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<p>Several industrial systems exhibit some degree of nonlinearity, and in some situations, it is essential to model them using nonlinear techniques, such as the Hammerstein structure. If, on the one hand, this represents an improvement in the quality of the model, on the other hand, it implies the use of advanced control techniques. However, since control strategies for linear systems are simpler and consolidated, an interesting and efficient approach is to linearize the model rather than implementing a nonlinear control methodology. Control methodologies in the literature for Hammerstein models exhibit challenges such as linearization limited to narrow operating ranges, inability of the design to meet objective performance criteria, and high computational burden. In this paper, these limitations are addressed by employing the algebraic inverse of the static nonlinearity of the Hammerstein model, enabling its linearization and subsequent control using linear techniques. A discrete-time proportional integral controller designed in state space is proposed to follow a reference with zero steady-state error and also to satisfy some performance criteria. For this purpose, synthesis conditions based on linear matrix inequalities have been used, which not only allow the assignment of control loop eigenvalues in a specific and stable region of the complex plane and ensure compliance with the performance criteria, but also are robust to model variations resulting from modeling and linearization. The following numerical results demonstrate the efficacy of the proposed approach: a 56% reduction in settling time, a lower integral of time-weighted squared error index, and execution about 15 times faster than methods in the literature.</p>

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A new approach for robust control based on parametric Hammerstein models

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Luís Henrique Santos,
  • Márcio Feliciano Braga,
  • Rodrigo Augusto Ricco

摘要

Several industrial systems exhibit some degree of nonlinearity, and in some situations, it is essential to model them using nonlinear techniques, such as the Hammerstein structure. If, on the one hand, this represents an improvement in the quality of the model, on the other hand, it implies the use of advanced control techniques. However, since control strategies for linear systems are simpler and consolidated, an interesting and efficient approach is to linearize the model rather than implementing a nonlinear control methodology. Control methodologies in the literature for Hammerstein models exhibit challenges such as linearization limited to narrow operating ranges, inability of the design to meet objective performance criteria, and high computational burden. In this paper, these limitations are addressed by employing the algebraic inverse of the static nonlinearity of the Hammerstein model, enabling its linearization and subsequent control using linear techniques. A discrete-time proportional integral controller designed in state space is proposed to follow a reference with zero steady-state error and also to satisfy some performance criteria. For this purpose, synthesis conditions based on linear matrix inequalities have been used, which not only allow the assignment of control loop eigenvalues in a specific and stable region of the complex plane and ensure compliance with the performance criteria, but also are robust to model variations resulting from modeling and linearization. The following numerical results demonstrate the efficacy of the proposed approach: a 56% reduction in settling time, a lower integral of time-weighted squared error index, and execution about 15 times faster than methods in the literature.