順滑內模式控制船舶自航器設計與分析

On the Design and Analysis of Sliding Internal Model Control-Based Ship Steering Autopilot

船舶於海上航行時，受到波浪、風、海流、等多變之環境外力影響，不易於以精確的數學模式，描述其運動行為。而通常在設計船舶自航器時，為了簡化控制器設計程式及使之易於實現，多使用簡化之受控體模式為設計依據。此將導致真實受控體（Plant）與受控體數學模式（Model）之間存在著模式誤差，因此控制器必須具備容忍模式誤差之強健性和快速追蹤的能力，且控制量亦不能超過致動器工作範圍。基於上述要求，本文提出結合內模式控制（Internal Model Control, IMC），與順滑模式控制（Sliding Mode Control, SMC）兩種控制法，並以順滑層函數（Sliding Function）或輸出誤差（Output Error）為控制器切換之條件。本文動機在於結合內模式控制之平順控制力、設計簡便，與易於實現之優點，以及順滑模式控制之快速收斂和強健特性（Lyapunov漸近穩定），進而設計出順滑內模式控制（Sliding Internal Model Control, SIMC）自航器。經由模擬結果顯示，本文所提出結合內模式控制及順滑模式控制（SIMC）之自航器設計方法，能夠有效改善切跳現象。因而避免了由於切跳現象所引起的舵機飽和限制（Saturation）和舵機角速率限制（Slew Rate limitation）外，及因為高頻舵角切換造成之系統不穩定性，並快速的完成航向追蹤之目標。 Exact mathematical model description of ship maneuvering is known to be difficult due to ever changing sea states and variations in ship operation condition. To comply with availability of controller design tools and for ease of implementation, a much simplified ship model is usually preferred in the autopilot design. Consequently, the autopilot must possess certain robustness properties to be of practical use. In this work, the internal model control (IMC) method is incorporated with the sliding mode control (SMC) method to form the sliding internal model control (SIMC) method. This will eliminate the undesirable chattering behavior inherent with the sliding mode method, while maintaining the robustness properties. Consequently, the undesirable slew rate limitation (SRL) nonlinear behaviors and unnecessary wear of steering machining caused by chattering can be avoided. The proposed method is characterized by switching between two controllers and the switching criterion is based on a generalized error function that describes the zone of convergence. Numerical simulations indicate that tracking of sinusoidal reference heading is achieved with much improved chattering behavior in the presence of wave disturbances.