Frédéric Rotella

Minimal single linear functional observers for linear systems

A constructive procedure to design a single linear functional observer for a time-invariant linear system is given. The proposed procedure is simple and is not based on the solution of a Sylvester equation or on the use of canonical state space forms. Both stable observers or fixed poles observers problems are considered for minimality.

On Functional Observers for Linear Time-Varying Systems

The technical note deals with existence conditions of a functional observer for linear time-varying systems in the case where the order of the observer is equal to the number of observed variables. Constructive procedures for the design of such a linear functional observer are deduced from the existence conditions. As a specific feature, the proposed procedures do not require the solution of a differential Sylvester equation. Some examples illustrate the presented results.

Polynomial controller design based on flatness

By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. Polynomial controllers for finite-dimensional linear systems can then be designed with very natural choices for high level parameters design. This design leads to a Bezout equation which is independent of the closed loop dynamics but depends only on the system model.

Delta approach robust controller for constant turning force regulation

The adaptive implementation of a robust controller for the constant turning force regulation problem under varying cutting conditions is presented. The discrete control structure is based on a state variable feedback regulator obtained using the delta approach optimal control theory. The controller scheme is robust in the presence of cutting process nonlinearities and disturbances. The proposed adaptive scheme uses an estimation and controller algorithm including prior knowledge of the system. Simulations and experimental results obtained with an industrial lathe show the robustness of the proposed solution.

Fault tolerance in robotics

This work is a contribution to illustrate the fault tolerance concepts in robotics. Every step from the analysis phase to the fault accommodation phase is presented. A fault on joint 3 is taken into account and simulated to validate the detection algorithms. The fault accommodation is thus considered and is based on the kinematic redundancy principle. The establishment of the inverse kinematic model, under some conditions of joint failure, enables the generation of an alternative trajectory to ensure the robot goes on functioning.

New residual generation design for fault detection

Abstract A new design procedure of a reduced order unknown input observer (UIO) is proposed to generate residuals for fault detection isolation (FDI). The originality of this work consists in the adopted approach for the procedure implementation. Indeed the kernel of the actuator fault distribution matrix is generated thanks to generalized inverses. The Kronecker product is used to solve a Sylvester equation which appears in the equations of an UIO. Residuals generated by bank of observers allow on the one hand the detection isolation of every actuator fault and on the other hand the isolation between actuator faults and sensor faults.

Ultra-local model control based on an adaptive observer

In this paper, a new ultra-local model control approach is proposed. The concept is based on the linear adaptive observer to estimate the ultra-local model parameters instead of algebraic derivation technique. The importance of adaptive observer is deduced in the join estimation of state and unknown parameters of parametric systems. The closed-loop control is implemented via an adaptive PID controller to reject disturbances due to exogenous parameter uncertainties. In this paper, a performance comparison between the adaptive observer based method and the algebraic derivation technique is developed to show the efficiency of the proposed control strategy. The approaches are applied to a two-tank system for the water level control. Several successful simulation results are shown to demonstrate the effectiveness of the proposed controller.

A Note on Functional Observability

In this note, we propose an alternative to characterize the functional observability for linear systems. The main feature is that we obtain a necessary and sufficient condition for the existence of a stable multi-functional observer of a time-invariant linear system. The proof of this condition is constructive and it leads to design a stable observer via a new procedure, neither based on the solution of a Sylvester equation nor on the use of canonical state space forms.

Model-free control of a 3-DOF piezoelectric nanopositioning platform

A model-free controller is designed for a nanopositioning platform with three degrees of freedom. The system is specially difficult to control because of the coupling between the different movements and the hysteresis present in the piezoelectric actuators. The authors propose a control design methodology based on the so called ultra-local system description. The developed controller has been implemented and validated on a real test bench and it has proven a good performance in handling the nonlinearities and uncertainties present in the platform.

Time-varying controller based on flatness for nonlinear anti-lock brake system

It is shown that by the use of flatness the problem of pole placement, which consists in imposing closed-loop system dynamics, can be related to track desired trajectories in the finite-dimensional linear time-invariant case. Polynomial two-degree-of-freedom controller can then be designed with the use of an exact observer and without resolving the Bézouts equation. In this paper, an extension of these developments is proposed in the linear time-varying (LTV) framework. The proposed approach is illustrated with the control of nonlinear model of an anti-lock brake system. The time-varying controller obtained from the LTV model ensures the trajectory tracking of the nonlinear model.