Generalized Multivariable Gain Scheduling With Robust Stability Analysis

In this work we introduce a methodology for the design of multivariable gain-scheduled controllers for nonlinear systems and an approach for determining the local stability of a nonlinear closed loop system. The gain-scheduled global control is designed by scheduling different local controllers using a Local Controller Network. The individual local controllers are assumed to be LTI MIMO controllers that can be designed via some user-specified multivariable method. In this paper, different portions of outputs from different local controllers are combined into the total control by using interpolation-weighting functions. The variation in the control behavior as a result of the scheduling variable is posed in a robust control framework. The dynamics of the scheduling variables are incorporated into the global control framework as an unstructured uncertainty. This allows the use of computational tools to analyze the stability of the overall global system and verify whether or not a given gain-scheduled approach will remain stable locally. To demonstrate the practical significance of the method, a multivariable electrohydraulic earthmoving powertrain problem is solved using the approach. The nonlinear power train was locally modeled as an LTI MIMO system and a local LTI MIMO controller was designed at each operating point using an $H∞$ algorithm. The analysis approach introduced is utilized to verify system stability and is supported closely by experimental results.