JULY 06-07, 2023
Professor and Director of Institute for Aerospace Studies,
University of Toronto
Research Interest: the development of control systems for formation flying spacecraft, the development of robust controllers for (possibly) nonlinear systems, the passivity theorem and small gain theorem, the development of control systems for solar sails.
Speach Title: Nonlinear H-infinity Attitude Control Using Modified Rodrigues Parameters
Abstract: The attitude control problem for rigid spacecraft is considered from the point of view of L2-disturbance attenuation. The attitude kinematics are parameterized using the modified Rodrigues parameters (MRPs) in conjunction with their shadow parameters. Given the nonlinear nature of the attitude dynamics and kinematics, the problem is treated using the nonlinear H-infinity theory. The solution to the Hamilton-Jacobi equation associated with this problem is approximated using a Taylor series expansion. An analytical solution method is used for the second-, third-, and fourth-order terms. Disturbance rejection properties are compared by including the gravity-gradient and geomagnetic disturbance torques. The results indicate that a linear controller performs as well as those obtained using higher-order solutions for the Hamilton-Jacobi equation. Motivated by this result, it is shown analytically that that a linear feedback law consisting of a linear combination of the spacecraft angular velocity and the generic MRPs locally solves the (suboptimal) nonlinear H-infinity state feedback problem. The proof of this result is constructive and is used to establish analytical formulas for the gain parameters in terms of the desired L2-gain, the control weighting parameters in the performance output, and the moments of inertia.
Short-biography: Chris Damaren received the BASc in Engineering Science (Aerospace Option) from the University of Toronto in 1985. He went on to receive the MASc and PhD degrees in 1987 and 1990, respectively, both in aerospace engineering from the University of Toronto Institute for Aerospace Studies (UTIAS). From 1990 to 1995 he was an Assistant Professor in the Department of Engineering at Royal Roads Military College in Victoria, British Columbia, Canada. From 1995 to 1999 he was a Senior Lecturer in the Department of Mechanical Engineering at the University of Canterbury in Christchurch, New Zealand. Since 1999 he has been at UTIAS and is currently a Professor and the Director. From 2008 to 2013, he served as the Vice-Dean Graduate Studies for the Faculty of Applied Science and Engineering. His research interests are in the areas of dynamics and control of space systems. He is a Fellow of the Canadian Aeronautics and Space Institute and an Associate Fellow of the American Institute of Aeronautics and Astronautics.