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1、符合追蹤與強健功能要求之切換控制器設計( 結案報告) Design of Switching Controllers for Satisfying Tracking and Robust Performance Requirements計畫編號：NSC89-2218-E-146-002 執行期限：89 年 8 月 1 日 至 90 年 7 月 31 日 持人：吳 政 郎 職稱：助理教授 電子信箱：wujlcc.hwh.edu.tw 執行機構：私立華夏工商專校電子工程科一、中文摘要 在此計劃中, 我們研究對參數未知 之非線性系統的切換控制。控制目標是 設計切換控制器使系統穩定。對參數未 知的系統
2、，我們用多個數學模型去代表 它的可能動態，然後據以設計一組控制 器，一組預測器及一個切換法則，使得 系統實際操作時，能根據預測器的估計 誤差，依切換法則線上決定何時該切換 及該切換到哪個控制器去控制受控系統 讓閉迴路系統穩定。二、英文摘要 Based on observations of the past inputs and outputs of an unknown affine nonlinear system, a countable set of predictors is used to predict the system output sequence. Moreover, a
3、 countable set of controllers is designed to control the unknown system. Using performance measures derived from the resultant prediction errors, a decision rule is to be designed to select a controller at times i. We study the structure of decision rules that converge to some q such that the qth pr
4、ediction error sequence has desirable properties. Based on the selection of decision rule at time k, a controller for the considered systems is chosen from a family of predesigned control systems. We show that for certain continuous-time nonlinear systems, the result closed-loop controlled system is
5、 asymptotically stable.三、緣由與目的 We examine the problem of controlling a fixed nonlinear continuous-time plant with unknown parameters so that the closed-loop system is asymptotically stable. The control strategy that we analyze is based on switching among a family of fixed controllers at certain deci
6、sion times based on a switching logic that attempts to select a good predictor for the plant.There are several elements to the controller architecture. First, we have available a family of model-controller pairs ()ii, Pi. The index set Pis finite, countable. Controller i stabilizes i. For each model
7、, we run a corresponding predictor Oi driven by the inputs and outputs of the plant, and the resultant prediction errors are used to form a real-valued performance measure for ithpredictor. Then at certain decision times, a supervisor uses the performance measures to select a controller from the fam
8、ily i, i to be connected in feedback with the plant. The resultant nonlinear- switched control system must ensure asymptotical stability of the process states. We consider the simplest case in which the transfer function of the unknown plant exactly matches that of one of the known deterministic mod
9、els i , i. Although unrealistic, this situation is of theoretical interest since it provides a lower bound on what can be expected in practice. The above architecture for on-line controller switching has been proposed and examined in several special cases in 1-8, 10, 12, and 13. In 12 and 13 the pro
10、blem of tracking a constant set point for SISO linear time-invariant (LTI) systems is studied. At a sequence of decision times, the performance of the predictors is compared, and the controller corresponding to the best predictors at that time is selected. The sequence of selections is not required
11、to converge and in general will not do so. Nevertheless, the system variables remain bounded and the output of the SISO system converges to the constant set-point. In 7 and 10 switching is used to select a controller structure matched to the similarity invariants of the plant, and in 8 it is used to
12、 improve the transient performance of stable adaptive control schemes. In 4 convergent decision rules are studied. It is shown that for MIMO LTI systems there exists a convergent decision rule under which the supervised control system is stable and satisfies a 2performance criterion with respect to
13、a class of admissible inputs. Several other controller switching strategies have been examined in the literature. Generally, these involve strategies that use a predefined search sequence, e.g., 3, 5, and 6. Roughly, these operate by switching into feedback with the plant a predefined sequence of co
14、ntrollers in which each controller appears infinitely often. 四、研究方法及成果Consider a fixed but unknown discrete- time nonlinear system described by: =+=)()()0( ),()()()(:0 txhtyxxtutxgtxftx&wherenRtx)(is the state，mRtu)(is the control input, and rRty)(is the output. In this project, the control objectiv
15、e is to design a family of controllers p, p and a family of corresponding predictors pO, p, and choose a switching rule, such that at certain decision times, a supervisor uses the performance measures to select a controller from the family p, p to be connected in feedback with the plant such that th
16、e resultant nonlinear-switched control system is asymptotically stable.(a)、Predictors:We are given (or have constructed) a family of LTI Oi, Pipredictor with a state realization of the form=+=)()()( ),()()( )()()()( :00 tCtyttytytKtutNtMt Oiiiiiiiiiiii &Suppose )()()()(tCtKtMtiiiiii+=&is exponential
