Paper detail

Model-Free Design and Analysis of 2DOF PI Controller for Noisy LTI Systems

Set-point tracking for systems with unknown model parameters is a fundamental problem in control, and two-degree-of-freedom (2DOF) Proportional-Integral (PI) controllers -- consisting of a feedforward controller and PI controller -- are widely employed for this task. In this paper, we propose a model-free design of 2DOF PI controllers, establish its theoretical properties, and compare them with a model-based method from both theoretical and numerical perspectives. For the feedforward design, we extend an existing model-free algorithm to systems subject to Gaussian process and measurement noises. We derive a nonasymptotic lower bound on the required control input/output data length and characterize the resulting estimation error. For PI gain tuning, we formulate a constrained optimization problem and establish sample complexity of a zeroth-order optimization method. Moreover, we quantify how inaccuracies in the feedforward design propagate to the performance of the PI controller, highlighting an interaction that has not been examined in prior work. We further provide a theoretical comparison between the proposed method and the model-based method. In particular, for PI gain tuning, the proposed method is computationally more efficient by avoiding explicit gradient computations. Numerical experiments demonstrate that the 2DOF PI controller designed by the proposed method exhibits better control performance than the model-based method.