外文翻譯--雙速率數(shù)據(jù)采樣系統(tǒng)的仿真

1、<p><b>　　中文2630字</b></p><p>　　Simulation of dual-rate sampled-data system</p><p>　　Abstract: The simulation problem of a dual-rate system is studied by applying discrete lifting

2、 technology, quick sampling operator and quick hold operator. The method can achieve the result that is close to the simulation of continuous-time signal. The concrete simulation is steped and programmed with a real exam

3、ple under MATLAB environment.</p><p>　　Key words: Dual-rate sampled-data system; Discrete lifting technology; Quick sampling operator; Quick hold operator</p><p>　　Introduction</p><p&

4、gt;　　Sampling control system refers to the object controller for the continuous and digital systems. At present, most control systems are continuously charged by the object under the control of the computer realization o

5、f discrete sampling control system. With the continuous improvement of the system requirements, single-rate sampled-data systems can not meet the requirements, so multi-rate sampled-data systems in place. Multi-rate samp

6、ling control system works in practice with the prospect of a wide</p><p>　　1) In the complex multi-variable control system, requires that all physical signals in the same sampling frequency is not realistic.

7、</p><p>　　2) sampling and to maintain the higher frequency, the better the performance of the system, but the fast A / D and D / A conversion means that the cost is. So for different signal bandwidth, you sh

8、ould use a different A / D and D / A conversion rate, in order to achieve performance and the best compromise between price.</p><p>　　3) multi-rate controller is generally time-varying controller, it has a s

9、ingle-rate controller can not compare the merits. Such as increasing the system gain margin, consistent with the stability of the system to facilitate the realization of decentralized control. </p><p>　　A re

10、latively simple multi-rate sampled-data control system is dual-rate sampled-data systems, virtual box as shown in Figure 1. Simulation of the system is defined as: for a given input signal w, simulation of its continuous

11、 output signal z process.</p><p>　　Figure 1 dual-rate sampled-data systems wth a virtual sampler and holder</p><p>　　Literature [4] is given a single-rate sampling of high-precision control syst

12、em simulation. In single-rate sampled-data systems exist in only a single sampling period, thus only the application of the simulation process of some of the more sophisticated theory, such as the continuous transfer fun

13、ction of a single rate discrete. Dual-rate sampled-data systems, because of the existence of two types of sampling period, and the controller too variable controller, thus increasing the difficulty of th</p><p

14、>　　In this paper, discrete technological upgrading, the system in two different sampling period organically linked to the controller into a time-varying time-invariant controller. At the same time, the use of rapid sa

15、mpling and rapid operator to maintain, given the dual-rate sampling control system simulation method. </p><p>　　Prior knowledge</p><p>　　Figure 1 sampler sampling period T1 = ph, sampling operat

16、or S: y (k) = Syc (t) = yc (kph), holder of the sampling period T2 = qh, maintain operator H: uc (kqh + r) = Hu (k), 0 <r <qh. One: p and q for coprime positive integer, h as the basic sampling interval. L set up f

17、or the least common multiple of p and q, then T = lh for T1 and T2 times of the smallest cycle of the public. So p1 = l / p, q1 = l / q, while T = lh = p1ph = q1qh set up.</p><p>　　G for the generalized plan

18、t, the state-space realization for</p><p>　　K discrete controller for dual-rate should be appropriate to meet the causal nature of the cyclical and finite-dimensional.</p><p>　　For any T> 0,

19、Dr space for the continuous delay operator, that is, Druc (t) = uc (tT); U space for the discrete step lag operator; U2 for the discrete space operator step ahead. </p><p>　　1 If the definition of (U2) q1KUp

20、1 = K to set up, said K for the (p, q) - discrete controller cycle. </p><p>　　2 If the definition of G for the system to meet the DrG = GDr, said the G for the T-cycle for time-varying systems. </p>&

21、lt;p>　　3 Simulation Algorithm</p><p>　　Simulation of the expression </p><p>　　K is a known theorem (p, q) - cycle of discrete controllers, operator and maintenance of sampling operator as men

22、tioned above, the HKS for the T-cycle for time-varying systems. See Figure 1 to prove the relationship between the signal, there are established under the style</p><p>　　we can see from the definition 2,HKS

23、for the T-cycle for time-varying systems. HKS is a cycle as a result of T, so the case with the single rate is similar to Figure 1 in the relationship between input and output systems can be expressed as</p><p

24、><b>　　Or</b></p><p>　　Dual-rate sampling control system input and output channels, by adding a virtual sampler and maintain fast, and as shown in Figure 1, the virtual fast sampler and holder

25、of the sampling period T / n.</p><p>　　Wd is the w to T / n for the sampling period of the sampling signal, when the input signal mph time for the simulation, there Wd = w (kT / n), k = 0,1, ..., mn/p1 </

26、p><p>　　zd and the relationship between z Ibid. Clearly, when n → ∞ when, wd = w, zd = z. To make the number of discrete-time sequence for positive integer, n as the integer multiple of l. Study shown in Figure

27、 1 of the simulation system, virtual box can be dual-rate sampling control system input and output signals for the simulation results. </p><p>　　Figure 1 zd = Snz, w = Hnwd, it is by the type (2) </p>

28、<p>　　Which G11n, G12n, G21n to correspond to the cycle of T / n of the discretization.</p><p>　　Formula (4) is dual-rate sampling control system simulation expression. </p><p>　　Simulatio

29、n of the calculation of expression </p><p>　　Expression of desire (4), first obtained G11n, G12n, G21n, SnH, SHn, (I-KSG22H)-1K, etc. value. Which G11n, G12n, G21n continuous transfer function of G11, G12, G

30、21 single-cycle T / n of the discretization are easy to calculate. Discussed below SnH, SHn, (I-KSG22H)-1K calculations. </p><p>　　(1) SnH calculation</p><p>　　Figure 2 Expressiong for Input an

31、d Output of SHn</p><p>　　Figure 2 of the cycle in Hn for T / n = lh / n, S the cycle ph, while x2 (0) = x1 (0), x2 (1) = x1 (n/p1), ..., x2 (m -1) = x1 ((m-1) n/p1), It is SHn =</p><p>　　(2) SnH

32、 calculation</p><p>　　Similarly available expression SnH</p><p>　　(3) (I-KSG22H)-1K calculation </p><p>　　By discrete sampling and the discrete operator to maintain the definition o

33、f operator, there are</p><p>　　Ψ (k) = Φ (kp)Sp2l → l, Ψ = SpΦ </p><p>　　υ (kq + r) = Φ (k)Hq2l → l υ = HqΦ</p><p>　　R = 0,1, ..., q-1 </p><p>　　SG22H = SrSAG22HhHq =

34、SpG22dHq (5) </p><p>　　G22d which can be separated by a single rate process h been. For (I-KSpG22dHq)-1K is still the cycle of change SpG22dHq and K, this paper discrete operator to upgrade to turn it into t

35、ime-invariant systems, the specific process as shown in Figure 3. Simulation of expression at this time (4) can be expressed as Figure 4. </p><p>　　Enhanced by the discrete, periodic time-varying link SpG22d

36、Hq and K into the time-invariant Lp1SpG22dHqL-1 q1 and Lq1K L-1 q1, calculated as follows: </p><p>　　Lq1K L-1 q1 calculation</p><p>　　If the dual-rate controller of the state equation for K</

37、p><p>　　While Lq1K L-1 q1 state equation can be expressed as</p><p>　　Among which</p><p>　　Figure 3 (I-KSG22H)-1K to upgrade the discrete signal</p><p>　　Figure 4 (4) simu

38、lation indicate</p><p><b>　　,</b></p><p>　　Lp1SpG22dHqL-1 q1 calculation </p><p>　　Lemma 1 for P for the state variables x, the state model for [A, B, C, D], m, n and s

39、meet the following relationship is positive integer. The system state variables for the discrete sampling operator can be expressed as a state model. Which</p><p>　　Among which</p><p>　　Characte

40、ristics function X</p><p><b>　　Take,</b></p><p>　　Conclusions from the Appeal, G22d obtained from Lp1SpG22dHqL-1 q1 of the state space model. </p><p>　　Integrated on the

41、 system, we can see in Figure 4 for the simulation process: mph input signal period, then</p><p>　　Simulation example</p><p>　　Figure 1 for the generalized plant G</p><p>　　And cont

42、roller K is </p><p>　　Sampling period T1 = 2s, T2 = 3s, p = 2, q = 3, h = 1, p1 = 3, q1 = 2, l = 6, T = 6. So that m = 6, n, respectively, for 4800,7200, 9600, wd for unit step input signal. Using MATLAB pro

43、gramming language, and the system simulation, the results shown in Figure 5.</p><p>　　Conclusion</p><p>　　In this paper, dual-rate sampling control system of the characteristics of discrete appl

44、ications to upgrade their skills, rapid sampling and rapid operator to maintain operator to study the dual-rate sampling control system simulation methods, and gives concrete examples of simulation steps and guidelines.

45、Dual-rate controller as a result of changing the controller too, so the dual-rate sampled-data control system simulation to verify the accuracy of the problem to be further studied.</p><p>　　Sampling control

46、 system technology has undergone more than a decade of development, but there is a fundamental problem. Especially since the use of upgraded technology, sampling control theory has entered a new stage of development. Bec

47、ause it can take into account the performance between the sampling moment, therefore seems to enhance the transformation has become a sampling control system analysis and design of the only correct way, and their use is

48、also expanding, but in the real design was b</p><p>　　雙速率數(shù)據(jù)采樣系統(tǒng)的仿真</p><p>　　摘要：雙速率系統(tǒng)的仿真問題是采用離散提升技術(shù)、快速采樣算子和快速保持算子來研究的。該模型實現(xiàn)的結(jié)果與連續(xù)信號非常相近。最后給出具體地仿真步驟，并結(jié)合實例在MATLAB環(huán)境下編程實現(xiàn)。</p><p>　　關(guān)鍵詞：

49、雙速率數(shù)據(jù)采樣系統(tǒng)，離散提升技術(shù)，快速采樣算子，快速保持算子</p><p><b>　　1.簡介</b></p><p>　　采樣控制系統(tǒng)是指連續(xù)和數(shù)字系統(tǒng)的對象控制器。目前，大多數(shù)的控制系統(tǒng)是繼續(xù)的由計算機(jī)實現(xiàn)的采樣控制系統(tǒng)控制器實現(xiàn)的。隨著對系統(tǒng)要求的不斷提高，單速率的采樣控制系統(tǒng)變得不能滿足應(yīng)用的要求，因此其地位被混合采樣速率的采樣控制系統(tǒng)所替代?；旌喜蓸铀俾?/p>

50、控制系統(tǒng)在實際應(yīng)用中能夠滿足于很廣泛的應(yīng)用場合，這是因為：</p><p>　　1）在復(fù)雜的多變量控制系統(tǒng)中，要求所有的物理量在被采樣的時候都具備相同的采樣速率是不現(xiàn)實的事情。</p><p>　　2）在對信號進(jìn)行采樣的工程中，采樣的頻率越高，系統(tǒng)對信號的復(fù)現(xiàn)性能就越好，但是快速的A/D和D/A轉(zhuǎn)換器意味著更高的花費(fèi)。因此，對于不同的信號帶寬，，你應(yīng)該使用不同速率的A/D及D/A轉(zhuǎn)換器，進(jìn)

51、而是的系統(tǒng)的功能達(dá)到一個較高的水平的同時，又不致使系統(tǒng)的花費(fèi)太大。</p><p>　　3）多速率控制器一般而言是采樣時間可變的控制器，這是但速率采樣控制器不能與之相較的優(yōu)點。如增加系統(tǒng)增益裕度，則就要保持系統(tǒng)的穩(wěn)定性從而保證系統(tǒng)離散控制功能的實現(xiàn)。</p><p>　　雙速率采樣控制系統(tǒng)是一個相對簡單的多速率采樣控制系統(tǒng)，其系統(tǒng)的框圖如圖1所示?？刂葡到y(tǒng)仿真被定義為：對于一個給定的輸入W

52、，對系統(tǒng)的輸出信號Z進(jìn)行模擬的過程。</p><p>　　圖1 帶虛擬采樣器和保持器的雙速率采樣控制系統(tǒng)</p><p>　　文獻(xiàn)[4]中給出了一個高精度的單速率采樣控制系統(tǒng)仿真的樣本。在單速率采樣控制系統(tǒng)中僅存在一種采樣周期，這樣因而其仿真過程只需應(yīng)用一些較成熟的理論。例如單速率連續(xù)傳遞函數(shù)的離散化。對于雙速率采樣控制系統(tǒng)而言，由于系統(tǒng)中存在兩種不同的采樣周期，并且控制器為時變控制器，

53、這樣就增加了仿真的難度。</p><p>　　本文采用離散提升技術(shù)，將系統(tǒng)中兩種不同的采樣周期有機(jī)地聯(lián)系起來，把時變控制器變?yōu)闀r不變控制器。同時采用快速采樣算子和快速保持算子，給出了雙速率采樣控制系統(tǒng)的仿真方法</p><p><b>　　2.知識背景</b></p><p>　　圖1采樣器的采樣周期T1=ph，采樣控制器S：y(k)=Syc(

54、t)=yc(kph)，保持器的采樣周期T2=qh，保持器算子：uc=(kqh+r)=Hu(k),0<r<qh。其中:p和q為互質(zhì)正整數(shù)，h為基本采樣時間間隔。設(shè)l為p和q的最小公倍數(shù)，則T=lh為T1和T2的最小公倍周期。令p1=l/p,q1=l/q，則有T=lh=p1ph=q1qh成立。</p><p>　　G是廣義被控對象，其狀態(tài)空間模型為：</p><p>　　K是雙速率

55、離散控制器應(yīng)該被適當(dāng)調(diào)整去滿足相應(yīng)的因果性、周期性和有限維性。</p><p>　　對于任意的T>0，Dr為連續(xù)空間上的延遲算子，Druc (t) = uc (tT);U為離散空間上的一步滯后算子；U2為離散空間上的一步超前算子。</p><p>　　定義1 如果（U2）q1KUp1=K成立，則稱K為（p,q）-周期離散控制器。</p><p>　　定義2

56、如果連續(xù)系統(tǒng)G滿足DrG=GDr，則稱G為T-周期連續(xù)時變系統(tǒng)。</p><p><b>　　3.仿真算法</b></p><p><b>　　3.1仿真表達(dá)式</b></p><p>　　K是一個已知的定義（p,q）-周期的離散控制器，采樣算子和保持算子如上所述，則HKS以T為周期的時變系統(tǒng)。如圖1即可證明信號之間的關(guān)系

57、，在已知既定的條件下下式成立：</p><p>　　我們可以由定義2看到，HKS為T周期的時變系統(tǒng)。由于HKS的周期是T，因此同單速率系統(tǒng)類似，圖1中輸出與輸入的關(guān)系可以表示為：</p><p><b>　　或者是</b></p><p>　　在雙速率采樣控制系統(tǒng)輸出與輸入通道中，通過增加一個可見的采樣器且保持快速，像在圖1中顯示的一樣，這個可

58、見快速采樣器及保持器的采樣周期均為T/n。</p><p>　　Wd是w以T/n為采樣周期的采樣信號，當(dāng)輸入信號的仿真時間為mph時，有：</p><p>　　Wd=w(kT/n)，k=0,1,…,mn/p1</p><p>　　zd與z的關(guān)系同上。顯然，當(dāng)n→∞時，wd=w，zd=z。為使離散時間序列的個數(shù)為正整數(shù)，n選為l的整數(shù)倍。研究圖1所示系統(tǒng)的仿真，便可得

59、到虛框中雙速率采樣控制系統(tǒng)連續(xù)輸入輸出信號的仿真結(jié)果。</p><p>　　圖1中的zd=Snz,w=Hnwd，故由式（2）得</p><p>　　其中G11n,G12n,G21n為對應(yīng)于周期T/n的離散化。式(4)即為雙速率采樣控制系統(tǒng)的仿真表達(dá)式。</p><p>　　3.2 仿真表達(dá)式的計算</p><p>　　欲求表達(dá)式（4），首先要

60、得到G11n， G12n,，G21n,，SnH,，SHn，以及(I-KSG22H)-1K等等變量 ，G11n, G12n, G21n 分別是連續(xù)傳遞函數(shù)G11, G12, G21以T為采樣周期采樣后的離散傳遞函數(shù)，均以計算。下面討論SnH,SHn,(I-KSG22H)-1K的計算。</p><p><b>　　計算SnH</b></p><p>　　圖 2 SHn的輸

61、入與輸出框圖</p><p>　　圖2中Hn的周期為T/n=lh/n，S的周期為ph，當(dāng)x2 (0) = x1 (0), x2 (1) = x1 (n/p1), ..., x2 (m -1) = x1 ((m-1) n/p1)， SHn =</p><p><b>　　計算SnH </b></p><p>　　同理可得到SnH的表達(dá)式：<

62、/p><p>　　計算(I-KSG22H)-1K </p><p>　　由離散采樣以及離散算子的定義，有：</p><p>　　Ψ (k) = Φ (kp)Sp2l → l, Ψ = SpΦ </p><p>　　υ (kq + r) = Φ (k)Hq2l → l υ = HqΦ</p><p>　　R = 0,1,

63、..., q-1 </p><p><b>　　可得：</b></p><p>　　SG22H = SrSAG22HhHq = SpG22dHq (5) </p><p>　　其中G22d可通過單一速率h離散化過程得到。對于 (I-KSpG22dHq)-1K而言，仍然是變量SpG22dHq和K的周期，本文應(yīng)用離散提升算子將其變成為是不變系統(tǒng)，具

64、體的過程如圖3所示。此時仿真表達(dá)式（4）可表示為圖4。</p><p>　　經(jīng)離散提升后，周期時變環(huán)節(jié) SpG22dHq 和K變成了時不變的Lp1SpG22dHqL-1 q1 和 Lq1K L-1 q1，具體的計算過程如下：</p><p>　?。?）Lq1K L-1 q1 的計算</p><p>　　如果雙速率控制器K的狀態(tài)方程是</p><p

65、>　　與此同時，Lq1K L-1 q1的狀態(tài)方程可以被標(biāo)識為： </p><p><b>　　其中</b></p><p>　　圖 3 用于提升離散信號的(I-KSG22H)-1K </p><p><b>　　圖4 仿真示意</b></p><p>　　（2）Lp1SpG22dHqL-1

66、q1的計算</p><p>　　引理1：設(shè)P的狀態(tài)變量為x，狀態(tài)模型參數(shù)矩陣為[A、B、C、D]，m、n和s 是滿足如下關(guān)系式的正實數(shù)。對離散采樣算子的系統(tǒng)狀態(tài)變量可被表示成為一個狀態(tài)模型。即：</p><p><b>　　其中</b></p><p><b>　　特征函數(shù)X為：</b></p><p&

67、gt;　　有上述結(jié)論，可由G22d求得Lp1SpG22dHqL-1 q1 狀態(tài)空間模型矩陣。</p><p>　　綜上所述，在圖4中我們可以看到整個的仿真過程為：mph輸入信號周期，然后：</p><p><b>　　仿真舉例</b></p><p>　　圖1中廣義被控對象G為：</p><p><b>　　控

68、制器K為：</b></p><p>　　采樣周期： T1 = 2s， T2 = 3s， p = 2， q = 3， h = 1， p1 = 3， q1 = 2， l = 6， T = 6。令m=6，n依次令其等于4800，7200，9600，wd是單位階躍輸入信號。使用MATLAB 編程語言，并且進(jìn)行系統(tǒng)仿真， 結(jié)果如圖五所示：</p><p><b>　　結(jié)論<

69、;/b></p><p>　　本文針對雙速率采樣控制系統(tǒng)的特點，應(yīng)用離散提升技術(shù)、快速采樣算子和快速保持算子，研究雙速率采樣控制系統(tǒng)的仿真方法，并給出了具體的仿真步驟和方針實例。由于雙速率控制器為時變控制器，所以有關(guān)雙速率采樣控制系統(tǒng)仿真精度的驗證問題還有待于進(jìn)一步研究。</p><p>　　采樣控制系統(tǒng)技術(shù)已經(jīng)歷十多年的發(fā)展，卻存在著根本性的問題。尤其是自從采用了提升技術(shù)，采樣控制

70、理論進(jìn)入了一個新的發(fā)展階段。由于能夠計及采樣時刻之間的性能，所以提升變換似乎已經(jīng)成了采樣控制系統(tǒng)分析和設(shè)計的唯一正確的方法，其應(yīng)用也在逐步擴(kuò)大，但是在現(xiàn)實設(shè)計中的應(yīng)用卻對其提出了更高的要求。對其提升技術(shù)本來是為了相關(guān)設(shè)計的需要而提出的，但很多現(xiàn)實情況不僅僅局限于個別領(lǐng)域。這就是采樣控制系統(tǒng)的特殊性，尤其是在于其信號通道的結(jié)構(gòu)上。采樣控制系統(tǒng)的信號通道由兩部分所構(gòu)成，一個是連續(xù)通道，另一個是采樣通道。采樣控制系統(tǒng)提升后，其范數(shù)也不是完全等