Abstract
For a multivariable system, interaction between process variables exists.Using multivariable control can solve the interaction problem.Multivariable contrlo with constrained control is still a problem. Thisthesis is concentrated on the multivariable system with constrainedcontrol. The algorithm is based on adjustment of the direction vector ofthe system with constrained control as close as that of the system withoutconstrained control.Three control constraint strategies are used to investigate theirperformances. They are signal saturation,minimum distance,and minimumangle. In order to meet specifications of signal ranges, the controlleroutput signal is usually constrained by signal saturation elements. In thepresent study, MIMO systems are considered. Variables are represented by avector. Magnitude of a vector is measured by its length. Based on thisconcept, minimum distance approach is emphasized on the distance errorbetween output vectors with and without constraints. On the other hand,the vector direction is another important physical quantity. The minimumangle approach is focused on the direction of the output vector. Theresults of several illustrative examples obtained by computer simulationshow that minimum angle approach has the better performance for trajectorytracking on the phase plane.For a nonlinear process, adaptive control is applied. It consists of twoimportant parts: system identification and control design. Basically,system identification is used to construct a linear dynamic model bymeasuring the input and output signals of the process. In this thesis,weighted moving identification is used for determining the parameters of amoving model. It consists of two steps: discarding the old data and addingthe new data. Two weighting factors are used to ensure that the movingmodel has a good tracking property and the estimated parameters areconvergent. The identification interval for system identification isdifferent from the sampling interval while the parameters of acontinuous-time model is estimated. Selection of the identificationinterval is based on three requirements. They are measurement noise,adaptation gain, and modeling error. After these requirements aresatisfied, system identification is applied. Ill-conditioned situationscan be avoided, and the large computation error also be reduced. Theresults by computer simulation show that weighted moving identificationcan describe the dynamic behavior of a process accurately. For controldesign, the model-following control strategy is used. The advantages ofusing the strategy are (a) it is easy to determine the control law,(b)implementation is easily achieved, (c) computaton time is short.In a continuous stirred-tank reactor (CSTR) with a high exothermicreaction,the reaction temperature is a very important process variable. Ifthe temperature is too high, some dangerous situations like explosion mayhappen. In order to enhance the safety, the capacity of cooling systemmust be sufficient to maintain the reaction temperature, i.e. the heatgenerated can be removed by the cooling system. Otherwise, the temperaturewill increase continuously and explosion might occur. It is possible to dothis by using the identified model to estimate the cooling capacity formanipulating the reactor temperature. Computer simulation gives that thereactor temperature can be controlled sucessfully.在化學工業的製造程序中，許多程序變數之間會相互影響，可以採用多變數控制降低各程序變數之間的干擾現象。往往控制變數也受到各種條件的限制，如何調整控制律所計算的輸入向量，使輸出向量的誤差達到最小，即為本論文探討的主題。對於多變數控制系統，當輸入向量受到限制時，本文中分別採用輸入訊號飽和法、最短距離法與最小角度法等三種限制方式比較其控制效果。對於單變數控制系統，通常採用訊號飽和元件以限制輸入訊號的範圍，把這種限制方式延伸到多變數控制系統，並研究其控制效果。對於誤差向量的大小，通常是以向量的長度為準。最短距離法主要是使實際輸出向量與期望輸出向量之間的長度誤差達到最小值。除了長度之外，誤差向量的方向也是一個重要的物理量，因此最小角度法是以實際輸出向量與期望輸出向量的方向誤差為主要考慮因素。根據電腦模擬的結果顯示，三種限制方式中，以最小角度法遵循軌跡的性質較好。對於非線性系統，本文中是採用適應控制，其中包含系統識別與控制器設計兩個部份。基本上系統識別是量測程序之輸入變數與輸出變數以建立線性動態模式，並作為設計控制器的基礎。本文中是採用加權移動性識別法計算移動性模式的系統參數，其中包含加入新數據與捨棄舊數據兩個步驟，分別以加權因子使移動性模式具有良好的追蹤性並確保系統參數之收斂性。對於連續時間系統模式，則採用可調變識別間隔之加權移動性識別法。分別以測量誤差、適應增益與模式誤差等三個準則決定識別間隔，不但可以減少計算誤差，也可以避免識別不良的情形。根據電腦模擬的結果顯示，移動性識別模式的確可以精確地描述程序之動態變化的特性。至於控制器設計的部份，本文中採用模式遵循控的制策略，由於推導過程簡單，也便於使用，可以節省部份電腦的計算時間。對於連續攪拌反應器，當其內部進行高放熱反應時，反應溫度是一個非常重要的程序變數。若反應溫度過高往往會造成危險，為了提高程序操作之安全性，就必須參考冷卻系統的操作範圍內，限制反應溫度使反應熱能被冷卻系統完全吸收，否則反應溫度持續升高之後，增加反應速率而產生更多的熱量，造成反應溫度高失控的情形。根據系統識別得到的動態模式，估計冷卻系統的降溫效果作為限制反應溫度的依據。電腦模擬的結果顯示，確實可以有效地避免反應溫度失控的情形。