摩擦為一般機構中普遍存在的非線性現象，本文研究控制系統受摩擦影響下的動態行為。本文首先研究此類系統在摩擦影響下的參數鑑別問題，提出對於轉動慣量、阻尼係數，以及動靜摩擦力等重要參數的估測方式。接著研究摩擦的數學模型，分析連續與不連續模型間的差異，並針對不連續模型提出創新的雙階段積分法，解決此模型在零速度時的數值問題，去除在Karnopp 方法中的零速度區間限 制。此外，利用雙階段式積分法，本文修正傳統庫倫摩擦模型，並依據修正模型探討摩擦對系統定位性能的影響。此研究發現，接觸面間因靜摩擦造成的順預滑位移(presliding displacement)會改變自激性抖動(hunting)的穩定性，並會在使用積分控制的系統中產生特有的慢動態行為，影響精密定位系統的性能甚巨。據此，本文提出三段式（比例、脈波，以及斜坡，PPR）控制器，其中斜坡控制為本文提出之獨特創新方式。PPR 控制器主要依據與摩擦相關的兩項數據設計：最大靜摩擦力與順預滑位移。此二者均無須精確估測，前者甚至容許達200%的變化。實驗證實，PPR 控制器僅以位置回授，可在0.3-0.7 秒間完成精度1 微米的定位控制，而一最佳調測的PID 控制器至少需3 秒以上。本文末以Lyapunov 理論證明PPR 控制器的穩定性。 Friction is inherent in mechanisms. In this dissertation we study the dynamics of pointing systems involving conspicuous friction. First we develop a general method for the identification of systems with friction. Then an analytic algorithm for simulation of discontinuous friction model is presented. In the proposed algorithm we remove the requirement of the zero-velocity region in the Karnopp-like method and develop a two-stage integration algorithm to solve the differential equations involving a discontinuity at zero velocity. A procedure to estimate the Stribeck velocity, which specifies how the friction force decreases in the range of very low velocities, is also presented. Next we study the influence of presliding displacement on hunting. Through experimental and numerical evaluations, we found that presliding displacement could affect the stability of hunting. Such displacement is also crucial to the performance of high-accuracy pointing applications. With this observation, we propose a modified Coulomb friction model to increase its accuracy in the sticking regime. Finally a controller consisting of three schemes, proportional gain, pulse, and ramp (PPR), is proposed to achieve precise and fast pointing control under the presence of friction. Design of the PPR controller is based on two distinctive features of friction, the varying sticking force and presliding displacement of contacts. The latter is the main idea behind the ramp scheme to replace integration control, which induces slow dynamics in the sticking state. Experimental results demonstrate the robustness and effectiveness of the proposed controller. Stability investigated by the Lyapunov theorem is given in this dissertation.
