Robust model reference adaptive controller for atmospheric plasma spray process

Abstract

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 $$\sigma$$ 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 $$2 \le \gamma \le 20,$$ 2 ≤ γ ≤ 20 , $$10 \le \sigma \le 100,$$ 10 ≤ σ ≤ 100 , and $$20 \le \lambda \le 80$$ 20 ≤ λ ≤ 80 for the MR-MRAC provide fast adaptation, no overshoot, and low tracking error in the controlled response. The parameter $$\lambda > 0$$ λ > 0 suppresses high-frequency oscillations in the closed-loop control system, and $$\gamma$$ γ serves to tune the controller gains. The control scheme has been tested using the software, LAVA-P, that simulates well an APSP.

Adaptive Control of the Atmospheric Plasma Spray Process for Functionally Graded Thermal Barrier Coatings

“…illustrates three diferent MR-MRACs along with the corresponding measured output variables and the input parameters they adjust. Guduri and Batra [12] have described the development of the MR-MRAC-1. It entails the following seven steps: (i) specifcation of the MPSs (output variables) and of the lower and the upper bounds of the signifcant input parameters selected using the screening analysis, (ii) quantifcation of disturbances to be considered, (iii) time duration allowed for the process parameters to respond to the disturbances, (iv) a mathematical model of the process linearized around a steady (or an equilibrium) state, (v) system identifcation, (vi) controller design, and (vii) implementation and testing of the controller.…”

“…It entails the following seven steps: (i) specifcation of the MPSs (output variables) and of the lower and the upper bounds of the signifcant input parameters selected using the screening analysis, (ii) quantifcation of disturbances to be considered, (iii) time duration allowed for the process parameters to respond to the disturbances, (iv) a mathematical model of the process linearized around a steady (or an equilibrium) state, (v) system identifcation, (vi) controller design, and (vii) implementation and testing of the controller. Te material in this subsection extends the work described in reference [12] for a single powder port to two powder ports and is included for completeness. Te mathematical formulations of the MR-MRAC-1, the MR-MRAC-2, and the MR-MRAC-3 are included in Figure 2 and their implementation in an APSP for generating FGCs are briefy discussed below.…”

“…For the MR-MRAC-1 [12], the model relating the three inputs, u(t) � P(t), Q(t), I(t) { } T , and the two outputs,…”

“…We investigate the signifcance of eight injection parameters, namely, the average injection velocities of the NiCrAlY and the ZrO 2 particles, y− and z− locations of their injectors, and their mass fow rates in the observation window averaged in the zdirection. Te process parameters used in this study are as follows: current = 500 A, Ar fow rate = 40 slm, H 2 fow rate = 10 slm, voltage = 60 V, and particle size = 30-100 μm, the average injection velocity and mass fow rates of the NiCrAlY and the ZrO 2 powders (m/s, g/minute)) (5,15), and (15, 40); (y, z)locations of the NiCrAlY and ZrO 2 injectors (mm) (4,6), and (12,10).…”

“…Here, we use controllers based on a model reference adaptive control (MRAC) framework [9] whose robustness has been enhanced by incorporating in it the σ modifcation [10] and the low-frequency learning [11]. We called it the "modifed robust MRAC" (MR-MRAC) and illustrated its capability [12] in the presence of bounded external disturbances to adaptively adjust input parameters for a onematerial coating to achieve the desired MPSs within small tolerances. Here, we propose the use of three MR-MRACs for producing FGCs comprised of NiCrAlY and ZrO 2 particles.…”