Velocity control design of hyperbolic distributed parameter systems using zeroing dynamics and zeroing-gradient dynamics methods

Velocity control proves to be an effective and a more easily implementable actuation than boundary and distributed actuations for hyperbolic distributed parameter systems. However, the design of velocity control for these systems, following the late lumping approach, i.e., using the partial differential equations model, poses a challenging problem in control engineering. Noticeably, the velocity controller faces a control singularity issue, resulting in a loss of controllability that renders the controller impractical. In this paper, we demonstrate that the zeroing dynamics method is a viable alternative design approach for velocity control of hyperbolic distributed parameter systems following the late lumping approach. Thus, employing the partial differential equations model, a velocity state feedback forcing output tracking is developed based on the zeroing dynamic method. Furthermore, to address the control singularity problem, the zeroing gradient method is combined with the zeroing method to design a state feedback that achieves output tracking even when a singularity occurs. The tracking error convergence is demonstrated for both developed state feedbacks. The effectiveness of these design approaches is clearly demonstrated in the case of a steam-jacketed heat exchanger and a non-isothermal plug flow reactor.