Iterative LMI-Based Plant–Controller Co-Design Using Explicit Model Following Control: A VTOL Application

A plant–controller co-design methodology is proposed in which the reference model dynamics are parameterized and incorporated directly into the optimization rather than prescribed a priori. Within an Explicit Model Following (EMF) architecture, plant-design variables and reference-model parameters are optimized simultaneously with the controller gains, subject to prescribed stability, performance, and maneuverability constraints. The framework accommodates H2, H∞, and mixed H2/H∞ state-feedback synthesis and can be extended to multiple design points. The bilinearities arising from the coupled plant–controller–reference model optimization are addressed through a perturbation-based iterative procedure that decomposes the resulting Bilinear Matrix Inequality (BMI) problem into sequential convex Linear Matrix Inequality (LMI) subproblems. The proposed framework is demonstrated and validated through an integrated sizing and control-design problem for a representative quad-wing tilt-rotor Vertical Take-Off and Landing (VTOL) air vehicle, where aircraft-specific maneuverability and handling-quality requirements are incorporated as design constraints. Compared with the initial controller design obtained for fixed plant parameters, the final co-designed plant–controller configuration achieves a substantial improvement in closed-loop performance, with the maximum control demand reduced by approximately 70% in the directional control case. Further optimization of the reference-model parameters yields an additional 3–5% improvement in control effort metrics, indicating that the prescribed closed-loop dynamics can influence the overall co-design optimum while maintaining the required handling-quality constraints.