應用模糊滑動控制與動態補償機制於自行車之平衡控制

Abstract

本研究旨在建立更具強健性的自動導引自行車系統。為了能使自行車在顛簸的路面上行走、抵抗外在撞擊、校正誤差、單側附載過重、擺動龍頭等因素，將使系統偏離理想情境而降低系統穩定性，需使用具有相當強健性的控制策略，故本研究係使用動態補償機制 (Dynamic compensation) 與具有高強健性的模糊滑動控制 (Fuzzy sliding mode control, FSMC) 策略結合，並利用能迅速提供平衡力矩的陀螺儀平衡器，開發更具強健性的自行車平台。 動態補償機制包含兩大主軸。第一是以過去系統控制表現進行補償的PID控制電壓補償機制 (PID control voltage compensation) 與PID滑模數值補償機制 (PID sliding value compensation)，當系統存在穩態誤差時，調整FSMC控制電壓輸出規則與滑模數值原點，以增進系統控制表現。第二是龍頭轉向之補償機制 (Handlebar compensation)，當轉動龍頭而造成前輪接地點位置改變時，能夠快速給予所需的補償數值，以維持系統穩定。 本研究中利用Lagrange方程式推導自行車平台之動力模型，再以FSMC策略使系統狀態收斂至平衡點，並將平台參數帶入系統模型，以數值模擬證明其穩定性，接著與前述動態補償機制結合，實現強健的自行車平台，最後在平台單側懸掛負重與轉動龍頭至不同角度，探討不同補償機制下，紀錄其系統狀態響應。 經多組不同負重測試後可得，以PID控制電壓補償策略結合FSMC，最高可承受8.20N-m單側負重，相較僅使用FSMC增加53%之單側負重能力；以PID滑模數值補償機制結合FSMC效果較佳，能提升至9.46N-m以上，相較於僅使用模糊滑動控制提升76%平衡能力。接著再利用迴歸分析找出龍頭轉角與補償數值間的關係，應用於龍頭轉向之補償機制，使自行車平台在快速轉動龍頭時，仍能維持其穩定性。最後將上述研究結果整合，在柏油路上進行定圓繞行，觀察系統狀態並測試其平衡穩定性。

This study aims to develop a more robust riderless bicycle system. In order to overcome external disturbance and internal uncertainty, we use a gyroscopic balancer and the control strategy combining fuzzy sliding mode control (FSMC) and dynamic compensation. There are two aspects of the dynamic compensation. First is to improve control performance by incorporating the steady state error of sliding value. With PID control voltage compensation and PID sliding value compensation, FSMC control voltage and sliding value zero are adjusted respectively by the state error. Second is to further improve the performance by applying the compensation for handlebar turning. If the turning angel is changed, results in movement of the system equilibrium position, the compensator adjusts immediately to maintain the balance stability. The dynamic model of the system is derived based on Lagrange equation; then all state variables converged to equilibrium point by FSMC, proved by the numerical simulation. Next, combining FSMC with the dynamic compensation makes the riderless bicycle system be more capable of resisting constant disturbance, proved by field testing with one-sided loading. Tested by multiple sets of one sided loading, PID control voltage compensation combined with FSMC can bear 8.20N-m one-sided loading, improving 53% one-sided loading capability compared with only using FSMC; PID sliding value compensation combined with FSMC has better effect and can bear 9.46N-m one sided loading above, improving 76% one sided loading capability compared to only using FSMC. Afterward, relation between turning angle and compensation value is found out by regression analysis and applied in handlebar compensation. In the end, the riderless bicycle with the approach developed in the study successfully circles on asphalt road without falling down.