A Practical Youla Gain-Tuning Framework for H_∞ Controller Realization

Standard H_∞ controller synthesis produces robust controllers with well-shaped sensitivity and complementary sensitivity transfer functions, S and T. However, at times H_∞ does not enforce strict requirements on sensitivity, in particular the desired requirement that T has unity gain at DC frequency. This results in typically negligible steady-state tracking error, as the H_∞ optimization produces T(0)≈1. In drive cycle applications where reference velocity profiles contain extended ramp segments, this negligible deviation is integrated over time into a growing, non-negligible bias. The conventional remedy is to augment the plant with an integrator prior to synthesis, but this increases the order of the plant model and can be inconvenient when the control designer’s modeling has already been completed. This paper presents a post-synthesis gain adjustment method using Youla parameterization that corrects the DC tracking deficiency without modifying the plant or repeating H_∞ synthesis. The poles and zeros corresponding to the H_∞ controller’s Youla transfer function Y are preserved, with a free parameter K replacing the gain of Y. Re-calculating the controller after solving for the value of K that enforces T(0)=1 results in a hybrid controller that retains the robustness of the original but with improved performance in ramp-input scenarios with minimal effort for the control designer. Simulation results on a vehicle speed tracking problem confirm elimination of accumulating bias while preserving robustness margins from the original H_∞ design.