Abstract
AbstractIn this chapter we start the development of feedback laws that compensate actuator (or sensor) dynamics of a more complex type than the pure delay. Having dealt with the pure delay, i.e., the transport PDE in Chapter 2, in this chapter we expand our scope to general first-order hyperbolic PDEs in one dimension.We first focus on first-order hyperbolic PDEs alone, without a cascade with an ODE. First-order hyperbolic PDEs serve as a model for such physical phenomena as traffic flows, chemical reactors, and heat exchangers.We design controllers using the backstepping method–with the integral transformation and boundary feedback, the unstable PDE is converted into a “delay line” system that converges to zero in finite time.KeywordsExponential StabilityVries EquationStatic Output FeedbackActuator DynamicsBoundary FeedbackThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
