Non-minimum phase (NMP) systems, characterized by unstable zeros or poles, pose significant challenges in control design due to their inherent inverse response and phase lag. This paper proposes a U-model-based control framework integrated with a pulling principle to address these limitations. By leveraging infinite impulse response (IIR) filters in feedforward and feedback paths, the method relocates unstable zeros and poles through summation/subtraction operations, converting NMP systems into stable minimum-phase (MP) models without relying on error-prone multiplicative cancellations. The design decouples the NMP-to-MP conversion from controller synthesis, enabling an invariant linear controller to achieve specified closed-loop dynamics while a U-model inverter dynamically resolves the plant’s inverse. Key contributions include: (1) A systematic zero/pole relocation framework with proven robustness against unit-circle positioning errors. (2) A separation principle that simplifies controller tuning and enhances adaptability, and (3) Comprehensive validation through MATLAB simulations on diverse NMP system of the altitude-hold autopilot. Results demonstrate superior performance compared LQG method. The approach reduces design complexity, avoids repetitive tuning, and ensures bounded-input bounded-output (BIBO) stability. This work bridges theoretical rigor with practical applicability, offering a generalized solution for NMP systems of the altitude-hold autopilot.

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U-Model Based Pole-Zero Pulling Control for Non-minimum Phase Systems with an Application to Altitude-Hold Autopilot

  • Dexin Meng,
  • Ji Qiu

摘要

Non-minimum phase (NMP) systems, characterized by unstable zeros or poles, pose significant challenges in control design due to their inherent inverse response and phase lag. This paper proposes a U-model-based control framework integrated with a pulling principle to address these limitations. By leveraging infinite impulse response (IIR) filters in feedforward and feedback paths, the method relocates unstable zeros and poles through summation/subtraction operations, converting NMP systems into stable minimum-phase (MP) models without relying on error-prone multiplicative cancellations. The design decouples the NMP-to-MP conversion from controller synthesis, enabling an invariant linear controller to achieve specified closed-loop dynamics while a U-model inverter dynamically resolves the plant’s inverse. Key contributions include: (1) A systematic zero/pole relocation framework with proven robustness against unit-circle positioning errors. (2) A separation principle that simplifies controller tuning and enhances adaptability, and (3) Comprehensive validation through MATLAB simulations on diverse NMP system of the altitude-hold autopilot. Results demonstrate superior performance compared LQG method. The approach reduces design complexity, avoids repetitive tuning, and ensures bounded-input bounded-output (BIBO) stability. This work bridges theoretical rigor with practical applicability, offering a generalized solution for NMP systems of the altitude-hold autopilot.