Benoit Boulet's Publications, Theses and Technical Reports
Department of Electrical and Computer Engineering
University of Toronto
Abstract: Dynamic models of large flexible space structures (LFSS) are characterized by their high order and their significant number of highly uncertain, lightly-damped, clustered low-frequency modes. Because of these characteristics, approaches to uncertainty modeling for robust control of LFSS such as, among others, additive or multiplicative perturbations in H-infinity, do not work very well. In this report, we propose the use of a left coprime factorization (LCF) of LFSS dynamics in modal coordinates for robust control design. The plant uncertainty is described as stable perturbations of the coprime factors. The structure of the LCF allows one to go easily from modal parameter uncertainty to an unstructured description of the uncertainty as stable normbounded perturbations of the factors. This allows a better, less conservative description of the model uncertainty and hence improves closed-loop performance and guaranteed robustness. Two multivariable H-infinity designs and two µ-synthesis designs based on LCFs of 46th-order colocated and noncolocated models of an LFSS experimental testbed are presented together with simulation and experimental results to illustrate the technique.
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Systems Control Group
Department of Electrical and Computer Engineering
University of Toronto
Abstract: The model/data consistency problem for coprime factorizations considered here is this: Given some possibly noisy experimental frequency-response data obtained by running open or closed-loop experiments on the system, show that these data are consistent with a given family of perturbed factor models and a noise model. In the noise-free open-loop case, the model/data consistency problem boils down to the existence of an interpolating function RH-infinity that evaluates to a finite number of complex matrices at a finite number of points on the imaginary axis. A theorem on boundary interpolation in RH-infinity is a building block that allows us to devise computationally simple necessary and sufficient tests to check if the perturbed coprime factorization is consistent with the data. For L-infinity noise corrupting the frequency-response measurements, a complete solution to the open-loop noisy SISO problem using the structured singular value µ is given, and a practical sufficient condition for consistency of the noisy open-loop MIMO case is derived. Separate necesary and sufficient conditions are given for the closed-loop noise-free MIMO and noisy SISO cases. Standard coprime factorizations and special factorizations for flexible systems are considered.
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Computer Vision and Robotics Laboratory
McGill Research Centre for Intelligent Machines
McGill University
Abstract: A robot joint prototype with two hydraulic actuators, one being redundant, is described. Two robust controllers are derived for the position control of this joint, as well as a method for selecting the allocation of actuation effort in terms of the solution of minimum norm problems. In each case, a particular physical interpretation is given. In the first part of the paper, a robust state feedback controller derived from the Internal Model Principle as well as a robust controller based on the H-infinity-optimal sensitivity minimization method are derived and both compared to a conventional SISO PD controller. In the first case, the designed controller resulted into a simple PID controller, while in the second, it resulted into a lead controller. Conclusions are drawn comparing the two approaches.
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Computer Vision and Robotics Laboratory
McGill Research Centre for Intelligent Machines
McGill University
Abstract: A robot joint prototype with two hydraulic actuators, one being redundant, was described in the first part of this article. Two robust controllers were derived for the position control of this joint, as well as a method for selecting the allocation of actuation effort in terms of the solution of minimum norm problems. In this part of the paper, practical controllers for use in robotics applications are described in terms of modulation of mechanical impedance, as well as a non-linear controller designed to take advantage of certain nonlinear characteristics of the presently studied hydraulic actuators. Extensive experimental results are described and discussed.
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