. Math Anal App, 2007.
28 KSENDAL B. Stochastic diffusions equations[M]. 6th ed. New York: Spring, 2005.
29 P. Dorato, C. Abdallah, and V. Cerone. Linear Quadratic Control, A Introduction. Prentice Hall, Englewood Cliffs, New Jersey, 1995.
30 A. P. Sage. Optimum Systems Control. Prentice Hall, Englewood Cliffs, New Jersey, 1968.
31 M. Athans and P. L. Falb. Optimal Control. McGraw-Hill. Inc., 1966.
32 B. D. O. Anderson and J. B. Moore. Optimal Control; Linear Quadratic Methods. Prentice-Hall. Inc., Englewood Cliffs, New Jersey, 1989.
33 V. Nevistie. Constrained control of nonlinear systems. Ph.D. thesis. ETH Zurich. 1997.
34 R. Bellman. The theory of dynamic programming. In Proc. Nat. Acad. Sci. USA, number 38, 1952.
35 A. E. Bryson and Y. Ho. Applied Optimal Control. Hemisphere Publ. Corp., Washington D.C., 1975.
36 M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design. john Wiley & Sons, New York, 1995.
37 R. Freeman and J. Primbs. Control lyapunov functions: New ideas from an old source. In Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, December 1996.
38 H. W. Kuhn and A. W. Tucker. Nonlinear programming. In Proc. 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, 1961.
39 R. Freeman and P. Kokotovic. Robust Nonlinear Control Design. Birkhauser, Boston, 1996.
40 J.R. Cloutier, C.N. D’Souza, and C.P. Mracek. Nolinear regulation and nonlinear H∞Control via the state-dependent riccati equation technique In Proc. 1st Internat. Conf. on Nonl. Problems in Aviation and Aerospace, Daytona Beach, Florida, 1996.
2 Kwon W H. Receding horizon control: model predictive control of state space model [M]. Springer-Verlag, 2004.
3 Johansen T A. Approximate explicit receding horizon control of constrained nolinear systems [J]. Automatica, 2004(40).
4 Ding B, Xi Y, Cychowski M T, et al. Improving off-line formulation of robust MPC based-on nominal performance cost [J]. Automatica, 2007.
5 Pluymers B, Suykens J A K, de Moor B. Min-max feedback MPC using a time-varying terminal constraint set and comments on“Efficient robust constrained model predictive control with a time-varying terminal constraint set”[J]. Systems and Control letters, 2005.
6 J. C. Doyle, K. Glover, P. Khargonekar, and B. Francis. State-space solutions to standard H 2 and H∞control problems. IEEE Trans. Aut. Control, 34(8):831{847, August 1989.
7 M. A. Dahleh and J. B. Pearson. l1 optimal feedback controllers for mimo discrete-time systems. IEEE Trans. Aut. Control, 32(4):314-322, 1987.
8 H. K. Khalil. Nonlinear systems. Macmillan Publishing Company, 1992.
9 E.D. Sontag. A 'universal' construction of Artstein's theorem on nonlinear stabilization. System & Control Letters, 13(2):117-123, 1989.
10 M. Krstic, I. Kanellakopoulos, and P. Kokotovic. Nonlinear and Adaptive Control Design. John Wiley & Sons, New York, 1995.
11 R. Kalman. When is a linear control system optimal. Trans. ASME Ser. D: J. Basic Eng., 86:1-10, 1964.
12 P. J. Moylan and B. D. O. Anderson. Nonlinear regulator theory and an inverse optimal control problem. IEEE Trans. Aut. Control, 18:460-464, October 1973.
13 R. Freeman and P. Kokotovic. Optimal nonlinear controllers for feedback linearizable systems. In Proceedings of the 1995 American Control Conference, pages 2722-2726, Seattle, Washington, June 1995.
14 R. Freeman and P. Kokotovic. Inverse optimality in robust stabilization. SIAM J. Contr. Optimiz., 34:1365-1391, July 1996.
15 C. E. Garc a, D. M. Prett, and M. Morari. Model predictive control: Theoryand practice - A survey. Automatica, 25(3):335-348, May 1989.
16 C. R. Cutler and B. L. Ramaker. Dynamic matrix control- A computer control algorithm. In Proceedings of the AIChE 86th National Meeting, Houston, Texas, April 1979.
17 J. Richalet, A. Rault, J. L. Testud, and J. Papon. Model predictive heuristic control: Applications to industrial processes. Automatica, 14(5):413-428, 1978.
18 J. Richalet. Industrial applications of model based predictive control. Automatica, 29:1251-1274, 1993.
19刘刚,李传江,马广富等.应用控制力矩陀螺的卫星姿态快速机动控制.航空学报,2011.
20金磊,徐世杰,采用单框架控制力矩陀螺和动量轮的航天器姿态跟踪控制研究.宇航学报,2008.
21李鹏奎,钱山,郭才发等.零动量轮卫星姿态控制系统研究.中国空间科学技术,2009.
22贾飞蕾,徐伟,李恒年等.基于联合飞轮和磁力矩器的航天器姿态控制算法研究.航天控制,2010.
23陈闽,张世杰,张迎春.基于反作用飞轮和磁力矩器的小卫星姿态联合控制算法.宇航学报, 2010.
24党冀萍,钱静.纳米卫星发展现状及纳米卫星中的微电子技术.半导体情报,1999.
25 S.W.Janson, H.Helvajian, E.Y.Tobinson. The concept of“nanosatellite”for revolutionary low-cost space systems, Proeeedings of the 44th Interantional Astronautics Federation Conference, Graz, Austria, Oct.1993.
26朱毅麟.电推进的现状与展望.上海航天,1998.
27 LUO JW. Fixed points and stability of neutral stochastic delay differential equations[J]. Math Anal App, 2007.
28 KSENDAL B. Stochastic diffusions equations[M]. 6th ed. New York: Spring, 2005.
29 P. Dorato, C. Abdallah, and V. Cerone. Linear Quadratic Control, A Introduction. Prentice Hall, Englewood Cliffs, New Jersey, 1995.
30 A. P. Sage. Optimum Systems Control. Prentice Hall, Englewood Cliffs, New Jersey, 1968.
31 M. Athans and P. L. Falb. Optimal Control. McGraw-Hill. Inc., 1966.
32 B. D. O. Anderson and J. B. Moore. Optimal Control; Linear Quadratic Methods. Prentice-Hall. Inc., Englewood Cliffs, New Jersey, 1989.
33 V. Nevistie. Constrained control of nonlinear systems. Ph.D. thesis. ETH Zurich. 1997.
34 R. Bellman. The theory of dynamic programming. In Proc. Nat. Acad. Sci. USA, number 38, 1952.
35 A. E. Bryson and Y. Ho. Applied Optimal Control. Hemisphere Publ. Corp., Washington D.C., 1975.
36 M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design. john Wiley & Sons, New York, 1995.
37 R. Freeman and J. Primbs. Control lyapunov functions: New ideas from an old source. In Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, December 1996.
38 H. W. Kuhn and A. W. Tucker. Nonlinear programming. In Proc. 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, 1961.
39 R. Freeman and P. Kokotovic. Robust Nonlinear Control Design. Birkhauser, Boston, 1996.
40 J.R. Cloutier, C.N. D’Souza, and C.P. Mracek. Nolinear regulation and nonlinear H∞Control via the state-dependent riccati equation technique In Proc. 1st Internat. Conf. on Nonl. Problems in Aviation and Aerospace, Daytona Beach, Florida, 1996.