双速率数据采样系统的仿真.doc

中文2630字
Simulation of dual-rate sampled-data system
Abstract: The simulation problem of a dual-rate system is studied by applying discrete lifting 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 example under MATLAB environment.

Key words: Dual-rate sampled-data system; Discrete lifting technology; Quick sampling operator; Quick hold operator

1. Introduction
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 of 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 sampling control system works in practice with the prospect of a wide range of practical, this is because:
1) In the complex multi-variable control system, requires that all physical signals in the same sampling frequency is not realistic.
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 should use a different A / D and D / A conversion rate, in order to achieve performance and the best compromise between price.
3) multi-rate controller is generally time-varying controller, it has a single-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.
A relatively 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 output signal z process.

Figure 1 dual-rate sampled-data systems wth a virtual sampler and holder
Literature [4] is given a single-rate sampling of high-precision control system 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 function 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 the simulation.
   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 sampling and rapid operator to maintain, given the dual-rate sampling control system simulation method.
2. Prior knowledge
Figure 1 sampler sampling period T1 = ph, sampling operator 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 for 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.
    G for the generalized plant, the state-space realization for

K discrete controller for dual-rate should be appropriate to meet the causal nature of the cyclical and finite-dimensional.
   For any T> 0, 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.
1 If the definition of (U2) q1KUp1 = K to set up, said K for the (p, q) - discrete controller cycle.
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.
3 Simulation Algorithm
2.1 Simulation of the expression
K is a known theorem (p, q) - cycle of discrete controllers, operator and maintenance of sampling operator as mentioned 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

we can see from the definition 2,HKS 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

Or

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

Which G11n, G12n, G21n to correspond to the cycle of T / n of the discretization.
Formula (4) is dual-rate sampling control system simulation expression.
2.2 Simulation of the calculation of expression
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, G21 single-cycle T / n of the discretization are easy to calculate. Discussed below SnH, SHn, (I-KSG22H)-1K calculations.
(1) SnH calculation

Figure 2 Expressiong for Input and Output of SHn
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 =

(2) SnH calculation
Similarly available expression SnH

(3) (I-KSG22H)-1K calculation
By discrete sampling and the discrete operator to maintain the definition of operator, there are
Ψ (k) = Φ (kp)óSp2l → l, Ψ = SpΦ
υ (kq + r) = Φ (k)óHq2l → l υ = HqΦ
R = 0,1, ..., q-1
SG22H = SrSAG22HhHq = SpG22dHq (5)
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 time-invariant systems, the specific process as shown in Figure 3. Simulation of expression at this time (4) can be expressed as Figure 4.
Enhanced by the discrete, periodic time-varying link SpG22dHq and K into the time-invariant Lp1SpG22dHqL-1 q1 and Lq1K L-1 q1, calculated as follows:
(1) Lq1K L-1 q1 calculation
If the dual-rate controller of the state equation for K

While Lq1K L-1 q1 state equation can be expressed as

Among which

Figure 3 (I-KSG22H)-1K to upgrade the discrete signal

Figure 4 (4) simulation indicate

,

(2) Lp1SpG22dHqL-1 q1 calculation
Lemma 1 for P for the state variables x, the state model for [A, B, C, D], m, n and s meet the following relationship is positive integer. The system state variables for the discrete sampling operator can be expressed as a state model. Which

Among which

Characteristics function X

Take,
Conclusions from the Appeal, G22d obtained from Lp1SpG22dHqL-1 q1 of the state space model.
Integrated on the system, we can see in Figure 4 for the simulation process: mph input signal period, then

3. Simulation example
Figure 1 for the generalized plant G

And controller K is

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 programming language, and the system simulation, the results shown in Figure 5.

4. Conclusion
   In this paper, dual-rate sampling control system of the characteristics of discrete applications 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. 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.
Sampling control 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. Because 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 also expanding, but in the real design was brought out higher requirements. Upgrade its technology was originally designed for the needs of related, but not limited to the actual situation in many areas of the individual. This is the special nature of sampled-data systems, especially in its structure on the signal path. Sampling control system signal channel constituted by two parts, a continuous channel, and the other is sampling channel. Sampling control system upgrade, its norm is not entirely equivalent. Taking into account the characteristics of the two-channel frequency response method proposed can also be given the system's frequency response induced by the true norm, will be sampled-data control systems analysis and design the right way.

双速率数据采样系统的仿真
摘要：双速率系统的仿真问题是采用离散提升技术、快速采样算子和快速保持算子来研究的。该模型实现的结果与连续信号非常相近。最后给出具体地仿真步骤，并结合实例在MATLAB环境下编程实现。

关键词：双速率数据采样系统，离散提升技术，快速采样算子，快速保持算子

1.简介
采样控制系统是指连续和数字系统的对象控制器。目前，大多数的控制系统是继续的由计算机实现的采样控制系统控制器实现的。随着对系统要求的不断提高，单速率的采样控制系统变得不能满足应用的要求，因此其地位被混合采样速率的采样控制系统所替代。混合采样速率控制系统在实际应用中能够满足于很广泛的应用场合，这是因为：
1）在复杂的多变量控制系统中，要求所有的物理量在被采样的时候都具备相同的采样速率是不现实的事情。
2）在对信号进行采样的工程中，采样的频率越高，系统对信号的复现性能就越好，但是快速的A/D和D/A转换器意味着更高的花费。因此，对于不同的信号带宽，，你应该使用不同速率的A/D及D/A转换器，进而是的系统的功能达到一个较高的水平的同时，又不致使系统的花费太大。
3）多速率控制器一般而言是采样时间可变的控制器，这是但速率采样控制器不能与之相较的优点。如增加系统增益裕度，则就要保持系统的稳定性从而保证系统离散控制功能的实现。
双速率采样控制系统是一个相对简单的多速率采样控制系统，其系统的框图如图1所示。控制系统仿真被定义为：对于一个给定的输入W，对系统的输出信号Z进行模拟的过程。

图1 带虚拟采样器和保持器的双速率采样控制系统
文献[4]中给出了一个高精度的单速率采样控制系统仿真的样本。在单速率采样控制系统中仅存在一种采样周期，这样因而其仿真过程只需应用一些较成熟的理论。例如单速率连续传递函数的离散化。对于双速率采样控制系统而言，由于系统中存在两种不同的采样周期，并且控制器为时变控制器，这样就增加了仿真的难度。
本文采用离散提升技术，将系统中两种不同的采样周期有机地联系起来，把时变控制器变为时不变控制器。同时采用快速采样算子和快速保持算子，给出了双速率采样控制系统的仿真方法
2.知识背景
图1采样器的采样周期T1=ph，采样控制器S：y(k)=Syc(t)=yc(kph)，保持器的采样周期T2=qh，保持器算子：uc=(kqh+r)=Hu(k),0<r<qh。其中:p和q为互质正整数，h为基本采样时间间隔。设l为p和q的最小公倍数，则T=lh为T1和T2的最小公倍周期。令p1=l/p,q1=l/q，则有T=lh=p1ph=q1qh成立。
G是广义被控对象，其状态空间模型为：

K是双速率离散控制器应该被适当调整去满足相应的因果性、周期性和有限维性。
对于任意的T>0，Dr为连续空间上的延迟算子，Druc (t) = uc (tT);U为离散空间上的一步滞后算子；U2为离散空间上的一步超前算子。
定义1 如果（U2）q1KUp1=K成立，则称K为（p,q）-周期离散控制器。
定义2 如果连续系统G满足DrG=GDr，则称G为T-周期连续时变系统。
3.仿真算法
3.1仿真表达式
K是一个已知的定义（p,q）-周期的离散控制器，采样算子和保持算子如上所述，则HKS以T为周期的时变系统。如图1即可证明信号之间的关系，在已知既定的条件下下式成立：

我们可以由定义2看到，HKS为T周期的时变系统。由于HKS的周期是T，因此同单速率系统类似，图1中输出与输入的关系可以表示为：

或者是

在双速率采样控制系统输出与输入通道中，通过增加一个可见的采样器且保持快速，像在图1中显示的一样，这个可见快速采样器及保持器的采样周期均为T/n。
Wd是w以T/n为采样周期的采样信号，当输入信号的仿真时间为mph时，有：
Wd=w(kT/n)，k=0,1,…,mn/p1
zd与z的关系同上。显然，当n→∞时，wd=w，zd=z。为使离散时间序列的个数为正整数，n选为l的整数倍。研究图1所示系统的仿真，便可得到虚框中双速率采样控制系统连续输入输出信号的仿真结果。
图1中的zd=Snz,w=Hnwd，故由式（2）得

其中G11n,G12n,G21n为对应于周期T/n的离散化。式(4)即为双速率采样控制系统的仿真表达式。
3.2 仿真表达式的计算
欲求表达式（4），首先要得到G11n， G12n,，G21n,，SnH,，SHn，以及(I-KSG22H)-1K等等变量 ，G11n, G12n, G21n 分别是连续传递函数G11, G12, G21以T为采样周期采样后的离散传递函数，均以计算。下面讨论SnH,SHn,(I-KSG22H)-1K的计算。
5. 计算SnH

图 2 SHn的输入与输出框图
图2中Hn的周期为T/n=lh/n，S的周期为ph，当x2 (0) = x1 (0), x2 (1) = x1 (n/p1), ..., x2 (m -1) = x1 ((m-1) n/p1)， SHn =

6. 计算SnH
同理可得到SnH的表达式：

7. 计算(I-KSG22H)-1K
由离散采样以及离散算子的定义，有：
Ψ (k) = Φ (kp)óSp2l → l, Ψ = SpΦ
υ (kq + r) = Φ (k)óHq2l → l υ = HqΦ
R = 0,1, ..., q-1
可得：
SG22H = SrSAG22HhHq = SpG22dHq (5)
其中G22d可通过单一速率h离散化过程得到。对于 (I-KSpG22dHq)-1K而言，仍然是变量SpG22dHq和K的周期，本文应用离散提升算子将其变成为是不变系统，具体的过程如图3所示。此时仿真表达式（4）可表示为图4。
经离散提升后，周期时变环节 SpG22dHq 和K变成了时不变的Lp1SpG22dHqL-1 q1 和 Lq1K L-1 q1，具体的计算过程如下：
（1）Lq1K L-1 q1 的计算
如果双速率控制器K的状态方程是

与此同时，Lq1K L-1 q1的状态方程可以被标识为：

其中

图 3 用于提升离散信号的(I-KSG22H)-1K

图4 仿真示意

（2）Lp1SpG22dHqL-1 q1的计算
引理1：设P的状态变量为x，状态模型参数矩阵为[A、B、C、D]，m、n和s 是满足如下关系式的正实数。对离散采样算子的系统状态变量可被表示成为一个状态模型。即：

其中

特征函数X为：

有上述结论，可由G22d求得Lp1SpG22dHqL-1 q1 状态空间模型矩阵。
综上所述，在图4中我们可以看到整个的仿真过程为：mph输入信号周期，然后：

(3) 仿真举例
图1中广义被控对象G为：

控制器K为：

采样周期： 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是单位阶跃输入信号。使用MATLAB 编程语言，并且进行系统仿真， 结果如图五所示：

5. 结论
本文针对双速率采样控制系统的特点，应用离散提升技术、快速采样算子和快速保持算子，研究双速率采样控制系统的仿真方法，并给出了具体的仿真步骤和方针实例。由于双速率控制器为时变控制器，所以有关双速率采样控制系统仿真精度的验证问题还有待于进一步研究。
采样控制系统技术已经历十多年的发展，却存在着根本性的问题。尤其是自从采用了提升技术，采样控制理论进入了一个新的发展阶段。由于能够计及采样时刻之间的性能，所以提升变换似乎已经成了采样控制系统分析和设计的唯一正确的方法，其应用也在逐步扩大，但是在现实设计中的应用却对其提出了更高的要求。对其提升技术本来是为了相关设计的需要而提出的，但很多现实情况不仅仅局限于个别领域。这就是采样控制系统的特殊性，尤其是在于其信号通道的结构上。采样控制系统的信号通道由两部分所构成，一个是连续通道，另一个是采样通道。采样控制系统提升后，其范数也不是完全等价的。考虑到这两个通道特点而提出的频率响应法也可以给出系统真实的频率响应诱导范数，将是采样控制系统分析和设计的正确方法。目 录
第一章 总论 1
1.1项目名称与承办单位 1
1.2研究工作的依据、内容及范围 1
1.3编制原则 3
1.4项目概况 3
1.5技术经济指标 5
1.6结论 6
第二章 项目背景及建设必要性 8
2.1项目背景 8
2.2建设的必要性 9
第三章 建设条件 11
3.1项目区概况 11
3.2建设地点选择 错误！未定义书签。
3.3项目建设条件优劣势分析 错误！未定义书签。
第四章 市场分析与销售方案 13
4.1市场分析 13
4.2营销策略、方案、模式 14
第五章 建设方案 15
5.1建设规模和产品方案 15
5.2建设规划和布局 15
5.3运输 18
5.4建设标准 18
5.5公用工程 20
5.6工艺技术方案 21
5.7设备方案 21
5.8节能减排措施 24
第六章 环境影响评价 25
6.1环境影响 25
6.2环境保护与治理措施 26
6.3评价与审批 28
第七章 项目组织与管理 29
7.1组织机构与职能划分 29
7.2劳动定员 29
7.3经营管理措施 30
7.4技术培训 30
第八章 劳动、安全、卫生与消防 31
8.1编制依据及采用的标准 31
8.2安全卫生防护原则 31
8.3自然灾害危害因素分析及防范措施 32
8.4生产过程中产生的危害因素分析及防范措施 32
8.5消防编制依据及采用的标准 34
8.6消防设计原则 35
8.7火灾隐患分析 35
8.8总平面消防设计 35
8.9消防给水设计 36
8.10建筑防火 36
8.11火灾检测报警系统 37
8.12预期效果 37
第九章 项目实施进度 38
9.1实施进度计划 38
9.2项目实施建议 38
第十章 项目招投标方案 40
10.1招标原则 40
10.2项目招标范围 40
10.3投标、开标、评标和中标程序 40
10.4评标委员会的人员组成和资格要求 42
第十一章 投资估算和资金筹措 43
11.1投资估算 43
11.2资金筹措及使用计划 45
第十二章 财务评价 47
12.1费用与效益估算 47
12.2财务分析 48
12.3不确定性分析 49
12.5财务评价结论 50
第十三章 建设合理性分析 51
13.1产业政策符合性分析 51
13.2清洁生产符合性分析 51
13.3规划符合性分析 51
13.4项目建设环保政策符合性分析 51
13.5环境承载性分析 51
13.6结论 52
第十四章 结论与建议 53