即時AI模型估測及控制器設計應用於大行程精密定位平台

Abstract

本論文發展一套即時模型估測與控制器設計方法，透過模型估測得到系統模型，再根據此模型設計出相對應之控制器，搭配多重控制器切換機制，根據響應估測決定當下使用之控制器，並應用於大行程精密定位平台，以模擬及實驗呈現其成果。 在精密定位系統之範疇中，由於壓電材料具有精密度高和響應快速等優點，因此已有廣泛的應用；然而壓電材料具有非線性現象且行程小之特點，故本論文將模型估測器加入至系統中，藉此降低系統不確定性之影響，透過估測出更接近真實系統之模型來達到更好的精密定位。本論文亦將大行程之步進馬達平台加入系統中，透過壓電平台之壓電材料進行精密定位，步進馬達增加平台整體行程，將其整合為大行程且高精密度之整合平台。 在小行程之壓電平台控制中，本論文透過極端梯度演算法建立模型估測器，利用系統之電壓和位移訊號當作模型估測器之輸入，其輸出為即時估測之系統模型。在控制器設計中可分為兩個部份，第一部分為設計系統之響應，我們透過強韌控制理論得到符合性能要求之多組控制器，再經由粒子群演算法透過性能指標將高階強韌控制器降階為強韌PI控制器並保有要求之性能；第二部分為即時控制器設計，透過估測出的系統模型，擬合一個較為高階的控制器，再利用Hankel奇異值分析將控制器進行降階。我們利用上述估測模型和即時設計之控制器進行控制器切換，取得當下之最佳控制器排列，再透過加入相位補償機制，補償高頻之相位誤差。由上述機制，藉由估測系統模型、即時設計控制器、以及相位補償，增進壓電平台的精確性及性能。 在大行程之馬達平台控制部份，針對步進馬達平台設計前饋控制器並結合增益調變，其中前饋器可以減少追跡誤差與相位落後，而增益調變控制調配馬達的速度來增進馬達平台的追跡能力。 最後我們整合壓電平台與馬達平台，並提出雙迴圈控制架構，透過模型估測器得到更精準之系統模型，再配合相位補償機制消除在不同頻率之相位落後，以減小整合平台的追跡誤差，並藉由模擬與實驗展現大行程且精密的定位能力。

In this paper, we presents a real-time model estimation and controller design machanism. It involves estimating a mathematical model through model estimation and designing corresponding controllers based on the desired responses. Designed controller is used in multiple switching control that selects the appropriate controller based on the estimated response. The approach is applied to a high-precision positioning stage for both simulation and experiment. In the field of high-precision positioning systems, piezoelectric materials are widely used due to their advantages of high precision and fast response. However, there are few limitations of piezoelectric materials in travel range and nonlinear behavior. This paper proposes the incorporation of model estimators into the system to reduce the impact of system uncertainties by estimating a model that more resemble to the real system, which can improve precision in positioning. Additionally, this approach integrates a high-travel range stepper motor stage with a piezoelectric stage (PZT stage) to create an integrated stage with both large travel range and high precision. For the control of the small-travel PZT stage, we employs the eXtreme Gradient Boosting (XGBoost) algorithm to build model estimators. The input to the model estimator comprises voltage and displacement signals from the system, and the output is a real-time estimated system model. For the controller design machanism, we divided it into two parts. The first part involves designing the system response based on robust control theory to obtain controllers that meet different performance requirements. These high-order robust controllers are then reduced to robust PI controllers while retaining the desired performance through Particle Swarm Optimization (PSO) algorithm. The second part focuses on real-time controller design. Through the controller design mechanism, we can get a higher order controller for estimated model that maintain similar response, after that we reduce the controller order by Hankel singular value in real-time. By multiple switching control based on the estimated model and real-time design, the best controller arrangement for the current situation is obtained. A phase compensation mechanism is then added to compensate for high-frequency phase errors. This combination of model estimation, real-time controller design, and phase compensation enhances the accuracy and performance of the PZT stage. In the control of the large-travel motor stage, a feedforward controller is designed for the stepper motor stage, which is combined with gain modulation. The feedforward controller reduces tracking errors and phase lag, while gain scheduling adjusts the motor's speed to enhance the stage's tracking capability. Finally, the paper integrates the PZT stage and motor stage, proposing a dual-loop control structure. Model estimation is used to obtain a more precise system model, and a phase compensation mechanism is employed to reduce high-frequency phase lag, thereby reducing tracking errors in the integrated stage. Simulations and experiments demonstrate the stage's ability to achieve high-precision positioning over a large travel range.