褚義文獻翻譯

1、單位代碼 01 學 號 100119056 分 類 號 TP393 密 級 文獻翻譯基于單片機溫度控制系統(tǒng) 院（系）名稱信息工程學院 專業(yè)名稱電子信息工程 學生姓名褚義 指導教師付瑞玲 2014 年 月 日單片機溫度控制：一個跨學科的本科生工程設計項目JamesS.McDonald工程科學系三一大學德克薩斯州圣安東尼奧市78212摘要本文所描述的是作者領導由四個三一大學高年級學生組成的團隊進行的一個跨學科工程項目的設計。該項目的目標是設計一個氣室內溫度控制系統(tǒng)。該系統(tǒng)的要求是：當實際氣室的溫度階躍響應時，規(guī)定范圍內的溫度進入氣室后，穩(wěn)定時的溫度誤差和超調量必須少于一個絕對溫度。本組學生開發(fā)設計

2、是基于摩托羅拉MC68HC05系列單片機。該問題的教學價值也通過某些步驟的關鍵描述在本文說明。研究結果表明，解決該方案需要具有廣泛的工程學科知識，包括相關電子、機械和控制系統(tǒng)工程的知識。1引言該設計項目來自一個實際應用問題，一個關于顯微鏡載玻片干燥劑溫控器歐米茄CN-390溫度控制器，而這個設計的目標是研發(fā)一個自定義的通用溫度控制系統(tǒng)取代歐米茄系統(tǒng)、一個以更低的成本實現(xiàn)相同功能的自定義控制器，就像歐米茄系統(tǒng)一樣，并不需要能夠全方位的處理各種問題。該載玻片干燥機的機械布局如圖1-1所示。干燥機的主體是一個足夠大的絕緣充氣室，里面依次存放著薄紙包著的石蠟。為了使石蠟保持適當穩(wěn)定性，載玻片氣室的溫度

3、必須維持穩(wěn)定。第二個氣筒（電子圍繞元件）設有一個電阻加熱器、一個溫度控制器以及一個安裝在干燥機上的風扇，是為了把風吹過加熱器，把熱量帶到載玻片氣室。圖1-1載玻片干燥機的機械布局自1996-97學年來，本文作者帶領四位三一大學工程科學系的高年級學生開展此項目的研究。本文的目的說明了提出一些問題并詳細闡述學生的一些解決方案，而且討論了這種類型的跨學科設計項目在教學方面應用的問題。這份學生報告曾經(jīng)在1997年全國本科畢業(yè)生研討會上提出過并討論過。第2節(jié)給出該設計的更多詳細情況，包括性能規(guī)格。第3節(jié)具體 學生的設計。第4節(jié)是論文的主體，討論該設計在教學應用方面的實施問題。最后，第5節(jié)全文總結。2問題

4、闡述該項目基本的思想是設計一個自定義溫度控制系統(tǒng)來取代相關的歐米茄CN-390溫度控制器。溫度時通常保持在一個穩(wěn)定的常數(shù)，但重要的是階躍變化可以被“合理”的跟蹤。因此主要要求如下：·可以對空氣室的溫度進行設定，·同時顯示設定值和實際溫度，·以及在設定溫度值情況下，可接受范圍內的跟蹤階躍變化，穩(wěn)態(tài)誤差，超調量。表1精確的規(guī)格說明設定溫度接口設定溫度顯示室內溫度顯示范圍精度準確度60-991°C±1°C室內溫度階梯響應范圍（穩(wěn)定狀態(tài)）精度（穩(wěn)定狀態(tài)）最大超調設定時間（到±1°）60-99±1°C 1

5、°C120s盡管表1部分說明并不明確，但是它清楚的反映了人們對數(shù)字顯示器在設定值和實際溫度的要求和溫度應該通過數(shù)值輸入來設定（而不是，通過電位器設置）。3系統(tǒng)設計根據(jù)微控設計，數(shù)字溫度顯示和單點輸入的要求可能是最合適的。圖2-2為學生的設計框圖。圖2-2溫度控制器硬件結構圖摩托羅拉MC68HC705B16（簡稱6805），是系統(tǒng)的核心。它通過一個簡單的4鍵小鍵盤對溫度進行設定，同時使用兩個顯示驅動控制7段LED數(shù)碼管來顯示定值和氣室溫度的測量值。所有這些，輸入和輸出信號與6805的并行口相連。氣室的溫度值使用預校準熱敏電阻測量，并通過6805的數(shù)模轉換輸入。最后，6085的脈沖寬度調

6、制（PWM）輸出用來驅動一個繼電器，以控制線性電阻加熱器的閉合和斷開。圖2-3更詳細的顯示了6805的接口和電子器件。使用暴風3K041103型號四鍵鍵盤，通過PA0-PA3端口進行數(shù)據(jù)輸入。其中一個重要的功能是進行模式切換。兩種模式：固定模式和運行模式。在固定模式下，其他兩個鍵用于設定溫度，一個增加，一個減少，第四個按鍵暫無作用。LED顯示屏由哈里斯半導體ICM7212進行驅動，通過PB0-PB6端口與芯片相連，作為輸出。熱敏電阻由電壓分頻器驅動，通過AN0針腳（八個模擬輸入端口中的一個）相連。最后，PLMA針腳（兩個PWM輸出端口中的一個）驅動加熱繼電器。圖2-3單片機原理圖圖3單片機原理

7、圖是關于用軟件實現(xiàn)溫度控制算法、保持溫度顯示以及改變鍵盤輸入響應，這將不會在本文詳細討論，因為這并不是本文的重點，也沒有編譯完成。軟件部分還沒有確定控制算法，但很可能是一個簡單的比例控制，比PID算法簡單。一些控制設計的問題將在第四節(jié)討論。4設計過程雖然該項目的本質是建立一個恒溫器，但它有許多很好的契機可以供教學借鑒。高級工程本科教育的知識只是能夠讓學生們具有解決問題的能力。然而，很多情況下，實際情況卻和理論有些不同。不過，這些不是問題，參與這個項目的設計，將獲得很多設計方面的寶貴經(jīng)驗。本節(jié)的其余部分著眼于其他的幾個方面：4.1節(jié)討論系統(tǒng)的一些特征，簡化系統(tǒng)熱性能的數(shù)學模型，以及一些簡單理論的

8、證明。4.2節(jié)介紹確定實際控制算法。4.3節(jié)指出控制設計程序的一些不足，并通過模擬環(huán)境，指出怎樣克服問題。4.4節(jié)給出單片機的一些設計相關概述，以及出現(xiàn)問題和值得借鑒之處。4.1數(shù)學模型集總元件熱系統(tǒng)符合線性控制，適用于載玻片干燥機的問題。圖4-1顯示了二階集總元件熱量模型的載玻片干燥機。狀態(tài)變量是溫度，Ta是箱內空氣的溫度，Tb是箱子本身的溫度。該系統(tǒng)輸入功率等于q(t)的熱量和環(huán)境溫度T的和。ma，mb分別對應空氣和箱子的質量。Ca和Cb則分別是其對應熱量。m1和m2分別是空氣與箱子間以及箱子與外界間的傳熱系數(shù)。圖4-1集總元件熱模型由圖4可以推出（線性）狀態(tài)方程拉普拉斯變換(1)和(2)

9、等式，并整理Ta(s)。有趣的是，可以推出一個開環(huán)的熱系統(tǒng)方程。其中K是一個常數(shù)，D(s)是一個二階的多項式。K,tz,以及系數(shù)D(s)和在(1)和(2)等式中出現(xiàn)的系數(shù)功能相近。當然，在(1)和(2)等式中各種參數(shù)在未知的情況下，不難證明D(s)與其他參數(shù)的值無關，具有兩個零點。因此傳遞函數(shù)可以寫成（我們假設環(huán)境溫度為常數(shù)）此外,可以推出1/tp1<1/tz<1/tp2,即，零點在兩極之間。開環(huán)零極點如圖4-2所示。圖4-2Gaq(s)的零極點為了獲取完整的熱模型，從(3)式中除去常數(shù)K和3個未知的時間常數(shù)。四個未知參數(shù)并不少，但由簡單的實驗表明，1/tp1<<1/t

10、z，1/tp2統(tǒng)基本上是一階函數(shù)，且tz,tp2近似為0。因此，開環(huán)系可以寫成：(下標p1已經(jīng)被去掉了)過初始溫度和熱量值大范圍內的設置，簡單的開環(huán)階躍響應實驗結果表明，K0.14o/W，295S。4.2控制系統(tǒng)設計使用(4)式的一階開環(huán)傳遞函數(shù)Gaq(s)，并且假定加熱器的輸出函數(shù)q(t)為線性，圖4-3是系統(tǒng)框圖代表閉環(huán)系統(tǒng)。Td(s)是設定溫度的函數(shù)，C(s)是傳遞函數(shù)，Q(s)是熱量輸出，單位是瓦特。圖4-3簡化的閉環(huán)系統(tǒng)框圖鑒于這種簡單情況，前面所指的線性控制設置，例如，根軌跡法設計法可以使C(s)中符合要求的階躍響應對應的上升時間、穩(wěn)態(tài)誤差和超調量符合表格1所示。當然，一個有足夠增

11、益的比例控制器就可以滿足各種要求。超調量改變是不可能既增加增益又減少穩(wěn)態(tài)誤差和上升時間的。不幸的是，如果要獲得足夠增益，需要生產(chǎn)超過實際生產(chǎn)能力的大容量加熱器。這是本系統(tǒng)的實際問題，將會致使上升時間不符合要求。這要求學生們如何利用這個經(jīng)過仔細計算的簡化模型，在整體性能上達到最佳控制。4.4模型仿真該設計的大部分性能和限制功能，應該可以使用圖4-3簡化模型來完成。但有一個數(shù)據(jù)對閉環(huán)系統(tǒng)其他方面的影響并非能夠如此簡單的仿真。其中最主要的是：·量化誤差的模擬和數(shù)模轉換，·測量溫度和使用PWM控制加熱器。這兩種都是非線性的、時變的。所以唯一切實可行的方法就是通過仿真（或實驗）加以研

12、究。圖7Simulink仿真閉環(huán)系統(tǒng)框圖顯示了Simulink情況下的閉環(huán)系統(tǒng)框圖，其中包括A/D轉換和使用標準Simulink量化飽和塊建立的飽和量化模型。建立PWM調制模型比較復雜，需要一個自定義的S函數(shù)來表示。圖4-3仿真閉環(huán)系統(tǒng)框圖這種仿真模型已經(jīng)被證明在衡量不同的PWM基本參數(shù)對設計的影響以及適當參數(shù)的選擇中特別有用。（即時間越長，PWM調制會產(chǎn)生更多溫度誤差。另一方面，時間越長，繼電器抖動機率越小。）PWM調制方法往往很難讓學生掌握，并且仿真模型允許研究測試運行和明顯的影響。4.4單片機簡單的閉環(huán)控制、鍵盤輸入和顯示控制是經(jīng)典單片機應用技術，這個設計項目包含上述三個方面。因此這是一

13、個優(yōu)秀的全面的單片機應用練習。此外，由于該項目是來源于現(xiàn)實，它不會是一個簡單的輸入輸出設計就能完成的。相反，這個項目需要制定一個完整的嵌入式應用。這需要從大量的單片機型號中選取適當?shù)男酒W著使用一個相當復雜的開發(fā)環(huán)境。最后，必須設計和選取印刷電路板和單片機，以及外接元件。單片機選擇從現(xiàn)有的實際經(jīng)驗來看，經(jīng)常選用摩托羅拉公司的單片機。不過，芯片的選擇不應該局限于此。研究表明，系統(tǒng)要求符合工作需求的單片機。這對學生很困難，因為他們缺乏良好的經(jīng)驗與判斷能力，只能通過制造商的產(chǎn)品選擇指南決定單片機的選擇。部分問題是各種外圍設備（例如，應該使用哪種顯示驅動程序？）連接方法的選擇。摩托羅拉的相關應用研究

14、2,3,4中的證明是非常有用的，基本闡述了可實用性的連接方法以及單片機和外圍連接的組合方式。在最終要求的基礎上，選擇MC68HC705B16，其現(xiàn)有A/D輸入和PWM輸出以及24個數(shù)字I/O線。這樣選擇是有必要的，因為此項目需要一個A/D通道、一個PWM通道和11個I/O引腳（見圖3）。該決定為了安全方面，因為選擇一個完整的開發(fā)系統(tǒng)是有必要的，該項目預算中沒有足夠的資金再次購買元件。單片機應用開發(fā)外圍設備的電路硬件、軟件的開發(fā)、最終調試、單片機的自定的印刷電路板和外設都需要某種形式的發(fā)展環(huán)境。如同單片機本身，一個開發(fā)環(huán)境的選擇是令人困惑并需要一些教師的專業(yè)知識。摩托羅拉三級發(fā)展環(huán)境，包括從簡單

15、的評估板（在約100美元）到全面的實時在線仿真器（在大約7500元）。中間選項被選為本項目的MMEVS，其中包括：·平臺板（支持所有6805-family部分），· 模擬器模塊（具體到B系列部分），和· 電纜頭和目標適配器（簡明包裝）?？傮w而言，該系統(tǒng)的成本為900美元，并且在一定局限下，提供了在線仿真能力。它還配備了簡單但足夠的軟件開發(fā)環(huán)境RAPID5。學生發(fā)現(xiàn)學習使用這類系統(tǒng)的挑戰(zhàn)。但他們在現(xiàn)實世界的微控制器應用獲得的經(jīng)驗大大超過了第一使用典型的簡單評估板的經(jīng)驗。印刷電路板一個簡單的（雖然布局絕對不平凡）印刷電路板是這個工程提供的另一個現(xiàn)實學習的機會。圖4-4

16、顯示最后的板布局與包輪廓（50%實際大?。?。相對簡單的電路使手工安置和路由實踐方面更實際，它有可能提供更好的結果比一個這樣的應用程的自動性。學生因此接觸到基本印刷電路布局問題和基本的設計規(guī)則。本排版軟件使用的是非常漂亮的包裝印刷電路板，板制作是在內部電子技術員的幫助下完成的。圖4-4單片機印刷版布局結論本文的目的是描述一個跨學科的本科工程設計項目：一個基于單片機的溫度控制系統(tǒng)，包括設定點輸入數(shù)字與設定值/實際溫度顯示。本文已描述了這樣系統(tǒng)的一個設計，并且討論了許多來自工程的問題。這些問題的解決通常需要入門課程要求的知識，尤其是在老師的建議和監(jiān)督下，實際上可以促進大學生發(fā)展。從教學方法觀點看，問

17、題的理想特征包括微控制器和外圍設備的簡單使用，有效地運用導論水平的物理系統(tǒng)建模和設計閉環(huán)控制。并需要相對簡單的實驗和模擬（詳細的性能預測）。并可取的是一些技術相關方面的問題，包括熱敏電阻和溫度傳感器（分別需要知識脈寬調制和校準技術）的實際使用、單片機選擇和開發(fā)系統(tǒng)的使用以及并印制電路設計。鳴謝作者要感謝參與這個項目的學生，馬克朗·斯道夫，馬特洛爾和戴維·舒克曼，表現(xiàn)出辛勤工作、奉獻和能力。這個工程和工程成功全賴他們。參考文獻1朗斯道夫,M.拉爾,D.舒克曼,和P.萊因哈特.“顯微鏡載玻片干燥劑溫控器”1997屆全國大學生研究,（奧斯汀，德克薩斯州,四月1997.海報介紹.2

18、摩托羅拉公司,鳳凰城,亞利桑那.溫度測量和使用它的顯示mc68hc05b4和mc14489,1990。摩托羅拉semiconductorapplicationnote an431.3摩托羅拉公司,鳳凰城，亞利桑那.hc05單片機驅動技術使用mc68hc705j1a,1995.摩托羅拉半導體應用筆記an1238.4摩托羅拉公司,鳳凰城,亞利桑那.hc05mcu鍵盤解碼技術使用mc68hc705j1a,1995.摩托羅拉半導體應用筆記an1239.5摩托羅拉公司,鳳凰城,亞利桑那.快速集成開發(fā)環(huán)境用戶手冊,1993.（快速是由寶潔微機系統(tǒng)，有限公司.）附錄:翻譯原文Temperature Cont

19、rol Using a Microcontroller:An Interdisciplinary Undergraduate Engineering Design ProjectJames S. McDonaldDepartment of Engineering ScienceTrinity UniversitySan Antonio, TX 78212AbstractThis paper describes an interdisciplinary design project which was done under the authors supervision by a group o

20、f four senior students in the Department of Engineering Science at Trinity University. The objective of the project was to develop a temperature control system for an air-filled chamber. The system was to allow entry of a desired chamber temperature in a prescribed range and to exhibit overshoot and

21、 steady-state temperature error of less than 1 degree Kelvin in the actual chamber temperature step response. The details of the design developed by this group of students, based on a Motorola MC68HC05 family microcontroller, are described. The pedagogical value of the problem is also discussed thro

22、ugh a description of some of the key steps in the design process. It is shown that the solution requires broad knowledge drawn from several engineering disciplines including electrical, mechanical, and control systems engineering.1 IntroductionThe design project which is the subject of this paper or

23、iginated from a real-world application. A prototype of a microscope slide dryer had been developed around an OmegaTM model CN-390 temperature controller, and the objective was to develop a custom temperature control system to replace the Omega system. The motivation was that a custom controller targ

24、eted specifically for the application should be able to achieve the same functionality at a much lower cost, as the Omega system is unnecessarily versatile and equipped to handle a wide variety of applications.The mechanical layout of the slide dryer prototype is shown in Figure 1. The main element

25、of the dryer is a large, insulated, air-filled chamber in which microscope slides, each with a tissue sample encased in paraffin, can be set on caddies. In order that the paraffin maintain the proper consistency, the temperature in the slide chamber must be maintained at a desired (constant) tempera

26、ture. A second chamber (the electronics enclosure) houses a resistive heater and the temperature controller, and a fan mounted on the end of the dryer blows air across the heater, carrying heat into the slide chamber. This design project was carried out during academic year 199697 by four students u

27、nder the authors supervision as a Senior Design project in the Department of Engineering Science at Trinity University. The purpose of this paper isto describe the problem and the students solution in some detail, and to discuss some of the pedagogical opportunities offered by an interdisciplinary d

28、esign project of this type. The students own report was presented at the 1997 National Conference on Undergraduate Research 1. Section 2 gives a more detailed statement of the problem, including performance specifications, and Section 3 describes the students design. Section 4 makes up the bulk of t

29、he paper, and discusses in some detail several aspects of the design process which offer unique pedagogical opportunities. Finally, Section 5 offers some conclusions.2 Problem StatementThe basic idea of the project is to replace the relevant parts of the functionality of an Omega CN-390 temperature

30、controller using a custom-designed system. The application dictates that temperature settings are usually kept constant for long periods of time, but its nonetheless important that step changes be tracked in a “reasonable” manner. Thus the main requirements boil down to·allowing a chamber tempe

31、rature set-point to be entered,·displaying both set-point and actual temperatures, and·tracking step changes in set-point temperature with acceptable rise time, steady-state error, and overshoot.Although not explicitly a part of the specifications in Table 1, it was clear that the customer

32、 desired digital displays of set-point and actual temperatures, and that set-point temperature entry should be digital as well (as opposed to, say, through a potentiometer setting).3 System DesignThe requirements for digital temperature displays and setpoint entry alone are enough to dictate that a

33、microcontrollerbased design is likely the most appropriate. Figure 2 shows a block diagram of the students design. The microcontroller, a MotorolaMC68HC705B16 (6805 for short), is the heart of the system. It accepts inputs from a simple four-key keypad which allow specification of the set-point temp

34、erature, and it displays both set-point and measured chamber temperatures using two-digit seven-segment LED displays controlled by a display driver. All these inputs and outputs are accommodated by parallel ports on the 6805. Chamber temperature is sensed using a pre-calibrated thermistor and input

35、via one of the 6805s analog-to-digital inputs. Finally, a pulse-width modulation (PWM) output on the 6805 is used to drive a relay which switches line power to the resistive heater off and on.Figure 3 shows a more detailed schematic of the electronics and their interfacing to the 6805. The keypad, a

36、 Storm 3K041103, has four keys which are interfaced to pins PA0 PA3 of Port A, configured as inputs. One key functions as a mode switch. Two modes are supported: set mode and run mode. In set mode two of the other keys are used to specify the set-point temperature: one increments it and one decremen

37、ts. The fourth key is unused at present. The LED displays are driven by a Harris Semiconductor ICM7212 display driver interfaced to pins PB0PB6 of Port B, configured as outputs. The temperature-sensing thermistor drives, through a voltage divider, pin AN0 (one of eight analog inputs). Finally, pin P

38、LMA (one of two PWM outputs) drives the heater relay.Software on the 6805 implements the temperature control algorithm, maintains the temperature displays, and alters the set-point in response to keypad inputs. Because it is not complete at this writing, software will not be discussed in detail in t

39、his paper. The control algorithm in particular has not been determined, but it is likely to be a simple proportional controller and certainly not more complex than a PID. Some control design issues will be discussed in Section 4, however.4 The Design ProcessAlthough essentially the project is just t

40、o build a thermostat, it presents many nice pedagogical opportunities. The knowledge and experience base of a senior engineering undergraduate are just enough to bring him or her to the brink of a solution to various aspects of the problem. Yet, in each case, realworld considerations complicate the

41、situation significantly.Fortunately these complications are not insurmountable, and the result is a very beneficial design experience. The remainder of this section looks at a few aspects of the problem which present the type of learning opportunity just described. Section 4.1 discusses some of the

42、features of a simplified mathematical model of the thermal properties of the system and how it can be easily validated experimentally. Section 4.2 describes how realistic control algorithm designs can be arrived at using introductory concepts in control design. Section 4.3 points out some important

43、deficiencies of such a simplified modeling/control design process and how they can be overcome through simulation. Finally, Section 4.4 gives an overview of some of the microcontroller-related design issues which arise and learning opportunities offered.4.1 MathematicalModelLumped-element thermal sy

44、stems are described in almost any introductory linear control systems text, and just this sort of model is applicable to the slide dryer problem. Figure 4 shows a second-order lumped-element thermal model of the slide dryer. The state variables are the temperatures Ta of the air in the box and Tb of

45、 the box itself. The inputs to the system are the power output q(t) of the heater and the ambient temperature T¥. ma and mb are the masses of the air and the box, respectively, and Ca and Cb their specific heats. 1 and 2 are heat transfer coefficients from the air to the box and from the box to

46、 the external world, respectively.Its not hard to show that the (linearized) state equationscorresponding to Figure 4 areTaking Laplace transforms of (1) and (2) and solving for Ta(s), which is the output of interest, gives the following open-loop model of the thermal system:where K is a constant an

47、d D(s) is a second-order polynomial.K, tz, and the coefficients of D(s) are functions of the variousparameters appearing in (1) and (2).Of course the various parameters in (1) and (2) are completely unknown, but its not hard to show that, regardless of their values, D(s) has two real zeros. Therefor

48、e the main transfer function of interest (which is the one from Q(s), since well assume constant ambient temperature) can be writtenMoreover, its not too hard to show that 1=tp1 <1=tz <1=tp2, i.e., that the zero lies between the two poles. Both of these are excellent exercises for the student,

49、 and the result is the openloop pole-zero diagram of Figure 5.Obtaining a complete thermal model, then, is reduced to identifying the constant K and the three unknown time constants in (3). Four unknown parameters is quite a few, but simple experiments show that 1=tp1 _ 1=tz;1=tp2 so that tz;tp2 _ 0

50、 are good approximations. Thus the open-loop system is essentially first-order and can therefore be written (where the subscript p1 has been dropped).Simple open-loop step response experiments show that,for a wide range of initial temperatures and heat inputs, K _0:14 _=W and t _ 295 s.14.2 Control

51、System DesignUsing the first-order model of (4) for the open-loop transfer function Gaq(s) and assuming for the moment that linear control of the heater power output q(t) is possible, the block diagram of Figure 6 represents the closed-loop system. Td(s) is the desired, or set-point, temperature,C(s

52、) is the compensator transfer function, and Q(s) is the heater output in watts.Given this simple situation, introductory linear control design tools such as the root locus method can be used to arrive at a C(s) which meets the step response requirements on rise time, steady-state error, and overshoo

53、t specified in Table 1. The upshot, of course, is that a proportional controller with sufficient gain can meet all specifications. Overshoot is impossible, and increasing gains decreases both steady-state error and rise time.Unfortunately, sufficient gain to meet the specifications may require large

54、r heat outputs than the heater is capable of producing. This was indeed the case for this system, and the result is that the rise time specification cannot be met. It is quite revealing to the student how useful such an oversimplified model, carefully arrived at, can be in determining overall perfor

55、mance limitations.4.3 Simulation ModelGross performance and its limitations can be determined using the simplified model of Figure 6, but there are a number of other aspects of the closed-loop system whose effects on performance are not so simply modeled. Chief among these are·quantization erro

56、r in analog-to-digital conversion of the measured temperature and· the use of PWM to control the heater.Both of these are nonlinear and time-varying effects, and the only practical way to study them is through simulation (or experiment, of course).Figure 7 shows a SimulinkTM block diagram of th

57、e closed-loop system which incorporates these effects. A/D converter quantization and saturation are modeled using standard Simulink quantizer and saturation blocks. Modeling PWM is more complicated and requires a custom S-function to represent it.This simulation model has proven particularly useful

58、 in gauging the effects of varying the basic PWM parameters and hence selecting them appropriately. (I.e., the longer the period, the larger the temperature error PWM introduces. On the other hand, a long period is desirable to avoid excessive relay “chatter,” among other things.) PWM is often difficult for students to grasp, and the simulation model allows an exploration of its operation and effects which is quite revealing.4.4 The Microcon