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Open Access Publications from the University of California

Control Design for Systems with Bounded Actuators and Applications

  • Author(s): Sadeghi Reineh, Maryam
  • Advisor(s): Jabbari, Faryar
  • et al.
Abstract

Input saturation is known as a common and inevitable challenge in control system design. Commands beyond the magnitude and rate limits of physical actuators are truncated by saturation bounds and, as a result, system performance can degrade substantially, even leading to instability. Therefore, reliable execution of control loops requires either rigorous guarantees that for the expected exogenous inputs the actuator saturation bounds will not be violated, or appropriate measures have to be in place to counteract the actuator saturation’s adverse effects.

In many applications, actuators can be saturated both in terms of the size of the input that the controller command implies and the rate at which the input can change; i.e., magnitude and rate actuator saturation, respectively. In this thesis, multiple Magnitude and Rate Anti-Windup (MRAW) structures are designed and their performance is evaluated on various physical systems. A novel structure for AW compensation for rate limited actuation is proposed which is less conservative than structures currently used accommodating energy and peak bounded exogenous signals. The new structure and the peak-to-peak analysis applied provide compensation for more practical problems with tighter rate bounds which could not be solved using the traditional AW structures. To reduce conservatism further, the proposed technique is combined with multi-stage AW loops to obtain different gains for different levels of saturation.

In the second part of the dissertation, the proposed theoretical results are applied to a few fields of application encountering control input saturation in an unconventional manner. As of the first application, the use of artificial actuator limits in control of energy systems is proposed with the objective of maximizing the net generated power. We study a Solid Oxide Fuel Cell (SOFC) controlled by a Multi-Input-Multi-Output (MIMO) compensator, which uses the blower/fan power and cathode inlet temperature as actuators. The usable

power of the FC is maximized by limiting the air flow rate deliberately, when an increase in power is demanded. Possible rate bounds on the cathode inlet temperature are also modeled. These bounds could represent the physical limitations (due to slow dynamics of

heat exchangers) and/or a control concept for accommodating the power saving objective. Applying proper limits to the amplitude and rate of the actuator signals, and incorporating Anti-Windup (AW) techniques, can raise the net power of the FC by 16% with negligible

effects on the spatial temperature profile.

In the second area of application, the issue of integrator overload in common Analog-to-Digital Converters is studied and modeled in terms of control saturation. This thesis presents a robust stabilized continuous-time (CT) DS modulator employing the anti-windup (AW) feedback control technique, preventing integrators overload and maintaining an acceptable performance simultaneously. This is considered as an unconventional use of AW technique applied to a system without an ordinary plant and controller. The proposed technique accommodates arbitrarily large inputs and can be applied to multi-loop modulators. According to simulations, using AW augmentations, for a 50% higher dynamic range (DR), integrators do not overload and the signal-to-distortion-ratio (SNDR) drops less than 1dB from the maximum SNDR of the modulator.

Finally, the issue of actuator saturation and benefits of AW augmentations for a specific type of leader-follower tracking problems in multi-agent systems is studied which best fits the types of problems analyzed in this thesis. We study the leader-follower tracking problem composed of agents with general linear dynamics and an active leader with nonzero unknown input. A distributed continuous state feedback controller is proposed with optimized performance ensuring the convergence of the followers’ trajectories to the leader agent. A general high performance output feedback control is also designed, based on the relative measurements of the neighbors, as an alternative to the state feedback approach, beneficial in case of measurement restrictions. Anti-Windup (AW) compensation scheme is then introduced in order to protect the stability of the network and improve the performance in the presence of actuator limitations. The effectiveness of results is finally supported by numerical simulations.

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