"Model-free control" and the corresponding "intelligent" PID controllers
(iPIDs), which already had many successful concrete applications, are presented
here for the first time in an unified manner, where the new advances are taken
into account. The basics of model-free control is now employing some old
functional analysis and some elementary differential algebra. The estimation
techniques become quite straightforward via a recent online parameter
identification approach. The importance of iPIs and especially of iPs is
deduced from the presence of friction. The strange industrial ubiquity of
classic PID's and the great difficulty for tuning them in complex situations is
deduced, via an elementary sampling, from their connections with iPIDs. Several
numerical simulations are presented which include some infinite-dimensional
systems. They demonstrate not only the power of our intelligent controllers but
also the great simplicity for tuning them
Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to "intelligent" PID controllers, the tuning of which becomes quite straightforward, even with highly nonlinear and/or time-varying systems. Our main tool is a newly developed numerical differentiation. Differential algebra provides the theoretical framework. Our approach is validated by several numerical experiments. 1 This communication is a slightly modified and updated version of (Fliess & Join [2008a]), which is written in French. Model-free control and control with a restricted model, which might be useful for hybrid systems (Bourdais, Fliess, Join & Perruquetti [2007]), have already been applied in several concrete case-studies in various domains
A flatness-based flight trajectory planning/replanning strategy is proposed for a quadrotor unmanned aerial vehicle (UAV). In the nominal situation (fault-free case), the objective is to drive the system from an initial position to a final one without hitting the actuator constraints while minimizing the total time of the mission or minimizing the total energy spent. When actuator faults occur, fault-tolerant control (FTC) is combined with trajectory replanning to change the reference trajectory in function of the remaining resources in the system. The approach employs differential flatness to express the control inputs to be applied in the function of the desired trajectories and formulates the trajectory planning/replanning problem as a constrained optimization problem.
Abstract-Intelligent PID controllers, or i-PID controllers, are PID controllers where the unknown parts of the plant, which might be highly nonlinear and/or time-varying, are taken into account without any modeling procedure. Our main tool is an online numerical differentiator, which is based on easily implementable fast estimation and identification techniques. Several numerical experiments demonstrate the efficiency of our method when compared to more classic PID regulators.
ALINEA, which was introduced almost thirty years ago, remains certainly the most well known feedback loop for ramp metering control. A theoretical proof of its efficiency at least when the traffic conditions are rather mild is given here, perhaps for the first time. It relies on tools stemming from the new model-free control and the corresponding "intelligent" proportional controllers. Several computer experiments confirm our theoretical investigations.
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