Page 202 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

200 Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics

employed. However, many actuators used in such cryogenic systems are the
valves, which can be opened between [0,100%] only, leading to valve sat-
urations. To address the potential poor transient control response from the
valve saturations, appropriate compensation (e.g., anti-windup) should be
considered in the control design [12].

12.5 CONCLUSION
This chapter introduces the saturation dynamics and the associated mathe-
matical models; this typical hard constraint imposed on the actuators (e.g.,
actuator displacement and rate saturations) is commonly encountered in
most of physical systems. In order to address the impact of these constraints
in the closed-loop control system, we also introduce a smooth approxi-
mated model of saturation dynamics, which will be used in the control
designs to be presented in this book. By using the tanh(·) function, the
saturation dynamics can be formulated as a linear-like system with a time-
varying gain and a bounded disturbance. This new formulation allows to
incorporate it into adaptive control design and analysis.

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