Nonlinear robust observer design using an invariant manifold approach

• A method to design a reduced order observer using an invariant manifold is proposed.
• The method uses specific mapping functions that minimizes the error dynamics close to zero.
• Another important aspect is the robustness property due to the manifold attractivity.
• The observer design is validated using both numerical simulation and hardware-in-loop testing.
• The proposed observer is then compared with a very well-known nonlinear observer.

This paper presents a method to design a reduced order observer using an invariant manifold approach. The main advantages of this method are that it enables a systematic design approach, and (unlike most nonlinear observer design methods), it can be generalized over a larger class of nonlinear systems. The method uses specific mapping functions in a way that minimizes the error dynamics close to zero. Another important aspect is the robustness property which is due to the manifold attractivity: an important feature when an observer is used in a closed loop control system. A two degree-of-freedom system is used as an example. The observer design is validated using numerical simulation. Then experimental validation is carried out using hardware-in-the-loop testing. The proposed observer is then compared with a very well known nonlinear observer based on the off-line solution of the Riccati equation for systems with Lipschitz type nonlinearity. In all cases, the performance of the proposed observer is shown to be very high.