Robust model-following controller design for LTI systems affected by parametric uncertainties: a design example for aircraft motion

Abstract

This article addresses the design problem of a robust model-following controller (MFC) which minimises the error between plant controlled output and model output for a linear time-invariant (LTI) plant system affected by parametric uncertainties and an LTI target model. To design such an MFC, a previously proposed MFC scheme, whose applicability has already been demonstrated with flight controller design, is adopted in this article. Our design procedure is as follows: first, a basic MFC is designed using the nominal LTI plant model and the LTI target model while a structured free matrix in the MFC is not assigned; second, model-following performance of the MFC for appropriately defined disturbance input and model input for the parametric uncertain plant model and the LTI target model is minimised using the structured free matrix; and finally, a robust MFC is obtained using the basic MFC and the optimal structured matrix. In the second step, an iterative design method for robust H ₂ controllers for LTI parameter-dependent (LTIPD) systems using parameter-dependent Lyapunov functions (PDLFs), which is also proposed in this article, is applied. Two MFCs for the lateral-directional (L/D) motions of a research aircraft, which has been developed for an in-flight simulator, for two different real aircraft models, i.e. a Boeing 747 model and a Lockheed Jetstar model, are designed and their performance is confirmed via numerical simulations and flight tests.

Keywords:

• robust model-following controller
• robust H ₂ synthesis
• linear time-invariant parameter-dependent systems
• aircraft motion
• flight test

Notes

Notes

1. if there exist no dynamic uncertainties for the plant, then n _u = 0 and [C _p 0] becomes C _p .

2. if n _u = 0 holds, then , [M _p 0], [Q ^1/2 0] and [C _p 0] respectively become , M _p , Q ^1/2 and C _p .

3. These two assumptions are made only when the matrices of the basic MFCs are calculated.