Iterative Learning Control for a Class of Multivariable Distributed Systems With Experimental Validation

Abstract

This paper develops an iterative learning control design for a class of multiple-input multipleoutput systems where a distributed heating system is used as a particular example to experimentally verify the design. The class of systems considered are described by a parabolic partial differential equation, which for control design is approximated by a finite dimensional state-space model obtained by applying the method of integro-differential relations combined with a projection approach. In some cases, including the distributed heating system, this approximation can result in a non-minimum phase system and hence an additional design challenge. In this work, the iterative learning control law is computed in the frequency domain by solving a convex optimization problem and its performance is evaluated in both simulation and experimentation.

Nonparametric Estimation of Continuously Parametrized Families of Probability Density Functions—Computational Aspects

“…Additional, significant possible applications include the estimation of quality indexes for decision-making and optimal control, especially for repetitive and/or spatially distributed processes (see [26,27] for most recent contributions).…”

The optimal design of repetitive controllers based on inverse frequency response

“…In comparison to the FIR compensator, compensator with the function in (27) for m = 3, n = 4 is chosen for demonstration. This is equivalent to the IIR compensator in the initial iteration, that is, I (1) (z).…”

“…Cost functions in the aforementioned algorithms are formulated in the time domain. Another category of optimization‐based methods designed in the frequency domain is robust repetitive control, composed of a band‐stop filter with $$$ {H}_{\infty } $$$ optimization, 26 convex optimization techniques, 27 an opt‐in approach 28 to provide a monotonically convergent update with the minimum steady‐state tracking error, and inverse frequency response RC. In this latter technique, the finite impulse response (FIR) compensator behaves as a reciprocal frequency response of the feedback control system.…”

Path Learning in Human–Robot Collaboration Tasks Using Iterative Learning Methods

“…Compared with the machine learning method that is widely used in computer science, iterative learning is a concept originated in the control field [20], [21]. In the iterative learning method, learning can be achieved using more intuitive online information, such as output errors, in a repeatable task, instead of using probabilistic information as in the machine learning method.…”

“…(1) In the traditional iterative learning method [20], the tracking error is needed as the feedback signal to achieve the control objective. However, in HRC, the human's desired path is unknown to the robot.…”