Optimal decentralized control of large scale systems. (English) Zbl 1374.93019
Summary: This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.
MSC:
| 93A14 | Decentralized systems |
| 93A15 | Large-scale systems |
| 93B35 | Sensitivity (robustness) |
| 93C05 | Linear systems in control theory |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
Keywords:
decentralized control; multivariable control; PID control; robustness; large-scale systems; flexible structuresReferences:
| [1] | M. J. Balas. Active control of flexible systems. Journal of Optimization Theory and Applications, 1978, 25(3): 415–436. · Zbl 0362.93008 · doi:10.1007/BF00932903 |
| [2] | P. C. Hughes, R. E. Skelton. Modal truncation for flexible spacecraft. Journal of Guidance and Control, 1981, 4(3): 291–297. · doi:10.2514/3.56081 |
| [3] | L. Meirovitch, H. Oz. Modal-space control of large flexible spacecraft possessing ignorable coordinates. Journal of Guidance and Control, 1980, 3(6): 569–577. · Zbl 0471.93039 · doi:10.2514/3.56035 |
| [4] | M. J. Balas. Modal control of certain flexible dynamic systems. SIAM Journal of Control and Optimization, 1978, 16(3): 450–462. · Zbl 0384.93036 · doi:10.1137/0316030 |
| [5] | I. Bar-Kana, R. Fischl, P. Kalata. Direct position plus velocity feedback control of large flexible space structures. IEEE Transactions on Automatic Control, 1991, 36(10): 1186–1188. · doi:10.1109/9.90232 |
| [6] | R. J. Benhabib, R. P. Iwens, R. L. Jackson. Adaptive control for large space structures. IEEE Conference on Decision and Control, New York: IEEE, 1979: 214–217. |
| [7] | Y. Fujisaki, M. Ikeda, K. Miki. Robust stabilization of large space structures via displacement feedback. IEEE Transactions on Automatic Control, 2001, 46(12): 1993–1996. · Zbl 1011.93100 · doi:10.1109/9.975507 |
| [8] | S. M. Joshi. Control of Large Flexible Space Structures. Lecture notes in control and information sciences. Berlin: Springer, 1989. |
| [9] | S. S. Ahmad, J. S. Lew, L. H. Keel. Fault tolerant controller design for large space structures. IEEE International Conference on Control Applications, New York: IEEE, 1999: 63–68. |
| [10] | S. T. C. Huang, E. J. Davison, R. H. Kwong. Decentralized robust servomechanism problem for large flexible space structures under sensor and actuator failures. IEEE Transactions On Automatic Control, 2012, 57(12): 3219–3224. · Zbl 1369.93026 · doi:10.1109/TAC.2012.2200378 |
| [11] | G. S. West-Vukovich, E. J. Davison, P. C. Hughes. The decentralized control of large flexible space structures. IEEE Transactions on Automatic Control, 1984, 29(10): 866–879. · Zbl 0549.93005 · doi:10.1109/TAC.1984.1103392 |
| [12] | M. J. Balas. Trends in large space structure control theory: fondest hopes, wildest dreams. IEEE Transactions on Automatic Control, 1982, 27(3): 522–535. · Zbl 0496.93007 · doi:10.1109/TAC.1982.1102953 |
| [13] | H. B. Hablani. Generic model of a large flexible space structure for control concept evaluation. Journal of Guidance and Control, 1981, 4(5): 558–561. · doi:10.2514/3.56105 |
| [14] | E. J. Davison. The robust decentralized control of a general servomechanism problem. IEEE Transactions on Automatic Control, 1976, 21(1): 14–24. · Zbl 0326.93006 · doi:10.1109/TAC.1976.1101138 |
| [15] | E. J. Davison, B. Scherzinger. Perfect control of the robust servomechanism problem. IEEE Transactions on Automatic Control, 1987, 32(8): 689–702. · Zbl 0625.93051 · doi:10.1109/TAC.1987.1104691 |
| [16] | E. J. Davison, S. H. Wang. Properties and calculation of transmission zeros of linear multivariable systems. Automatica, 1974, 10(6): 643–658. · Zbl 0299.93018 · doi:10.1016/0005-1098(74)90085-5 |
| [17] | E. J. Davison, D. E. Davison, L. Simon. Multivariable three-term optimal controller design for large-scale systems. IEEE Conference on Decision and Control, New York: IEEE, 2009: 940–945. |
| [18] | E. J. Davison. Multivariable tuning regulators: the feedforward and robust control of a general servomechanism problem. IEEE Transactions on Automatic Control, 1976, 21(1): 35–47. · Zbl 0326.93008 · doi:10.1109/TAC.1976.1101126 |
| [19] | L. Qiu, B. Bernhardsson, A. Rantzer, et al. A formula for computation of the real stability radius. Automatica, 1995, 31(6): 879–890. · Zbl 0839.93039 · doi:10.1016/0005-1098(95)00024-Q |
| [20] | S. Lam, E. J. Davison. Computation of the real controllability radius and minimum-norm perturbations of high-order, descriptor, and time delay LTI systems. IEEE Transactions on Automatic Control, 2014, 59(8): 2189–2195. · Zbl 1360.93100 · doi:10.1109/TAC.2014.2298991 |
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