- 期刊
單晶片微控制器於非線性系統之設計與實現
Design and Implementation of a Nonlinear System Based on a Microcontroller
摘要
由於倒單擺機構屬於典型的非線性與不穩定系統，因此極適合用來測試各種不同的控制器性能。本文提出新的控制法則，包含LQR(linear quadratic regulator)+PI(proportion and integration)與LQR + Fuzzy，並與傳統的PID(proportion, integration and derivation)與LQR等控制法則進行比較，結果顯示出較好的控制能力。除新控制法則的提出外，本文也實現了倒單擺系統機械架構與硬體控制電路之設計。在控制電路方面，至少完成：PIC18F452主控制電路、HCTL2020光學編碼器解碼電路、馬達驅動電路與RS232串列傳輸電路等設計。本文採用美商Microchip高階之八位元微控制器PIC18F452來做為本系統之控制核心，實現的控制法則有：PID控制器、LQR控制器、LQR+PI控制器與LQR + Fuzzy控制器等。透過實際量測可知：當僅採PID控制器時，且台車位置在原點附近時，單擺角度可控在－1.8~+1.1度之間，但台車位置則完全不可控；至於LQR控制器，倒單擺系統之直立角度可控在－1.8~+3.4度之間，而台車位置則在－1.4~+10.8公分間左右來回，因此位置控制並不理想；當PI控制器加入到LQR控制器時，其單擺角度與台車位置分別可控在±2度與±3公分以內。很明顯地，LQR+PI控制器在控制倒單擺系統之直立定位能力優於LQR與PID控制器。當結合Fuzzy控制法則到LQR控制器時，根據量測結果可知，單擺角度與台車位置可分別控在±2度與±3公分以內，表示LQR + Fuzzy控制器之能力與LQR+PI控制器相當，但卻可以避免PI控制器調整參數所帶來的麻煩。
並列摘要
An inverted-pendulum mechanism is typically a nonlinear unstable system. Therefore, it is quite suitable as an example for verifying the performance of various control rules. In this report we propose two new control rules, namely, an LQR (Linear Quadratic Regulator)+PI (Proportion and Integration) and an LQR + Fuzzy, both of which are compared in performance with traditional LQR and PID (Proportion, Integration and Derivation) control rules. A cart-and-pole inverted-pendulum system is implemented for comparing the performance of the different control rules. The designs of related control circuits include a PIC18F452 main control circuit, an HCTL2020 optical decoder, a motor-driven circuit, and an RS232 data acquisition circuit. For considering programming flexibility, an 8-bit microcontroller PIC18F452 is employed to implement the control rules, i.e., PID, LQR, LQR+PI, and LQR + Fuzzy, to achieve both the upright and position controls of the inverted-pendulum system. The experimental results indicate that the pole angle can be controlled within -1.8 to +1.1 degrees, but the cart position is completely uncontrollable when using only a PID controller. Furthermore, with the adoption of only an LQR controller, the pole angle and the cart position can be controlled within -1.8 to +3.4 degrees and -1.4 to +10.8 cm, respectively. This observation implies the poor controllability of the cart position for the LQR controller. When a PI control rule is added to the LQR controller, the pole angle and the cart position can be improved to within only ±2 degrees and ±3 cm, respectively. Clearly, the LQR+PI controller is superior in performance to that of only an LQR or a PID controller. Moreover, when adding the Fuzzy control rule to the LQR controller, the results show that the LQR + Fuzzy has comparable capabilities for controlling both the pole angle and the cart position in comparison with the LQR+PI controller; however, the LQR + Fuzzy can effectively eliminate the troubles in tuning the parameters in the PI controller.