ODEs with General Transport-Like Actuator Dynamics

Abstract

In 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.