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• W2187072009 abstract "It is shown that the state feedback matrix of a linear system optimal with respect to a quadratic performance index can be expanded in a MacLaurin series in parameters which change the order of the system. The first two terms of this series are employed in a near-optimum design for a plant. The result of the near-optimum design is superior to that achieved by a conventional low-order design, while the amount of computation is considerably less than that required for a design. An example of a second-order design for a fifth-order plant is given. A ISTHODVCTIOK AIETHOD for designing approximately opt.inlal regulators for linear plants with quadratic performance indexes is proposed in this paper. The method is motivat,ed by t,he fact t,hat, the applica,tion of the existing design procedure (l), (2) t.0 plants represents a computationally difficult, and cumbersome task. It is well known t.hat the number of scalar equations, which correspond t,o t.he mat.ris Riccati equation, in- creases wit.h the square of the order of the plant equation. A conventiona.1 attempt to avoid this difficulty is to neglect. some small t.ilne const.ants, momenk of inert.ia, and similar parasitic pamrneters which increase the cquation order. In thc following thc approach based on such a descript,ion of the plant. is called the low-order dc4gn. The design based on a high-order description of t,he plant in wllich these parasitic param- et,ers are not neglect,ed is called the design. At, t,he present time a designer is left with t.he dilemma.: eit,her to apply the design lvhich is comput,a- tionally involved or to use a loworder design which is simpler, but which may result in a.n unsat,isfactory syst.em performance. The singular perturbat,ion method proposed here provides an a.nalytica1 tool for resolving this dilemma. It results in better system performance than achieved by the low-order design and requires considerably less computa- tion than the design. In t.his met,hod attent.ion is focused upon the dependence of the opt,imal feedback gain mat,rix K on small parameters whose presence increases t,he order of the plant equation. It is proved that K can be expa.nded in a AlacLaurin series with respect to t.hese parameters. The first term of this ex- pansion corresponds to the low-order design. The second term and, if necessary, several more terms are used as a near-opt,imum correct,ion of the low-order design. The effectiveness of the proposed method is illustrat,ed by a second-order dmign for a fifth-order plant,. This paper makes use of the singular perturbation theory of ordinary differential equations (3)-(GI. It represents further ext,ension and application of the method proposed in an earlier paper (?I. LOW-ORDER -4h'D HIGH-ORDER DESIGKS A compa.rison of the and low-order designs motivates the method developed here. Let" @default.
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• W2187072009 date "1969-01-01" @default.
• W2187072009 modified "2023-09-26" @default.
• W2187072009 title "Near-Optimum Design of Linear Systems by a Singular Perturbation Method" @default.
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