Stiffness-compensated Load-port Control of Series Elastic Actuators Using Online Stiffness Estimation

Series elastic actuators place an elastic element between the motor and the load, which attenuates external impacts but can make precise load position control difficult. Load-Port Control (LPC) transforms the position control input into the load-port path, which reduces the phase lag seen by load position feedback, using complementary-filter-based acceleration estimation. However, LPC depends on the nominal stiffness in both the input transformation and the model-based acceleration estimation, so a mismatch between actual and nominal stiffness alters the reference response and the closed-loop characteristic equation, degrading performance. This paper proposes Stiffness-Compensated Load-Port Control (SC-LPC), which estimates stiffness from the motor-side dynamics residual and applies the estimate to the LPC input transformation, the feedback path, and the model-based acceleration branch. The singularity in the stiffness estimate at small spring deflections is mitigated through regularized regression of filtered signals with a projection. Closed-loop stability is assessed in two stages: a small-gain condition guarantees stability under the time-varying stiffness estimate, and equilibrium-point linearization evaluates local stability including motor model mismatch. Simulink simulations show that, for stiffness mismatch ratios from 0.5 to 2.0 with a matched motor model, SC-LPC reduces the worst-case root-mean-square error by about 95.3% and the worst-case peak difference by about 92.6% compared with the conventional complementary filter-based LPC. These results indicate that SC-LPC suppresses the effect of stiffness mismatch on the load position response.