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<p>Higher-order transfer functions or state space models describe the dynamics of most practical single-input single-output (SISO) and multi-input multi-output (MIMO) systems. However, the comprehension and control design for large-scale systems pose difficulties. Balanced realization and truncation methods are widely utilized for model order reduction (MOR) due to their ability to preserve stability, controllability, and observability. However, this method produces reduced models with steady-state inaccuracy for a step input. Preserving stability and steady-state accuracy is a prerequisite for effective closed-loop control design. This proposal discusses a method that addresses these limitations. Balanced realization and truncation are utilized to obtain a reduced-order dynamic model (RODM). Later, the static positional error constant of the RODM is matched with that of the original system, thereby ensuring zero steady-state error (SSE). The proposed technique also facilitates the design of PID controllers for complex, practical models, enabling the achievement of the desired closed-loop requirements. The effectiveness of the offered scheme was verified using practical power system models. This strategy outperforms traditional MOR methods, exhibiting enhancements in error indices such as the H∞ norm, integral squared error (ISE), impulse response energy (IRE), integral time absolute error (ITAE), and integral absolute error (IAE). The step responses of the proposed RODM are consistent with those of the initial system, demonstrating improved precision and reliability compared to existing strategies in recent literature.</p>

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Effective model approximation of linearized power systems via intensified balanced truncation: ensuring stability, static accuracy, and PID controller compatibility

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Bala Bhaskar Duddeti,
  • Vijaya Kumar Kadha,
  • Narendra Ankireddy,
  • Lakshminarayana Janjanam

摘要

Higher-order transfer functions or state space models describe the dynamics of most practical single-input single-output (SISO) and multi-input multi-output (MIMO) systems. However, the comprehension and control design for large-scale systems pose difficulties. Balanced realization and truncation methods are widely utilized for model order reduction (MOR) due to their ability to preserve stability, controllability, and observability. However, this method produces reduced models with steady-state inaccuracy for a step input. Preserving stability and steady-state accuracy is a prerequisite for effective closed-loop control design. This proposal discusses a method that addresses these limitations. Balanced realization and truncation are utilized to obtain a reduced-order dynamic model (RODM). Later, the static positional error constant of the RODM is matched with that of the original system, thereby ensuring zero steady-state error (SSE). The proposed technique also facilitates the design of PID controllers for complex, practical models, enabling the achievement of the desired closed-loop requirements. The effectiveness of the offered scheme was verified using practical power system models. This strategy outperforms traditional MOR methods, exhibiting enhancements in error indices such as the H∞ norm, integral squared error (ISE), impulse response energy (IRE), integral time absolute error (ITAE), and integral absolute error (IAE). The step responses of the proposed RODM are consistent with those of the initial system, demonstrating improved precision and reliability compared to existing strategies in recent literature.