The virtual reference feedback tuning (VRFT) is a non-iterative data-driven (DD) method employed to tune a controller's parameters aiming to achieve a prescribed closed-loop performance. In its most common formulation, the parameters of a linearly parametrized controller are estimated by solving a least squares (LS) problem, which in the presence of noise leads to a biased estimate of the controller's parameters. To eliminate this bias, an instrumental variable (IV) variant of the method is usual, at the cost of increasing significantly the estimate's variance. In the present work, we propose to apply the constrained total least squares (CTLS) solution to the VRFT problem. We formulate explicitly the VRFT solution with CTLS for controllers described by an autoregressive exogenous (ARX) model. The effectiveness of the proposed solution is illustrated by two case studies in which it is compared to the usual VRFT solutions and to another, statistically efficient, design method.

中文翻译：

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具有 ARX 控制器模型和约束总最小二乘法的 VRFT

虚拟参考反馈调整 (VRFT) 是一种非迭代数据驱动 (DD) 方法，用于调整控制器参数，以实现规定的闭环性能。在其最常见的公式中，线性参数化控制器的参数是通过求解最小二乘 (LS) 问题来估计的，该问题在存在噪声的情况下会导致对控制器参数的估计有偏差。为了消除这种偏差，通常使用该方法的工具变量 (IV) 变体，代价是显着增加估计的方差。在目前的工作中，我们建议将约束总最小二乘 (CTLS) 解决方案应用于 VRFT 问题。我们明确地为自回归外生 (ARX) 模型描述的控制器制定了带有 CTLS 的 VRFT 解决方案。