Didier Dumur

A parameterized polyhedra approach for explicit constrained predictive control

The elaboration of an explicit description for the constrained model based predictive control laws is a useful alternative to the usually time-consuming on-line optimization methods. The paper presents a geometrical approach in this direction based on parameterized polyhedra. Subdomains in the parameters space and the correspondent linear affine laws are defined based on the parameterized vertices and their validity domains. The theoretical insight for the overall control law is brought through a double description (constraints-generators) of the feasible domain. The gain in computational effort is due to a hierarchic organization of the piecewise affine controllers.

Zonotopic guaranteed state estimation for uncertain systems

This paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete-time multivariable systems with interval multiplicative uncertainties, in the presence of bounded state perturbations and noises. At each sample time, the presented approach computes a zonotope which contains the real system state. A P-radius-based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation. The proposed approach allows one to efficiently handle the trade-off between the complexity of the computation and the accuracy of the estimation. An illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique.

Generalized Predictive Cascade Control (GPCC) for Machine Tools Drives

Abstract The use of self synchronous motors in the machine tools field has many advantages: The absence of brushes gives better accuracies in position and a small rotor inertia allows shorter time responses in speed and position. We propose in this paper n performant real time algorithm (GPCC) development this kind of performant motors. The use of predictive control algorithms instead of classical controllers is now possible due to the rapidity of numerical processors, and takes into account more informations about the future. According to this, a first part will develop the GPCC algorithm in a theoretical point of view. Then a second part will present the results obtained with this algorithm on a brushless motor used to drive machine tools axes.

Avoiding constraints redundancy in predictive control optimization routines

This note concentrates on removing redundancy in the set of constraints for the multiparametric quadratic problems (mpQP) related with the constrained predictive control. The feasible domain is treated as a parameterized polyhedron with a focus on its parameterized vertices. The goal is to find a splitting of the parameters (state) space corresponding to domains with regular shape (nonredundant constraints), resulting in a table of regions where the constraints have a minimal representation, so that the online optimization routines can act with better performances. The procedure can be seen as a preprocessor either for the classical QP methods or for the routines based on explicit solutions. For important degrees of redundancy, the proposed technique may bring computational gains for real-time application or on the complexity of the positioning mechanism for evaluating the explicit solution.

High-Performance NC for HSM by means of Polynomial Trajectories

This paper summarises works carried out for defining tool trajectory formats well adapted to High Speed Machining (HSM). Advantages in using native polynomial formats, calculated directly from the CAD model, are highlighted. In particular, polynomial surface formats are presented as a generic format for tool trajectory. Illustrations show that surface formats represent a good compromise between smoothness machining time, and surface quality.

Nonlinear predictive control for maximization of CO2 bio-fixation by microalgae in a photobioreactor

In the framework of environment preservation, microalgae biotechnology appears as a promising alternative for CO2 mitigation. Advanced control strategies can be further developed to maximize biomass productivity, by maintaining these microorganisms in bioreactors at optimal operating conditions. This article proposes the implementation of Nonlinear Predictive Control combined with an on-line estimation of the biomass concentration, using dissolved carbon dioxide concentration measurements. First, optimal culture conditions are determined so that biomass productivity is maximized. To cope with the lack of on-line biomass concentration measurements, an interval observer for biomass concentration estimation is built and described. This estimator provides a stable accurate interval for the state trajectory and is further included in a nonlinear model predictive control framework that regulates the biomass concentration at its optimal value. The proposed methodology is applied to cultures of the microalgae Chlorella vulgaris in a laboratory-scale continuous photobioreactor. Performance and robustness of the proposed control strategy are assessed through experimental results.

Feedback nonlinear predictive control of rigid link robot manipulators

Three nonlinear continuous-time predictive control schemes are proposed to address the trajectory tracking control problem of rigid link robot manipulators. The control laws using state variable feedback minimize a quadratic performance index of the state predicted tracking error. Without online optimization, an asymptotic tracking of smooth reference trajectories is guaranteed. The proposed controllers achieve the positions and speed tracking objectives via link position measurements. Lyapunov theory is used to prove the boundedness and stability convergence of the state tracking. Robustness with respect to payload uncertainties and viscous friction is shown. Simulations for a two-link rigid robot are performed to validate the proposed controller.

Distributed model predictive control for building temperature regulation

This paper presents a predictive control structure for thermal regulation in buildings. The proposed method considers a dynamic cost function trying to exploit the intermittently operating mode of almost all types of buildings. One of the key idea is to use the knowledge about the occupation profile. For that purpose, the predictive control strategy is first presented for a single zone building then extended to a multizone building example. Two opposite control strategies commonly exists. The decentralized control structure, which does not offer good performances especially when the thermal coupling among adjacent rooms is not negligible, and on the other hand, the centralized control for which the computational demand grows exponentially with the size of the system, being very expensive for large scale buildings. Our solution is based on a distributed approach which takes the advantages of the both methods mentioned above. A distributed MPC algorithm with one information exchange per time step is proposed with good control performances and low computational requirements.

On the continuity and complexity of control laws based on multiparametric linear programs

The present paper proposes a geometrical approach for the multiparametric linear programs (mp-LP). The interest for this topic is motivated by the need for explicit formulations in the constrained predictive control (with non-quadratic cost indexes). It is shown how the double description of the feasible domains can offer access to the entire family of optimal mappings from the parameters space to the arguments space. Further the explicit solutions with guarantee of continuity and optimality are studied

Generalized Predictive Control of an anthropomorphic robot arm for trajectory tracking

This paper presents an effective model-based predictive approach for the precise trajectory tracking of an anthropomorphic robot arm. The proposed control strategy is based on feedback linearization and linear Generalized Predictive Control, requiring no on-line optimization procedure. Experimental evaluation of the proposed method and its comparison with two classic robot control approaches illustrate its tracking performances and robustness with respect to non-compensated load variations.