基於智慧型分數階超扭曲滑動模式控制之3-PRP型並聯式機械平台

Abstract

本論文以個人電腦作為控制單元，嘗試做出具有高精度、高強健性之智慧型分數階超扭曲滑動模式控制演算法，不僅自製3-PRP型並聯式機械平台上並實作驗證。並聯式機械平台是基於並聯式機械手臂，透過三顆旋轉伺服馬達加上連桿結構形成關節，根據連接的關節不同，在組合上相當靈活，可以被設計為3-RPP、3-PRP、3-PPR亦或上述的任意組合，而本論文選用3-PRP的架構進行自製。由於許多研究都指出並聯式機械平台都有著複雜耦合的動態特性，為了有效進行控制，透過拉格朗日方程式建立機械平台之動態模型。控制器部分，透過雅可比矩陣將 、 和 方向的目標軌跡進行轉換，將運動軌跡進行解耦合，再將命令輸入控制器。將傳統的滑動模式加入超扭曲的特性，除了保留傳統滑動模式優點外，也降低系統抵達滑動面之後的小範圍抖動，並將超扭曲滑動模式演算法引入分數階微積分概念，增加控制參數的自由度以提升控制效果。最後為了消除系統在外部干擾、參數變化等影響使其提升強健性，再提出循環神經網路估測器補償系統之不確定性誤差，發展出智慧型分數階超扭曲滑動模式控制系統，此系統也通過李亞普諾夫穩定性來證明穩定性及權重更新。經過實驗證實，本研究設計之控制演算法可以有效控制自製之3-PRP型並聯機械平台。This study mainly uses a personal computer as the algorithm control unit to make an intelligent fractional-order super-twist sliding mode control algorithm with high precision and high robustness and implement the algorithm on a self-made 3-PRP parallel mechanical platform for verification.The parallel mechanical platform is based on a parallel mechanical arm, which forms joints through three rotary servo motors and the link structure. Depending on the connected joints, the combination is quite flexible and can design as 3-RPP, 3-PRP, 3 -PPR, or any combination of the above, and this thesis uses the 3-PRP architecture by self-made.Since many studies have pointed out that the parallel mechanical platform has complex coupled dynamic characteristics, in order to control it effectively, this thesis establishes the dynamic model of the 3-PRP parallel mechanical platform through Lagrange mechanics. In the controller part, after decoupling target trajectories in x,y, and theta directions through the Jacobian matrix, the decoupled commands are the controller's inputs. In addition, the traditional sliding mode is added with super-twisting characteristics, which retains the advantages of the traditional sliding mode and reduces the phenomenon of small-scale shaking after the system state reaches the sliding surface. Then, adding the fractional-order concept into the super-twisting sliding mode algorithm increases the degree of freedom of the control parameters to improve the control effect. Finally, to eliminate the influence of external disturbanceand parameter changes to improve the system's robustness, a recurrent neural network estimator is proposed to compensate uncertainty of the system, and an intelligent fractional-order super-twist sliding mode control system is developed. Furthermore, stability prove and weight updates are divided by the Lyapunov theorem.The experiment result confirmed that the proposed control algorithm designed in this study could effectively control the self-made 3-PRP parallel mechanical platform.