Near optimal linear quadratic regulator for a singularly perturbed linear stochastic system with multiplicative white noise perturbations and Markovian jumping

Modeling and control of proton-exchange membrane fuel cells (PEMFC) has become a very popular research topic lately due to the increasing use of renewable energy. Despite this fact, most of the work in the current literature only studies standard dynamical models without taking into consideration possible parasitics such as small gas flow perturbations that could be available in the system. This paper addresses this issue by elaborating on time-scale modeling of an augmented eighteenth-order PEMFC-reformer system via singular perturbation theory. The latter captures time scales that arise in the model due to the presence of small perturbations. Specifically, a novel and efficient algorithm that helps identify the presence of different time-scales is developed. In addition, the method converts an implicit singularly perturbed model into an explicit equivalent where the time-scales are evident. Using this algorithm, a complete singularly perturbed dynamic model of the augmented eighteenth-order PEMFC-reformer system is obtained. Modeling of the PEMFC-reformer system is followed by linear quadratic regulator (LQR) design for the individual time-scales present in the system.

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Active Command-Steering Control of Tractor and Three Full Trailers for Tractor-Track Following

Design Engineering and Computers and Information in Engineering, Parts A and B ◽

10.1115/imece2006-15786 ◽

2006 ◽

Author(s):

Krishna Rangavajhula ◽

H.-S. Jacob Tsao

Keyword(s):

High Speed ◽

Control Strategies ◽

Linear Quadratic Regulator ◽

Cost Effective ◽

Steering Control ◽

Linear Quadratic ◽

Amplification Ratio ◽

High Speeds ◽

Lqr Controller ◽

Optimal Linear

A key source of safety and infrastructure issues for operations of longer combination vehicles (LCVs) is off-tracking, which has been used to refer to the general phenomenon that the rear wheels of a truck do not follow the track of the front wheels and wander off the travel lane. In this paper, we examine the effectiveness of command-steering in reducing off-tracking during a 90-degree turn at low and high speeds in an articulated system with a tractor and three full trailers. In command steering, rear front axles of the trailers are steered proportionately to the articulation angle between the tractor and trailing units. We then consider several control strategies to minimize off-tracking and rearward amplification of this system. A minimum rearward amplification ratio (RWA), as a surrogate for minimum off tracking, has been used as the control criterion for medium to high speeds to arrive at an optimal Linear Quadratic Regulator (LQR) controller. As for low speeds, the maximum radial offset between the tractor and trailer 3 is minimized in the design of the controller. Robustness of the optimal controller with respect to tyre-parameter perturbations is then examined. Based on the simulation results, we find that, active command steering is very effective in reducing off tracking at low- as well as high-speed 90-degree turns. To achieve acceptable levels of RWA and off tracking, at least two of the three trailers must be actively command-steered. Among the three two-trailer-steering possibilities, actively steering trailers 1 and 2 is most cost-effective and results in the lowest RWA for medium- to high- speeds (at which RWA is important), and off-tracking is practically eliminated for all speed regimes considered.

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