In this work, the design of a controller for a multiple-input multiple-output (MIMO) nonlinear system with uncertain control direction is proposed. A formal Lyapunov stability analysis is presented for the design of the MIMO controller by considering the system with and without parametric uncertainties. The design is applied to an additive manufacturing technology known as Laser Cladding (LC). The proposed MIMO controller is composed of a feedback linearization term (aimed at canceling the known nominal dynamics) and a sliding mode term with the boundary layer technique (aimed at compensating the system uncertainties). The proposed control scheme was tested via simulations by considering tracks of two different powder feedstock, Ti6Al4V and IN718. Simulation results confirm that the control objective is achieved under parametric uncertainties, including variations up to 40% of the convection coefficient. Moreover, the control law is easy to implement and the control signal has a continuous behavior precluding any high-frequency oscillation (chattering effect).

在这项工作中，提出了一种控制方向不确定的多输入多输出 (MIMO) 非线性系统的控制器设计。通过考虑具有和不具有参数不确定性的系统，为 MIMO 控制器的设计提出了正式的 Lyapunov 稳定性分析。该设计应用于称为激光熔覆 (LC) 的增材制造技术。所提出的 MIMO 控制器由反馈线性化项（旨在消除已知的标称动态）和具有边界层技术的滑模项（旨在补偿系统不确定性）组成。通过考虑两种不同粉末原料 Ti6Al4V 和 IN718 的轨迹，通过模拟测试了所提出的控制方案。仿真结果证实，在参数不确定性下达到了控制目标，包括高达 40% 的对流系数的变化。此外，控制律易于实施，控制信号具有连续行为，可排除任何高频振荡（颤振效应）。