Robust model reference adaptive controller for atmospheric plasma spray process

We add the σ-modification and the low-frequency learning to the model reference adaptive controller (MRAC) (Guduri et al. in SN Appl Sci 3:1–21, 2021) to make it robust in the presence of two simultaneous bounded disturbances and maintain consistent mean particles’ temperature and velocity collectively called mean particles’ states (MPSs) when they impact the substrate to be coated. The MPSs affect the coating quality. Even though results are applicable to several coating processes, we consider an atmospheric plasma spray process (APSP). It is shown that the proposed controller can quickly adopt to disturbances in the average injection velocity of powder particles and in the arc voltage to change the input current, and the argon and the hydrogen flow rates to maintain constant values of the MPSs. The effects of the parameter values in the MRAC, the MRAC with σ-modification (R-MRAC), and the R-MRAC with low-frequency learning (MR-MRAC) schemes on tracking error convergence, steady-state tracking error, disturbance rejection and the presence of overshoot have been studied. The numerical experiments suggest that 2 ≤ 𝛄 ≤ 20, 10 ≤ σ ≤ 100, and 20 ≤ λ ≤ 80 for the MR-MRAC provide fast adaptation, no overshoot, and low tracking error in the controlled response. The parameter 𝜆 > 0 suppresses high-frequency oscillations in the closed-loop control system, and 𝛄 serves to tune the controller gains. The control scheme has been tested using the software, LAVA-P, that simulates well an APSP.