Control for MIMO Systems with No Relative Degree: Output Redefinition versus Dynamic Extension

Abstract

Output redefinition-based dynamic inversion (ORDI) control is applied to solve the control problem for multi-input-multi-output (MIMO) systems with no relative degree and is compared with the traditional dynamic extension-based dynamic inversion (DEDI) control. A MIMO system has no relative degree if its control matrix is singular, preventing the direct use of the powerful nonlinear control method, dynamic inversion. For this problem, dynamic extension is a traditional solution, which makes dynamic extension at the input side to achieve a relative degree. DEDI results in a fully linearized system of higher order. But the requirement to calculate the higher order derivatives of the output makes it difficult to apply to complex systems. ORDI provides a new solution for the existing problem. It achieves a relative degree by redefinition of a new output, leading to a partially linearized system cascaded with stable zero dynamics. ORDI is much easier to implement for complex systems and reduces the computational burden, though it has some performance limitations. A linear system example along with the application to a hypersonic flight vehicle are provided to illustrate the concept of ORDI and its differences with DEDI.