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Frequency weighted controller reduction methods and loop transfer recovery. (English) Zbl 0714.93015

Summary: This paper shows that if one designs an LQG controller using the conventional technique of loop transfer recovery (LTR), then two frequency weighted controller reduction methods, the Enns’ frequency weighted balanced truncation [see D. F. Enns, “Model reduction for control systems design”, Ph.D. Thesis, Dep. Aeronatu. Astronaut., Stanford Univ./Calif. 1984; “Model reduction with balanced realizations”, Proc. 23rd IEEE Conf., Decis. Control, Las Vegas/NV (USA) 1984, Vol. 1, 127-132 (New York 1984)] and the Bezout identity induced frequency weighted reduction method [the authors, “Controller reduction: Concepts and approaches”, Proc. 1987 Am. Control Conf., Minneapolis/MN 1987, Vol. 1, 1-9 (Piscataway/NJ 1987); see also IEEE Trans. Autom. Control 34, No.8, 802-812 (1989; Zbl 0698.93034)] will be equivalent under the condition that the plant transfer function is square, nonsingular and minimum phase. We also show that Enns’ method is equivalent to the Bezout identity induced frequency weighted reduction method if the controller itself is stable and a particular representation for the controller is assumed.

MSC:

93B50 Synthesis problems
93B11 System structure simplification
49N05 Linear optimal control problems
49N70 Differential games and control
49N75 Pursuit and evasion games

Citations:

Zbl 0698.93034
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References:

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