Model-free control

Abstract

"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

Robust tracking control for linear vibrating mechanical systems

“…Then, the natural frequencies of the mechanical system are computed as: ω n 1 = 6.6854 rad/s, ω n 2 =17.361 rad/s and ω n 3 =35.174 rad/s. 3 3 kg k 3 400 N/m c 3 0 Ns/m Figure 3 Configuration of the perturbed vibrating mechanical system of the case study…”

“…Here, disturbances are estimated and compensated by the controller in real time. In [3], disturbance rejection has been also addressed from a modelfree control perspective, introducing recently the algebraic design methodology of intelligent Proportional-Integral-Derivative controllers (iPIDs), where an unknown mathematical model is replaced by an ultra-local model. This paper deals with efficient and robust tracking control in underactuated linear mass-springdamper systems with multiple degrees of freedom without on-line disturbance estimation.…”

Active magnetic bearing: A new step for model-free control

“…The setpoint follows a low-pass-filtered, 10-Hertz square signal. As magnetic bearings are subject to minimal damping, the chosen control law is an iPD controller (4) which is known to match a classical PID controller [11]. Its parameters are K I = 0, α = .9, K P = 14692 and K D = 266.…”

“…The purpose of this paper is thus to apply the new "modelfree control" approach (see [11]) to that problem. 1 This control synthesis, where a "good" mathematical model becomes pointless, has already been used successfully to solve numerous control problems spanning diverse application areas (see the references in [11]).…”

“…1 This control synthesis, where a "good" mathematical model becomes pointless, has already been used successfully to solve numerous control problems spanning diverse application areas (see the references in [11]). Moreover, for each real studied cases, the ultra-local model was of first order.…”