Optimal Output Modification and Robust Control Using Minimum Gain and the Large Gain Theorem

robust control;optimal output modification;parallel feedforward control;Large Gain Theorem;nonminimum phase zeros;LMIs;Aerospace Engineering;Engineering;Aerospace Engineering

Caverly, RyanKolmanovsky, Ilya Vladimir ;

University of Michigan

关键词: robust control;    optimal output modification;    parallel feedforward control;    Large Gain Theorem;    nonminimum phase zeros;    LMIs;    Aerospace Engineering;    Engineering;    Aerospace Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/143934/caverly_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

When confronted with a control problem, the input-output properties of the system to be controlled play an important role in determining strategies that can or should be applied, as well as the achievable closed-loop performance.Optimal output modification is a process in which the system output is modified in such a manner that the modified system has a desired input-output property and the modified output is as similar as possible to a specified desired output.The first part of this dissertation develops linear matrix inequality (LMI)-based optimal output modification techniques to render a linear time-invariant (LTI) system minimum phase using parallel feedforward control or strictly positive real by linearly interpolating sensor measurements.H-ininifty-optimal parallel feedforward controller synthesis methods that rely on the input-output system property of minimum gain are derived and tested on a numerical example.The H2- and H-infinity-optimal sensor interpolation techniques are implemented in numerical simulations of noncolocated elastic mechanical systems.All mathematical models of physical systems are, to some degree, uncertain.Robust control can provide a guarantee of closed-loop stability and/or performance of a system subject to uncertainty, and is often performed using the well-known Small Gain Theorem.The second part of this dissertation introduces the lessor-known Large Gain Theorem and establishes its use for robust control.A proof of the Large Gain Theorem for LTI systems using the familiar Nyquist stability criterion is derived, with the goal of drawing parallels to the Small Gain Theorem and increasing the understanding and appreciation of this theorem within the control systems community.LMI-based robust controller synthesis methods using the Large Gain Theorem are presented and tested numerically on a robust control benchmark problem with a comparison to H-infinity robust control.The numerical results demonstrate the practicality of performing robust control with the Large Gain Theorem, including its ability to guarantee an uncertain closed-loop system is minimum phase, which is a robust performance problem that previous robust control techniques could not solve.