Model-Free Two-Degree-of-Freedom PID Controller Design for Unknown LTI Systems

In this paper, we consider the set-point tracking problem in MIMO LTI systems with unknown model parameters. The proposed method integrates (i) the feedforward design and (ii) the PID gain tuning. We also establish a unified theoretical analysis for both components. For the feedforward design, we develop an algorithm that constructs the feedforward controller directly from the input/output data, and provide a theoretical analysis on the time horizon of the data. For the PID gain tuning, we formulate an optimization problem and solve it by employing a model-free policy gradient method combined with a variance reduction method. We further provide theoretical analyses on the required time horizon and the sample complexity of the input/output data. These analyses incorporate the result of the feedforward design into that of the PID gain tuning. In the numerical experiments, the proposed method successfully designs a 2DOF PID controller in the model-free setting.