Page 197 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

CHAPTER 12

Saturation Dynamics and
Modeling

12.1 INTRODUCTION
In most practical control systems, the actuators are widely used as the driv-
ing devices, such as stepper motors, permanent magnet synchronous motors
(PMSM), hydraulic actuators, and so on [1]. The existence of inherent
physical constraints on the actuators always leads to the hard limits on the
control input, which are usually modeled by a saturation non-linearity, i.e.,
there are certain constraints imposed on the amplitude of control input,
such as finite voltage of electrical motors and finite capacity of a pump,
are the most common cases. As a potential problem coming from the ac-
tuators in the control systems, the actuator saturation is unavoidable, and it
could affect the system transient performance and even lead to undesirable
inaccuracy.
In most cases, the existence of the actuator saturation cannot be ig-
nored because it may result in performance deterioration and even trigger
system instability. Consequently, the impact of this non-smooth constraint
on the closed-loop control system should be addressed and investigated in
the control designs. For well-designed control systems, the operational re-
quirements are always taken into consideration, and the performance will
be consistent with the applicable physical constraints [2], [3]. In particu-
lar, the compensator for the input saturation, e.g., anti-windup [4], should
be able to recover the closed-loop system performance as possible as that
without actuator saturation, while retaining the system stability.
Fig. 12.1 provides the structure of a realistic system with actuator satu-
ration. As shown in Fig. 12.1, u is the controller output (e.g., the voltage
applied on the motor) and v is the actuator output (e.g., realistic driving
force of the motor) [5–9].
In this chapter, we will briefly review the actuator saturation existing in
the control plants, introduce a proper approximation of the saturation by
using a smooth function. Moreover, several typical examples with control
saturation will also be introduced in this chapter.
Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics.
DOI: https://doi.org/10.1016/B978-0-12-813683-6.00016-7 195
Copyright © 2018 Elsevier Inc. All rights reserved.