【正文】 the multivariable controller gives the set points to the controllers at the lower level. The PID controller can thus be said to be the “bread and butter of control engineering. It is an important ponent in every control engineer’s tool box.PID controllers have survived many changes in technology, from mechanics and pneumatics to microprocessors via electronic tubes, transistors, integrated circuits. The microprocessor has had a dramatic influence the PID controller. Practically all PID controllers made today are based on microprocessors. This has given opportunities to provide additional features like automatic tuning, gain scheduling, and continuous adaptation. The AlgorithmWe will start by summarizing the key features of the PID controller. The “textbook” version of the PID algorithm is described by: where y is the measured process variable, r the reference variable, u is the control signal and e is the control error（e = ? y）. The reference variable is often called the set point. The control signal is thus a sum of three terms: the Pterm （which is proportional to the error）, the Iterm （which is proportional to the integral of the error）, and the Dterm （which is proportional to the derivative of the error）. The controller parameters are proportional gain K, integral time Ti, and derivative time Td. The integral, proportional and derivative part can be interpreted as control actions based on the past, the present and the future as is illustrated in Figure . The derivative part can also be interpreted as prediction by linear extrapolation as is illustrated in Figure . The action of the different terms can be illustrated by the following figures which show the response to step changes in the reference value in a typical case.Effects of Proportional, Integral and Derivative ActionProportional control is illustrated in Figure . The controller is given by with Ti = and Td=0. The figure shows that there is always a steady state error in proportional control. The error will decrease with increasing gain, but the tendency towards oscillation will also increase.Figure illustrates the effects of adding integral. It follows from that the strength of integral action increases with decreasing integral time Ti. The figure shows that the steady state error disappears when integral action is used. Compare with the discussion of the “magic of integral action” in Section . The tendency for oscillation also increases with decreasing Ti. The properties of derivative action are illustrated in Figure .Figure illustrates the effects of adding derivative action. The parameters K and Ti are chosen so that the closed loop system is oscillatory. Damping increases with increasing derivative time, but decreases again when derivative time bees too large. Recall that derivative action can be interpreted as providing prediction by linear extrapolation over the time Td. Using this interpretation it is easy to understand that derivative action does not help if the prediction time Td is too large. In Figure the period of oscillation is about 6 s for the system without derivative Chapter 6. PID ControlFigure Figure Derivative actions cease to be effective when Td is larger than a 1 s (one sixth of the period). Also notice that the period of oscillation increases when derivative time is increased.A PerspectiveThere is much more to PID than is revealed by （）. A faithful implementation of the equation will actually not result in a good controller. To obtain a good PID controller it is also necessary to consider.Figure Noise filtering and high frequency roll off我的設(shè)計(jì)較為煩瑣，但是舒老師仍然細(xì)心地指導(dǎo)了我論文的每個細(xì)節(jié)。鑒于時間與條件的限制，實(shí)驗(yàn)系統(tǒng)需要進(jìn)一步改進(jìn)與完善。5 總結(jié)兩輪自平衡小車是復(fù)雜的非線性系統(tǒng)，是驗(yàn)證各種控制算法的理想平臺。 （423）由于穩(wěn)定是控制系統(tǒng)能夠運(yùn)行的前提，因此選擇調(diào)節(jié)時間和超調(diào)量作為考察系統(tǒng)動態(tài)性能的指標(biāo)。此時系統(tǒng)能觀，可以設(shè)計(jì)控制器對那些不能測量的量進(jìn)行觀測，觀測系統(tǒng)變動對它們的影響。狀態(tài)能觀性問題是指對于任意給定的輸入u(t)在有限觀測時間tft0，使得根據(jù)[t0，tf]期間的輸出y(t)能唯一的確定系統(tǒng)在初始時刻的狀態(tài)x(t0)，則該狀態(tài)x(t0)是能觀測的。狀態(tài)能控性問題只考察系統(tǒng)在u(t)作用下狀態(tài)的轉(zhuǎn)移情況，與輸出量y(t)無關(guān)。控制系統(tǒng)的各種特性及其各種品質(zhì)指標(biāo)很大程度上由閉環(huán)系統(tǒng)的零點(diǎn)和極點(diǎn)位置決定。因此其參數(shù)可按模擬PID控制器中的方法來選擇。PID算法應(yīng)用如此廣泛，是因?yàn)樗哂腥缦聝?yōu)點(diǎn):(1)算法較為簡單，易于實(shí)現(xiàn)；(2)基于線性控制理論，具備許多成熟的穩(wěn)定性分析方法，有較高的可靠性；(3)可以在很寬的操作條件內(nèi)保持較好的魯棒性，對于控制對象模型參數(shù)小范變化不敏感；(4)不要求了解控制對象的精確數(shù)學(xué)模型。由上面的數(shù)學(xué)模型可得到該系統(tǒng)的狀態(tài)方程如下：其中：上述狀態(tài)方程亦可以寫成：=Ax+Bu；系統(tǒng)的輸出則通常與系統(tǒng)狀態(tài)變量和輸入信號有關(guān)，即y=Cx+Du。根據(jù)受力分析可知：其車輪不但受電機(jī)的輸出轉(zhuǎn)矩、地面支持力、摩擦力的影響，同時還通過電機(jī)軸受到機(jī)器人車身作用力。為了研究其原理及其可行性，有必要對其系統(tǒng)進(jìn)行相應(yīng)的平衡分析以及合理的數(shù)學(xué)建模，為后續(xù)的控制策略等工作提供必要的理論支撐。數(shù)據(jù)信息融合的方法是多傳感器數(shù)據(jù)信息融合最重要的部分，由于其應(yīng)用上的復(fù)雜性和多樣性，決定了信息融合的內(nèi)容極其豐富。[19]g 加速度計(jì)輸出與重力的關(guān)系可表示為： （31） （32） 式中：Ax和Ay——加速度計(jì)x靈敏軸和y靈敏軸的輸出； g——重力加速度； θ——傾斜角度。第二類:隨機(jī)性質(zhì)的漂移MEMS陀螺隨機(jī)性質(zhì)的漂移主要源自于由摩擦、溫度梯度等因素引起的干擾力矩。由于內(nèi)部無需集成旋轉(zhuǎn)部件，因此微機(jī)械陀螺儀具有成本低和體積小等特點(diǎn)，便于小型化和批量生產(chǎn)。傳感器傾角計(jì)加速度計(jì)陀螺儀被測量角度加速度角速度優(yōu)點(diǎn)靜態(tài)性能好靜態(tài)性能好動態(tài)性能好缺點(diǎn)動態(tài)相應(yīng)慢，不適合跟蹤動態(tài)角速度運(yùn)動動態(tài)相應(yīng)慢，不適合跟蹤動態(tài)角速度運(yùn)動存在積累漂移誤差，不適合長時間單獨(dú)工作表31三種傳感器性能比較綜合考慮各傳感器優(yōu)缺點(diǎn)、兩輪自平衡小車實(shí)際的控制和經(jīng)濟(jì)性要求，選用的是加速度計(jì)和陀螺儀兩種傳感器，用于檢測小車車身傾斜角度和傾斜角速度。第三章將詳細(xì)介紹該系統(tǒng)所用到的主要傳感器的基本原理以及如何提高它們檢測的可靠性。 電流檢測電路電流檢測電路設(shè)計(jì)的目的是防止電機(jī)起動、過載或異常運(yùn)行時由于電流過大而對控制電路、功率場效應(yīng)管和電動機(jī)本體的損害。該器件采用雙極型模擬工藝，在任何惡劣的工業(yè)環(huán)境條件下都具有高品質(zhì)和穩(wěn)定性。（a）、（b）所示。它是指在直流無刷電機(jī)定子上安裝位置傳感器來檢測轉(zhuǎn)子在運(yùn)轉(zhuǎn)過程中的位置，將轉(zhuǎn)子磁極的位置信號轉(zhuǎn)換成電信號，為電子換相電路提供正確的換相信息，來控制電子換相電路中的功率開關(guān)管的開關(guān)狀態(tài)，保證電機(jī)的各相按正確的順序?qū)?，在空間形成跳躍式的旋轉(zhuǎn)磁場，驅(qū)動永磁轉(zhuǎn)子連續(xù)不斷地旋轉(zhuǎn)。通過脈寬調(diào)制變換器進(jìn)行調(diào)制的方法又稱PWM(Pulse Frequency Modulation)。（2） 改變電機(jī)的主磁通。為了實(shí)現(xiàn)無電刷換向的目的，直流無刷電動機(jī)一般將其電樞繞組放在定子上，把永磁磁鋼放在轉(zhuǎn)子上，這與傳統(tǒng)直流永磁電動機(jī)的結(jié)構(gòu)剛好相反。步進(jìn)電機(jī)能直接實(shí)現(xiàn)數(shù)字控制，控制性能好，能快速啟動、制動和反轉(zhuǎn)，抗干擾能力強(qiáng)等優(yōu)點(diǎn)。（4） 研究自平衡小車的控制策略。上述的機(jī)器人和代步小車對本課題的研究提供了很好的指導(dǎo)作用，為下面的研究工作提供了很好的參考。圖 SEGWAY HT Bender 國內(nèi)的研究成果我國在兩輪自平衡機(jī)器人方面的研究也取得了一定的成就：西安電子科技大學(xué)研究出了自平衡兩輪機(jī)器人[5]，它是一種兩輪式左右并行布置結(jié)構(gòu)的自平衡系統(tǒng)。它使用了五個陀螺儀和一個收集其他角度傳感器數(shù)據(jù)的集成器來保持自身的直立狀態(tài)。 國外的研究成果在兩輪自平衡小車的研究上，國外的專家和愛好者們?nèi)〉昧艘幌盗械某晒韵陆榻B國外幾個比較先進(jìn)的兩輪自平衡小車：由美國科學(xué)家David P. Anderson[2]研發(fā)的兩輪自平衡機(jī)器人Nbot基于倒立擺的小型自平衡兩輪車模型，是由HCllrobotcontr0ller進(jìn)行控制的。近年來，隨著移動機(jī)器人研究不斷深入、應(yīng)用領(lǐng)域更加廣泛，所面臨的環(huán)境和任務(wù)也越來越復(fù)雜。機(jī)器人經(jīng)常會遇到一些比較狹窄，而且有很多大轉(zhuǎn)角的工作場合，如何在這樣比較復(fù)雜的環(huán)境中靈活快捷的執(zhí)行任務(wù)，成為人們頗為關(guān)心的一個問題。2004年，Homebrew