Robust control of uncertain LTI plant with input saturation constraint: H_∞ loop-shaping approach

Abstract

This article addresses a robust controller design technique for an uncertain linear time invariant plant with input saturation constraint. The uncertainty of the plant is presented in a normalised coprime factorisation framework, which is a general description of the unstructured uncertainty of the system. For controller synthesis, the H _∞ loop-shaping method adopted is new to the actuator saturation control problem. In the presence of input saturation, the H _∞ loop-shaping framework has been transformed into an equivalent Lur'e-type system, and then Popov absolute stability criteria are applied to ensure closed-loop stability against unstructured uncertainty and saturation nonlinearity of the system. For the synthesising controller, a sequence of design steps has been addressed by formulating the design constraints in a bilinear matrix inequality framework. To show the effectiveness of the proposed method, a numerical example has been demonstrated.

Keywords:

• H _∞ loop-shaping control
• coprime factor uncertainty description
• Lur'e system
• Popov stability criteria
• actuator saturation
• bilinear matrix inequality

Acknowledgement

The authors wish to thank the anonymous reviewers for their constructive comments.