Implicit integral equations for modeling systems with a transport delay

International audienceIn this chapter, we present a particular class of transport delay systems (e.g. systems involving transportation of material), in which the delay is definedthrough an implicit integral equation. To illustrate the practical interest of this class, experimental use of such models is presented for two different examples of physical systems, both from the field of automotive gasoline engines (specifically, exhaust gas recirculation and exhaust catalyst thermal dynamics). We also discuss related control challenges, together with some solution

Prediction-Based Control for Linear Systems with Input- and State- Delay - Robustness to Delay Mismatch

International audienceThis paper addresses the design of a robust prediction-based controller for linear systems with both input and state delays. We extend the usual prediction-based scheme to state delay and prove its robustness to sufficiently small delay mismatches. Our approach is grounded on the linking of two recently proposed infinite-dimensional techniques: a Complete-Type Lyapunov functional, which enables state delay systems stability analysis, and tools from the field of Partial Differential Equations, reformulating the delays as transport equations and introducing a tailored backstepping transformation. We illustrate the merits of the proposed technique with simulations on a process dryer system

Adaptive compensation of diffusion-advection actuator dynamics using boundary measurements

International audience— For (potentially unstable) Ordinary Differential Equation (ODE) systems with actuator delay, delay compensation can be obtained with a prediction-based control law. In this paper, we consider another class of PDE-ODE cascade, in which the Partial Differential Equation (PDE) accounts for diffusive effects. We investigate compensation of both convec-tion and diffusion and extend a previously proposed control design to handle both uncertainty in the ODE parameters and boundary measurements. Robustness to small perturbations in the diffusion and convection coefficients is also proved

Prediction-based control of moisture in a convective flow

International audience— This work studies a convective flow system and presents experimental closed-loop results carried out on a test-bench representative of several industrial processes. This test bench consists of a horizontal column equipped with a mist actuator located at the inlet and fans generating an air flow circulating along the tube. Following our recent theoretical design, we implemented a prediction-based control strategy aiming at stabilizing the mist at the output of the tube actuating on the wind speed. Correspondingly, this setup involves a transport input-dependent delay (between the inlet and the output of the tube). We propose a control-oriented model, in which the transport delay satisfies an integral equation, and compared our prediction-based design with a conventional Proportional-Integral controller. Experimental results underline the relevance of the proposed approach

Estimation for decentralized safety control under communication delay and measurement uncertainty

International audienceThis paper addresses the design of a decentralized safety controller for two agents, subject to communication delay and imperfect measurements. The control objective is to ensure safety, meaning that the state of the two-agent system does not enter an undesired set in the state space. Assuming that we know a feedback map designed for the delay free-case, we propose a state estimation strategy which guarantees control agreement between the two agents. We present an estimation technique for bounded communication delays, assuming that the agents share the same internal clock, and extend it for infinitely-distributed communication delays by determining a lower bound for the probability of safety. We also explain how the proposed approach can be extended to a general system of N agents and discuss efficient computation of our estimation strategy. Performance of the controller and relevance of the proposed approach are discussed in light of simulations performed for a collision avoidance problem between two semi-autonomous vehicles at an intersection

Estimation for decentralized safety control under communication delay and measurement uncertainty

This paper addresses the design of a decentralized safety controller for two agents, subject to communication delay and imperfect measurements. The control objective is to ensure safety, meaning that the state of the two-agent system does not enter an undesired set in the state space. Assuming that we know a feedback map designed for the delay free-case, we propose a state estimation strategy which guarantees control agreement between the two agents. We present an estimation technique for bounded communication delays, assuming that the agents share the same internal clock, and extend it for infinitely-distributed communication delays by determining a lower bound for the probability of safety. We also explain how the proposed approach can be extended to a general system of N agents and discuss efficient computation of our estimation strategy. Performance of the controller and relevance of the proposed approach are discussed in light of simulations performed for a collision avoidance problem between two semi-autonomous vehicles at an intersection. Keywords: Multi-agent systems; Communication delay; Estimation/prediction approaches; Safety contro

Prediction-based control of linear input-delay system subject to state-dependent state delay – Application to suppression of mechanical vibrations in drilling

International audienceIn this paper, we consider linear dynamics subject to a distributed state-dependent delay and a pointwise input-delay. We propose a prediction-based controller which exponentially stabilizes the plant. The controller design is based on a backstepping approach where delays are reformulated as hyperbolic transport PDEs. Infinity-norm stability analysis of the corresponding closed-loop system is addressed. We show that this result is of interest to suppress mechanical vibrations arising in drilling facilities, which have been attributed recently to a coupling between torsional and vertical displacement involving an implicit state delay equation. Numerical simulations illustrate the merits of our controller in this context

Prediction-Based Stabilization of Linear Systems Subject to Input-Dependent Input Delay of Integral-Type

International audienceIn this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral model. This situation is representative of systems where transport phenomena take place, as is frequent in the process industry. The sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems