MIMO U-model based control: Real-time tracking control and feedback analysis via small gain theorem

In this paper, MIMO U-model based IMC is used for the tracking control of multivariable nonlinear systems. The algorithm is implemented in real-time on a 2DoF robot arm. The stability and convergence issues for the control-oriented U-model are also discussed. In order to guarantee stability and faster convergence speeds, bounds are suggested for the learning rate of adaptation algorithm that estimate the parameters of U-model. The adaptation algorithm is first associated with a feedback structure and then its stability is investigated using l₂ stability and small gain theorem. The paper also discusses about the robustness of adaptation algorithm in the presence of noise and suggests optimal choices for faster convergence speeds.