×

Design of an optimal preview controller for continuous-time systems. (English) Zbl 1228.49002

Summary: This paper studies the preview control problem for continuous-time control systems. A design method for an optimal preview controller is presented, when the desired tracking and disturbance are piecewise-continuously differentiable functions. Applying the same techniques as for in linear quadratic optimal control problems, we derive a type-one servomechanism with both desired tracking preview and disturbance preview compensation. A proof is presented that if the original system is stabilizable and detectable, the closed-loop system is asymptotically stable. We also design a full-dimensional state observer for the considered system. Finally, numerical simulations show the efficiency of the controller.

MSC:

49J15 Existence theories for optimal control problems involving ordinary differential equations
93B52 Feedback control
34K35 Control problems for functional-differential equations
Full Text: DOI

References:

[1] Liao F., Chinese J. Autom. 10 pp 329–
[2] DOI: 10.1080/0020718508961156 · Zbl 0566.93041 · doi:10.1080/0020718508961156
[3] DOI: 10.1002/(SICI)1099-1239(200002)10:2<101::AID-RNC465>3.0.CO;2-9 · Zbl 0944.93504 · doi:10.1002/(SICI)1099-1239(200002)10:2<101::AID-RNC465>3.0.CO;2-9
[4] DOI: 10.1115/1.1286869 · doi:10.1115/1.1286869
[5] DOI: 10.1142/S0219691309003094 · Zbl 1175.94027 · doi:10.1142/S0219691309003094
[6] Liao F., Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 10 pp 727–
[7] Liao F., J. Univ. Sci. Technol. Beijing 29 pp 542–
[8] Liao F., J. Univ. Sci. Technol. Beijing 30 pp 452–
[9] Liao F., Control Eng. China 16 pp 299–
[10] Liao F., J. Univ. Sci. Technol. Beijing 31 pp 520–
[11] Katayama T., Int. J. Control 43 pp 407–
[12] Briand D. O. A., Optimal Control (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.