Jumping in controls

Plug-in or add-on control is integral for high- performance control in modern precision systems. Despite the capability of greatly enhancing the steady-state performance, add-on compensation can introduce output discontinuity and significant transient response. Motivated by the vast application and the practical importance of add-on control designs, this paper identifies and investigates how general nonsmoothness in signals transmits through linear control systems. We explain the jump of system states in the presence of nonsmooth inputs in add- on servo enhancement, and derive formulas to mathematically characterize the transmission of the nonsmoothness. The results are then applied to devise fast transient responses over the traditional choice of add-on design at the input of the plant. Application examples to a manufacturing control system are conducted, with simulation and experimental results that validate the developed theoretical tools.