Model error compensator design for continuous- and discrete-time non-minimum phase systems with polytopic-type uncertainties

Abstract

This paper presents a design for a model error compensator with a parallel feedforward compensator for continuous- and discrete-time non-minimum phase multiple input multiple output (MIMO) plants. The model error compensator can easily achieve robustness for several types of control systems. By appending the compensator to the actual plant, the output trajectory of the plant can be made close to that of the control system with the intended nominal model. Our previous study proposed a design for the model error compensator using particle swarm optimization and linear matrix inequalities based on the common Lyapunov function. The compensator design for the plants addresses polytopic-type uncertainties. However, it is challenging to design the appropriate gain for the model error compensator if the plant is a non-minimum phase MIMO system. In this study, a parallel feedforward compensator is attached to the model error compensator to achieve minimum phase characteristics. An evaluation system, including a parallel feedforward compensator, can be derived as a system with polytopic uncertainties via the addition of some assumptions. Thus, it is easy to design the gain of the model error compensator in the proposed method and achieve robust performance. The effectiveness of the proposed design is evaluated using numerical examples.

Keywords

• model error compensator
• robust control
• $ h_\infty $ performance
• particle swarm optimization
• linear matrix inequality
• non-minimum phase system