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TECHNICAL PAPERS

Generalized Multivariable Gain Scheduling With Robust Stability Analysis

[+] Author and Article Information
Rong Zhang

Electrical and Controls Integration Lab, General Motors R&D and Planning, 30500 Mound Road, MC 480-106-390, Warren, MI 48090-9055rzhang@asme.org

Andrew G. Alleyne

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 W Green Street, Urbana, IL 61801alleyne@uiuc.edu

Don E. Carter

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 W Green Street, Urbana, IL 61801

J. Dyn. Sys., Meas., Control 127(4), 668-687 (Apr 04, 2005) (20 pages) doi:10.1115/1.2101843 History: Received April 12, 2004; Revised April 04, 2005

In this work we introduce a methodology for the design of multivariable gain-scheduled controllers for nonlinear systems and an approach for determining the local stability of a nonlinear closed loop system. The gain-scheduled global control is designed by scheduling different local controllers using a Local Controller Network. The individual local controllers are assumed to be LTI MIMO controllers that can be designed via some user-specified multivariable method. In this paper, different portions of outputs from different local controllers are combined into the total control by using interpolation-weighting functions. The variation in the control behavior as a result of the scheduling variable is posed in a robust control framework. The dynamics of the scheduling variables are incorporated into the global control framework as an unstructured uncertainty. This allows the use of computational tools to analyze the stability of the overall global system and verify whether or not a given gain-scheduled approach will remain stable locally. To demonstrate the practical significance of the method, a multivariable electrohydraulic earthmoving powertrain problem is solved using the approach. The nonlinear power train was locally modeled as an LTI MIMO system and a local LTI MIMO controller was designed at each operating point using an H algorithm. The analysis approach introduced is utilized to verify system stability and is supported closely by experimental results.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Linear local closed-loop

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The nonlinear global closed loop

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Local linearization of the nonlinear global closed loop

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Local analysis model of a global closed-loop system

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Local analysis model of a global closed-loop system with additional filter, Tf

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Proposed earthmoving vehicle powertrain with MIMO control

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Earthmoving vehicle powertrain simulator

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Schematic of the earthmoving vehicle powertrain simulator

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Figure 9

Pole locations of the local models

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Plant and controller dynamics at design point 1

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Robust performance at design point 1

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Schematic of global gain scheduling controller

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Interpolation weighting over in the scheduling variable domain

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Analytical model

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Scheduling robustness of global system without filtering scheduling variables

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Transition of operating condition in off-design-point tracking without filtering scheduling variables

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Robust performance of global system with filtered scheduling variables

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Scheduling robustness of global system with filtered scheduling variables

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Pressure outputs in on-design-point tracking

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Engine and load speed outputs in on-design-point tracking

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Transition of operating condition in on-design-point tracking

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Interpolation weighting functions in on-design-point tracking

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Control inputs in on-design-point tracking

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Transition of operating condition in off-design-point tracking

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Interpolation weighting functions in off-design-point tracking

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Control inputs in off-design-point tracking

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