Internal Model based SMC for FJRs using Singular Perturbation Approach

The trajectory tracking performance of flexible joint robots (FJRs) is adversely affected in the presence of measurement noise, unmodelled system dynamics, external disturbances, and parametric variations. This paper proposes singular perturbation (SP) based continuous sliding mode controller (CSMC) schemes for the FJRs system to attain superior tracking accuracy. Firstly, the SP is applied to split the high-order FJRs system into two second-order quasi-steady-state and boundary layer models, which relaxes the requirements of high derivatives of system states in the control design. Secondly, two state-differentiators are developed for both subsystems to estimate unavailable velocity and acceleration signals. Then, based on estimated signals, the two CSMC schemes are constructed for both subsystems to attain the asymptotic convergence of tracking errors and fast variables, reduce chattering, and ensure robustness against external disturbance, measurement noise, and system uncertainties. Furthermore, the internal model method is applied to ease the tuning process of the sliding surface gains in the CSMC for both models. More importantly, the bandwidth of a fast control is chosen based on a slow subsystem bandwidth using Ruth Hurwitz stability criteria. Thus, the hectic gains tuning process is hugely simplified by applying an internal model based tuning on both subsystems. Finally, the provided simulation results verify the effectiveness of our proposed control in terms of measurement noise suppression, less chattering, robustness, and high tracking accuracy comparatively.