Nonlinear Adaptive Robust Control Theory

Currently funded under the NSF grant CMS-0600516 

Goals: 

·   Develop a general theoretical framework for the design of a new generation of performance oriented nonlinear adaptive robust controllers (ARC) that are practical, explicitly take into account the effects of process nonlinearities and uncertainties, and have accurate on-line parameter estimation for secondary purposes such as machine component health monitoring and prognosis.

·   Apply the new integrated ARC design to the intelligent and precision control of modern mechanical systems such as electro-hydraulic actuated and high-speed electro-magnetic motor driven ones.

    Method of Solution

The framework will be based on the PI’s extensive theoretical and experimental work on the adaptive robust control (ARC) that was supported in part by NSF through a CAREER award and a subsequent regular grant award during the past several years. Specifically, extensive work has been carried out by the PI to establish a mathematically rigorous theoretical framework for the design of high-performance ARC controllers. The underlying parameter adaptation laws in existing ARC controllers are mainly based on direct adaptive control designs, where the control law and the parameter adaptation law are synthesized simultaneously to meet the sole objective of reducing the output tracking error. This direct ARC design cannot produce reliable and accurate on-line parameter estimates. To overcome poor parameter estimation, the project will develop indirect adaptive robust control (IARC) designs that use estimation algorithms with better parameter convergence properties. However, IARC may suffer from a loss of tracking performance. To overcome this, an integrated direct and indirect adaptive robust control (DIARC) will be developed. The design will not only use the same adaptation process as IARC for accurate estimation of physical parameters, but also introduce dynamic compensation type fast adaptation for better transient and steady-state performance. In addition, the project will explore explicit on-line monitoring of persistent-excitation conditions to measure richness of excitation and, along with the batched least square algorithm, to achieve quantitative robust parameter estimation in the presence of disturbances and uncertain nonlinearities..   

    Impact of the Work

The proposed IARC design provides a fundamentally different approach from the existing estimation based modularized adaptive backstepping designs to achieve a complete separation of estimation and control designs, even in the presence of uncertain nonlinearities. The proposed DIARC
design will not only have significant practical value, but also make fundamental theoretical contributions to the adaptive control community by bridging the gap between the two distinct classes of adaptive control designs: direct and indirect. The proposed quantitative robust parameter estimation will have a profound practical impact since it is also a key enabler for other industrial technologies such as automated on-board modelling. Once successfully completed, the results will have a lasting impact on future control curriculum, at both the undergraduate and the graduate level. The results should also have a direct impact on industry as they directly address the common concerns of practicing engineers in applying advanced nonlinear controls. 

    Technical Background

Introduction to Adaptive Robust Control Theory

Publications

Reference

Bin Yao, "Engineering synthesis of high performance adaptive robust controllers for mechanical systems and manufacturing processes," National Science Foundation CAREER Award, 1998.

Bin Yao,“Practical and Performance Oriented Nonlinear Adaptive Robust Control – Theory and Applications to Precision Control of Modern Mechanical Systems”, National Science Foundation. Regular grant No. CMS-0220179 for the period of 09/15/2002-08/31/2005.