Nonlinear feedback control and dead time compensation for systems with dead time

A new class of relays, "negative bandwidth" relays, which have not been cited in previous literature are introduced and defined. Along with another new concept of "reduced dead time," these newly defined relays allow the design of a novel dead time compensation technique based on the linearized process model. Even when a significantly large dead time exists, this control design strategy provides a successful control implementation for the relay feedback control scheme.

The existence of considerable dead time in a control loop often prevents effective control from being achieved and even degrades the performance of the process. A perhaps surprising fact is that relay feedback control does not influence the dynamics of a process even in the presence of dead time. Thus the ability to easily compensate for dead time provides a strong motivation to investigate the use of the nonlinear feedback controller.

Previous studies have addressed another potential advantage of using relay with hysteresis feedback controllers instead of conventional linear controllers to maintain a process state near a steady state which is open loop unstable. When employing the design derived from the linearized model, in treating the actual nonlinear plant this design strategy gives good starting values for the controller parameters. Subsequently, a successful control implementation may be achieved by on-line tuning or by relay modification based on the nonlinear simulation of the process without dead time.

Tsypkin's method provides an exact representation of the relay and has been shown to be superior to describing function analysis. Thus Tsypkin's method will be extended in this study. By following the procedures exploited for systems without dead time, a mathematical framework for dead time systems is developed to obtain the waveform characteristics and its stability. The new concepts of "reduced dead time" and "negative bandwidth relays" lead to a mathematical methodology based on Tsypkin's formalisms for a dead time compensation strategy which achieves a successful control scheme no matter how large the system dead time.

A nonisothermal CSTR which carries out a homogeneous, irreversible, first order, exothermal reaction serves as an example to demonstrate the concepts of the research.