【正文】 擺擺桿和小車(chē)之間，以及多級(jí)倒立擺系統(tǒng)的上下擺桿之間都是強(qiáng)耦合的。 無(wú)論哪種類(lèi)型的倒立擺系統(tǒng)都具有如下特性 ： （ 1） 非線(xiàn)性 ，實(shí)際控制 可以通過(guò)線(xiàn)性化得到系統(tǒng)的近似模型，線(xiàn)性化處理后再進(jìn)行控制。 在 倒立擺系統(tǒng) 控制過(guò)程中能有效地反映現(xiàn)代控制中的許多關(guān)鍵問(wèn)題，如系統(tǒng)的魯棒性問(wèn)題、非線(xiàn)性問(wèn)題、隨動(dòng)問(wèn)題、跟蹤問(wèn)題及鎮(zhèn)定問(wèn)題等。 關(guān)鍵詞：倒立擺； PID 控制； LQR 控制；復(fù)合控制 II Design of posite controller based on inverted pendulum ABSTRACT Inverted pendulum system is a nonlinear unable systems, control theory is to carry put a variety of teaching and an ideal platform for testing control, so by the countries and engineering studies concern the experts and scholars. Many abstract concepts such as stability control systems, controllability, speed of system convergence and systems such as antiinterference ability, to pass though the inverted pendulum system shown intuitive. So far, it has been the use of classical control theory ,modern control and a variety of intelligent control a variety of methods to achieve the stability of inverted pendulum control system. Inverted pendulum control methods there are many, there is the more mon PID control, LQR control, fuzzy control. In the use of a single control, can not at the same time inverted pendulum system robustness and steadystate error at the same time to achieve a satisfactory effect, subject to the pany’s line of highsolid inverted pendulum for the study, the bination of LQR control PID control pound control, that is based on LQR control and PID control of the plementary strengths and weaknesses. Their system with simple structure, easy to implement and has strong adaptability and robustness, and can get a good dynamic performance and steadystate performance. KEY WORDS: Inverted pendulum； PID control； LQR control； Composite control III 目 錄 第一章 緒論 .................................................................................................................................... 1 概述 ...................................................................................................................................... 1 倒立擺系統(tǒng)概述 .......................................................................................................... 1 倒立擺系統(tǒng)研究現(xiàn)狀 ................................................................................................... 2 MATLAB 簡(jiǎn)介 ...................................................................................................................... 3 Simulink 簡(jiǎn)介 .............................................................................................................. 3 Simulink 功能 .............................................................................................................. 4 研究?jī)?nèi)容與章節(jié)安排 ............................................................................................................. 4 第二章 直線(xiàn)一級(jí)倒立擺系統(tǒng)概述 .................................................................................................... 6 直線(xiàn)一級(jí)倒立擺系統(tǒng)硬件結(jié)構(gòu) .............................................................................................. 6 直線(xiàn)一級(jí)倒立擺數(shù)學(xué)模型 ..................................................................................................... 7 直線(xiàn)一級(jí)倒立擺系統(tǒng)分析 ....................................................................................................12 系統(tǒng)穩(wěn)定性分析 .........................................................................................................12 系統(tǒng)能控性分析 .........................................................................................................14 系統(tǒng) 可觀測(cè)性分析 .....................................................................................................15 本章小結(jié) .............................................................................................................................17 第三章 直線(xiàn)一級(jí)倒立擺系統(tǒng) PID 控制 ............................................................................................18 PID 控制算法 .......................................................................................................................18 直線(xiàn)一級(jí)倒立擺 PID 控制器設(shè)計(jì) .........................................................................................18 直線(xiàn)一級(jí)倒立擺的 PID 控制器仿真 ......................................................................................24 本章小結(jié) .............................................................................................................................27 第四章 直線(xiàn)一級(jí)倒立擺系統(tǒng) LQR 控制 ...........................................................................................28 線(xiàn)性二次最優(yōu)控制算法 ........................................................................................................28 直線(xiàn)一級(jí)倒立擺的 LQR 控制器設(shè)計(jì) ....................................................................................30 直線(xiàn)一級(jí)倒立擺的 LQR 控制器仿真 ....................................................................................31 本章小結(jié) .............................................................................................................................33 第五章 直線(xiàn)一級(jí)倒立擺系統(tǒng) PID 與 LQR 復(fù)合控制設(shè)計(jì) ..................................................................34 兩種控制算法的對(duì)比分析 ....................................................................................................34 直線(xiàn)一級(jí)倒立擺 PID 與 LQR 復(fù)合控制器設(shè)計(jì) ......................................................................34 直線(xiàn)一級(jí)倒立擺的復(fù)合控制器仿真 ......................................................................................36 本章小結(jié) .............................................................................................................................37 第六章 總結(jié)與展望 ........................................................................................................................38 總結(jié) .....................................................................................................................................38 進(jìn)一步展望 ............................................................................