双速率数据采样系统的仿真.doc

中文2630字Simulation of dual-rate sampled-data systemAbstract: 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 operator1. 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 holderLiterature 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 knowledgeFigure 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 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 Algorithm2.1 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 stylewe 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 asOrDual-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 calculationFigure 2 Expressiong for Input and Output of SHnFigure 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 calculationSimilarly available expression SnH(3) (I-KSG22H)-1K calculation By discrete sampling and the discrete operator to maintain the definition of operator, there are (k) = (kp)Sp2l l, = Sp (kq + r) = (k)Hq2l l = HqR = 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 calculationIf the dual-rate controller of the state equation for KWhile Lq1K L-1 q1 state equation can be expressed asAmong whichFigure 3 (I-KSG22H)-1K to upgrade the discrete signalFigure 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 whichCharacteristics function XTake,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, then3. Simulation exampleFigure 1 for the generalized plant GAnd 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 systems 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),0r0，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： (k) = (kp)Sp2l l, = Sp (kq + r) = (k)Hq2l l = HqR = 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11.1项目名称与承办单位11.2研究工作的依据、内容及范围11.3编制原则31.4项目概况31.5技术经济指标51.6结论6第二章 项目背景及建设必要性82.1项目背景82.2建设的必要性9第三章 建设条件113.1项目区概况113.2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134.1市场分析134.2营销策略、方案、模式14第五章 建设方案155.1建设规模和产品方案155.2建设规划和布局155.3运输185.4建设标准185.5公用工程205.6工艺技术方案215.7设备方案215.8节能减排措施24第六章 环境影响评价256.1环境影响256.2环境保护与治理措施266.3评价与审批28第七章 项目组织与管理297.1组织机构与职能划分297.2劳动定员297.3经营管理措施307.4技术培训30第八章 劳动、安全、卫生与消防318.1编制依据及采用的标准318.2安全卫生防护原则318.3自然灾害危害因素分析及防范措施328.4生产过程中产生的危害因素分析及防范措施328.5消防编制依据及采用的标准348.6消防设计原则358.7火灾隐患分析358.8总平面消防设计358.9消防给水设计368.10建筑防火368.11火灾检测报警系统378.12预期效果37第九章 项目实施进度389.1实施进度计划389.2项目实施建议38第十章 项目招投标方案4010.1招标原则4010.2项目招标范围4010.3投标、开标、评标和中标程序4010.4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4311.1投资估算4311.2资金筹措及使用计划45第十二章 财务评价4712.1费用与效益估算4712.2财务分析4812.3不确定性分析4912.5财务评价结论50第十三章 建设合理性分析5113.1产业政策符合性分析5113.2清洁生产符合性分析5113.3规划符合性分析5113.4项目建设环保政策符合性分析5113.5环境承载性分析5113.6结论52第十四章 结论与建议53