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research-article

STABILIZATION AND OPTIMIZATION OF DESIGN PARAMETERS FOR CONTROL OF INVERTED PENDULUM

[+] Author and Article Information
Sayani Maity

Department of Mechanical Engineering, Iowa State University, Ames IA 50011
smaity@iastate.edu

Greg R Luecke

Department of Mechanical Engineering, Iowa State University, Ames IA 50011
grluecke@iastate.edu

1Corresponding author.

ASME doi:10.1115/1.4042953 History: Received January 24, 2018; Revised February 20, 2019

Abstract

In this work we study the dynamic response of the most popular unstable control problem, the inverted pendulum in terms of classical control theory. The theoretical and experimental results presented here explore the relationship between changes in the indirect tuning parameters from the Linear Quadratic Regulator (LQR) design, and the final system performance effected using the feedback gains specified as the LQR weight constraints are changed. First, we review the development of the modern control approach using full state-feedback for stabilization and regulation, and present simulation and experimental comparisons as we change the optimization targets for the overall system, and as we change one important system parameter, the length of the pendulum. Second, we explore trends in the response by developing the generalized root locus for the system using incremental changes in the LQR weights. Next, we present a family of curves showing the local root-locus and develop relationships between the weight changes and the system performance. We describe how these locus trends provide insight that is useful to the control designer during the effort to optimize the system performance. Finally, we use our general results to design an effective feedback controller for a new system with a longer pendulum, and present experiment results that demonstrate the effectiveness of our analysis.

Copyright (c) 2019 by ASME
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